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Oct 30, 1977 - Capabilities of Shuttle with Interim Upper Stage---------. 19. 4. Solar System ... As space exploration has progressed to the outer planets of the ...
JPL PUBLICATION 77-70

An InterstellarPrecursor Mission

(NASA-CR-156152) Al fIlERSTELLAR PRECURSOR MISSION (Jet Propulsion Lab.) 111 p HC A06/UF A01 CSCL 22A

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JPL PUBLICATION 77-70

An Interstellar Precursor Mission

L. D. Jaffe C. Ivie J--. Lewis

R. Lipes H. N. Norton J. W. Stearns L. D. Stimpson P. Weissman

October 30, 1977

National Aeronautics and Space Administration Jet Propulsion Laboratory California Institute of Technology Pasadena, California

Prepared Under Contract No NAS 7-100

National Aeronautics and Space Administration

77-70

PREFACE-

The work described in this report was performed by the Earthand Space

Sciences, Systems, Telecommunications Science and Engineering, Control and

Energy Conversion, Applied Mechanics, and Information Systems Divisions of

the Jet Propulsion Laboratory for NASA Ames Research Center under NASA

OAST Program 790, "Space Systems Studies," Stanley R. Sadin, sponsor.

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ABSTRACT

A mntsion out of the planetary system, with launch about the year 2000,

could provide valuable scientific data as well as test some of the technology

A mission to a star is not expected to

for a later mission to another star.

be practical around 2000 because the flight time with the technology then

available is expected to exceed 10,000 yr.

Primary scientific objectives for the precursor mission concern

characteristics of the heliopause, the interstellar medium, stellar distances

(by parallax measurements), low energy cosmic rays, interplanetary gas distri­ bution, and mass of the solar system. tion of Pluto.

Secondary objectives include investiga­

Candidate science instruments are suggested.

The mission should extend to 500-1000 AU from the sun.

A heliocentric

hyperbolic escape velocity of 50-100 km/s or more is needed to attain this

distance within a reasonable mission duration. toward the incoming interstellar wind. ter can be included.

The trajectory should be

For a year 2000 launch, a Pluto encoun­

A second mission targeted parallel to the solar axis

would also be worthwhile.

The mission duration is 20 years, with an extended mission to a total

of 50 years.

A system using 1 or 2 stages of nuclear electric propulsion was

selected as a possible baseline.

The most promising alternatives are ultralight

solar sails or laser sailing, with the lasers in Earth orbit, for example.

The NEP baseline design allows the option of carrying a Pluto orbiter as a

daughter spacecraft.

Within the limited depth of this study, individual spacecraft systems

for the mission are considered, technology requirements and problem areas

noted, and a number of recommendations made for technology study and advanced

development.

The most critical technology needs include attainment of 50-yr

spacecraft lifetime and development of a long-life NEP system.

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RECOMMENDATIONS FOR TECHNOLOGY DEVELOPMENT

FOR EXTRAPLANETARY MISSION

To permit an extraplanetary mission such as that described in this

report, to commence about the year 2000, efforts are recommended on the

following topics.

In general, a study should be initiated first, followed

by development effort as indicated by the study.

First priority

Starting work on the following topics is considered of first priority,

in view of their importance to the mission and the time required for the

advance development.

Design and fabrication techniques that will provide 50-year space­

1)

craft lifetime.

Nuclear electric propulsion with operating times of 10 years or more at

2)

full power and able to operate at low power levels for attitude control and

spacecraft power to a total of 50 years.

Ultralight solar sails, including their impact upon spacecraft and

3)

mission design.

Laser sailing systems, including their impact upon spacecraft and

4)

mission design.

Detailing and application of spacecraft quality assurance and reli­

5)

ability methods utilizing test times much shorter than the intended lifetime.

Second

priority

Other topics that will require advance effort beyond that likely without

special attention include:

Spacecraft bearings and moving parts with 50-yr lifetime.

of 10­ 2

7) Neutral gas mass spectrometer for measuring concentrations 6)

-10-

0

atom/cm 3 , with 50-yr lifetime.

8)

Techniques to predict long-time behavior of spacecraft materials from

short-time tests.

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9)

Compatibility of science instruments with NEP.

10)

Methods of calibrating science instruments for 50-yr lifetime.

11)

Optical vs. microwave telecommunications with orbiting DSN.

12)

Stellar parallax measurements in deep-space.

FOR STAR MISSION

For a star mission, topics which warrant early study include:

13)

Antimatter propulsion.

14)

Propulsion alternatives for a star mission.

15)

Cryogenic spacecraft.

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TABLE OF CONTENTS

Page PREFACE ABSTRACT

----------------------------------------------------------------------------------------------------------

RECOMMENDATIONS FOR TECHNOLOGY DEVELOPMENT-------------------For Extraplanetary Mission --------------------------------------------------------------------------------First Priority Second Priority ---------------------------------------------For Star Mission

iii

iv

v

v

v

v-----------------------------vi

INTRODUCTION-------------------------------------------------Background---------------------------------------------------Study Objective ---------------------------------------------Study Scope -------------------------------------------------

I

I

I

I

STUDY APPROACH -----------------------------------------------

3

Task I Task 2 Star Mission

3----------------------------3----------------------------4-----------------------------

SCIENTIFIC OBJECTIVES AND REQUIREMENTS -----------------------Scientific Objectives Primary Objectives Secondary Objectives Trajectory Requirements Scientific Measurements--------------------------------------Heliopause and Interstellar Medium-------------------------Stellar and Galactic Distance Scale -------------------------

5

5----------------------------5----------------------------5----------------------------5----------------------------B

8

9

9---------------------------

Cosmic Rays Solar System as a Whole Observations of Distant Objects ----------------------------Pluto

0----------------------------10

0-----------------------------

Simulated Stellar Encounter ---------------------------------

11

Gravity Waves ---------------------------------------------

12

Measurements Not Planned ------------------------------------

12

Advantages of Using Two Spacecraft

-------------------------

Candidate Science Payload -------------------------------------

TRAJECTORIES

----------------------------------------

Units and Coordinate Systems ---------------------------------Units ------------------------------------------------------Coordinate Systems -----------------------------------------Directions of Interest ---------------------------------------Extraplanetary ----------------------------------------------

12

13

14

14

14

14

14

14

-------------------------------------------------------

15

Solar System Escape Trajectories ------------------------------

15

Launchable Mass

15---------------------------

Pluto-

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Page TRAJECTORIES (continued)

Direct Launch from Earth ----------------------------------------------------------------------------------Jupiter Assist Jupiter Gravity Assist ------------------------------------------------------------------------Jupiter Powered Flyby Launch Opportunities to Jupiter ------------------------------------------------Venus-Earth Gravity Assist Powered Solar Flyby -------------------------------------Low-Thrust Trajectories ---------------------------------Solar Sailing -------------------------------------------Laser Sailing --------------------------------------. --------Solar Electric Propulsion ---------------Laser Electric Propulsion -------------------------Nuclear Electric Propulsion -------------------------------Fusion ----------------------------------------------Antimatter ------------------------------------------------Low Thrust Plus Gravity Assist-------------------------Solar Plus Nuclear Electric -------------------------------Choice of Propulsion -----------------------------------------

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MISSION CONCEPT ----------------------------------------------

38

MASS DEFINITION AND PROPULSION -------------------------------

40

INFORMATION MANAGEMENT --------------------------------------44

Data Generation ---------------------------------------------44

Information Management System ---------------44

45

-----------------------------------Operations Data Transmission Rate --------------------------------------46

46

Telemetry ---------------------------------------------------47

The Telecommunication Model -------------------------------Range Equation -------------------------47

Data Coding- Considerations --------------------47

Tracking Loop Considerations ---------------47

Baseline Design ---------------------------------------------49

Parameters of the System ----------------------------------49

Decibel Table and Discussion ----------------50

Options ----------------------------------------50

More Power -------------------------------------------------50

Larger Antennas and Lower Noise Spectral Density----------53

Higher Frequencies --------------------------------------53

Higher Data Rates -----------------------------------55

Selection of Telemetry Option .-------------------------------

55 RELATION OF THE MISSION TO SEARCH FOR EXTRATERRESTRIAL

INTELLIGENCE -----------------------------------------------

58

TECHNOLOGY REQUIREMENTS AND PROBLEM AREAS -------------------Lifetime -------------------------------------------Propulsion and Power -----------------------------------------

59

59

59

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Page TECHNOLOGY REQUIREMENTS AND PROBLEM AREAS (continued) Propulsion/Science Interface --------------------------------Interaction of Thrust with Mass Measurements--------------Interaction of Thrust Subsystem with Particles and. Fields Measurements -------------------------------------Interaction of Power Subsystem with Photon Measurements ---Telecommunications ------------------------------------------Microwave vs. Optical Telemetry Systems -------------------Space Cryogenics ------------------------------------------Lifetime of Telecommunications Components -----------------Baseline Enhancement vs. Non-Coherent Communication System --------------------------------------------------Information Systems -----------------------------------------Thermal Control ---------------------------------------------Components and Materials -----------------------------------Science Instruments -----------------------------------------Neutral Gas Mass Spectrometer ------------------------------Camera Field of View vs, Resolution --------------

ACKNOWLEDGEMENT ----------------------------------REFERENCES APPENDICES

----

------------------------------------------------------------------------------------------------

Appendix A - Study Participants

------------------

60 61 61 61 62 62 63 63 64 64 64 67 67 69 69

71 72 75 76

----------------------------

77

Appendix C - Thoughts for a Star Mission Study---------------Propulsion ------------------------------------------------Cryogenic Spacecraft --------------------------------------Locating Planets Orbiting Another Star ---------------------

8 78 79 81

Appendix D - Solar System Ballistic Escape Trajectories ------

83

Appendix B - Science Contributors

TABLES

1. Position of Pluto, 1990-2030 ----------------------------2. Summary of Solar System Ballistic Escape Trajectories Initial Condition: Circular Orbit at 1 AU -------------3. Capabilities of Shuttle with Interim Upper Stage--------4. Solar System Escape Using Direct Ballistic Launch from Earth -------------------------------------------5. Solar System Escape Using Jupiter Gravity Assist --------6. Jupiter Gravity Assist Versus Launch Energy -------------7. Jupiter Powered Flyby ------------------------------8. Launched Mass for 300 kg Net Payload After Jupiter

Powered Flyby -----------------------------------------9, Powered Solar Flyby -------------------------------------10, Performance of Ultralight Solar Sails --------------------

ix

16 17 19 20 23 24 26 27 29 35

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Page TABLES (continued)

11. Mass and Performance Estimates for Baseline System ...-.. Baseline Telemetry at 1000 AU ----------------Optical Telemetry at 1000 AU -------------------------Telemetry Options ------------------------ Proposed Data Rates -------------------------------------Thermal Control Characteristics of Extraplanetary Missions ----------------------------------------------17. Technology Rdquirements for Components & Materials

12. 13. 14. 15. 16.

43

52 54 56 57 66 68

FIGURES

1. Some Points of Interest on the Celestial Map -----------2. Geometry of Jupiter Flyby -------------------3. Solar System Escape with Ultralight Solar Sails ---------4. Performance of NEP for Solar Escape plus Pluto ----------5. Data Rate vs. Ratio of Signal Power to Noise Spectral

Power Density ------------------------------------------

x

7

21

34

41

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INTRODUCTION

BACKGROUND

Even before the first earth satellites were launched in 1957, there

was popular interest in the possibility of spacecraft missions to other

stars and their planetary systems.

As space exploration has progressed

to the outer planets of the solar system, it becomes appropriate to begin

to consider the scientific promise and engineering difficulties of mission

to the stars and, hopefully, their accompanying planets.

In a conference on "Missions Beyond the Solar System", organized by

L. D. Friedman and held at JPL in August 1976, the idea of a precursor

mission out beyond the planets, but not nearly to another star, was

suggested as a means of bringing out and solving the engineering pro­ blems that would be faced in a mission to a star.

At the same time, it

was recognized that such a precursor mission, even though aimed primarily

at engineering objectives, should also have significant scientific objec­ tives.

Subsequently, in November 1976, this small study was initiated to

examine a precursor mission and identify long lead-time technology develop­ ment which should be initiated to permit such a mission.

This study was

funded by the Study, Analysis, and Planning Office (Code RX) of the NASA

Office of Aeronautics and Space Technology.

STUDY OBJECTIVE

The objective of the study was to establish probable science goals,

mission concepts and technology requirements for a mission extending from

outer regions of the solar system to interstellar flight.

An unmanned

mission was intended.

STUDY SCOPE

The study was intended to address science goals, mission concepts,

and technology requirements for the portion of the mission outward from

the outer portion of the planetary system.

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Because of the limited funding available for this study, it was

originally planned that the portion of the mission between the earth

and the outer portion of the planetary system would not be specifically

addressed; likewise, propulsion concepts and technology would not be

included.

Problems encountered at speeds approaching that of light were

excluded for the same reason.

In the course of the study, it became

clear that these constraints were not critical, and they were relaxed,

as indicated later in this report.

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STUDY APPROACH

The study effort consisted of two tasks.

Task 1 concerned science

goals and mission concepts, Task 2 technology requirements.

TASK I

In Task 1, science goals for the mission were to be examined, and

the scientific measurements to be made.

Possible relation of the mission

to the separate effort on Search for Extraterrestrial Intelligence was

also to be considered.

Another possibility to be examined was that of

using the data, in reverse time sequence, to examine a star and its sur­ roundings (in this case, the solar system) as might be done from an

approaching spacecraft.

Possible trajectories would be evaluated with respect to the inter­ action of the direction of the outward asymptote and the speed with the

science goals.

A very limited examination might be made of trajectories

within the solar system and accompanying propulsion concepts to assess

the feasibility of the outward velocities considered.

During the study, science goals and objectives were derived by series

of conversations and small meetings with a large number of scientists.

Most of these were from JPL, a few elsewhere.

Appendix B gives their

names.

The trajectory information was obtained by examination of pertinent

work done in other studies and a small amount of computation carried out

specifically for this study.

TASK 2

In this task, technology requirements that appear to differ signi­ ficantly from those of missions within the solar system were to be identi­ fied.

These would be compared with the projected state-of-the-art for

the year 2000 ± 15.

It was originally planned that requirements associated

with propulsion would be addressed only insofar as they interact with power

or other systems.

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This task was carried out by bringing together study team partici­ pants

from each of the technical divisions of the Laboratory.

pants

are listed in Appendix A-.)

discussed at study team meetings.

(Partici­

Overal-i concepts were developed and

Each participant obtained inputs from

other members of his division on projected capabilities and development

needed for individual subsystems.

These were iterated at team meetings.

In particular, several iterations were needed between propulsion and tra­ jectory calculations.

STAR MISSION

Many of the contributors to this study, both scientific and engineer­ ing, felt an actual star mission should be considered.

Preliminary exam­

ination indicated, however, that the hyperbolic velocity attainable for

solar system escape during the time period of interest (year 2000 ± 15)

was of the order of 102 km/s or 3 x 109 km/year.

Since the nearest star

013

is at a distance of 4.3 light years or about 4 x 10 ation would exceed 10,000 years.

km, the mission dur­

This did not seem worth considering for

two reasons.

First, attaining, and especially establishing, a spacecraft life­ time of 10,000 years by the year 2000 is not considered feasible.

Secondly,

propulsion capability and hence hyperbolic velocity attainable is expected

to increase with time.

Doubling the velocity should take not more than

another 25 years of work, and would reduce the mission duration to only

5000 years. earlier.

Thus, a spacecraft launched later would be expected to arrive

Accordingly, launch to a star by 2000 ± 15 does not seem reasonable.

For this reason, a star mission is not considered further in the body

of this report.

A few thoughts which arose during this study and pertain

to a star mission are recorded in Appendix C.

It is recommended that a

subsequent study address the possibility of a star mission starting in

2025, 2050, or later, and the long lead-time technology developments that

,will be needed to permit this mission.

77-70

SCIENTIFIC OBJECTIVES AND REQUIREMENTS

Preliminary examination of trajectory and propulsion possibilities

indicated that a mission extending to distances of some hundred or per­ haps a few thousand AU from the sun with a launch around the year 2000

was reasonable.

The following science objectives and requirements are

considered appropriate for such a mission.

SCIENTIFIC OBJECTIVES

Primary Objectives

1)

Determination of the characteristics of the heliopause, where the solar wind presumably terminates against the incoming interstellar medium.

2)

Determination of the characteristics of the interstellar medium.

3)

Determination of the stellar and galactic distance scale, through measurements of the distance to nearby stars.

4)

Determination of the characteristics of cosmic rays at energies excluded by the heliosphere.

5)

Determination of characteristics of the solar system as a whole, such as its interplanetary gas distribution and total mass.

Secondary Objectives

i)

Determination of the characteristics of Pluto and its satellites

and rings, if any. If there had been a previous mission to Pluto,

this objective would be modified.

2)

Determination of the characteristics of distant galactic and extra­ galactic objects.

3)

Evaluation of problems of scientific observations of another solar

system from a spacecraft.

TRAJECTORY REQUIREMENTS

The primary science objectives necessitate passing through the helio­ pause, preferably in a relatively few years after launch to increase the

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reliability of data return.

Most of the scientists interviewed preferred

a mission directed toward the incoming interstellar gaswhere the helio­ pause is expected to be closest and most well defined.

The "upwind"

direction with respect to neutral interstellar gas is approximately R.A.

250', Decl - 160 (Weller and Meier, 1974; Ajello, 1977).

(See Fig. 1.

The sun's motion with respect to interstellar charged particles and mag­ netic fields is not known.)

Presumably any direction within, say, 400

of this would be satisfactory.

A few scientists preferred a mission

parallel to the sun's axis (perpendicular to the ecliptic), believing

that interstellar magnetic field and perhaps particles may leak inward

further along this axis.

Some planetary scientists would like the mis­

sion to include a flyby or orbiter of Pluto, depending on the extent to which

Pluto

might have been explored by an earlier mission.

Although a Pluto flyby

is incompatible with a direction perpendicular to the ecliptic, it happens

that in the period of interest (arrival around the year 2005) Pluto will

lie almost exactly in the "upwind" direction mentioned, so an "upwind"

trajectory could include a Pluto encounter.

The great majority of scientists consulted preferred a trajectory

that would take the spacecraft out as fast as possible.

This would mini­

mize time to reach the heliopause and the interstellar medium.

Also, it

would, at any time, provide maximum earth-S/C separation as a base for

optical measurements of stellar parallax.

A few scientists would like

to have the S/C go out and then return to the solar system to permit

evaluating and testing methods of obtaining scientific data with a

future S/C encountering another solar system.

Such a return would,

roughly, halve the duration of the outward portion of the flight for

any fixed mission duration.

Also, since considerable propulsive energy

would be required to "stop and turn around", this approach would con­ siderably reduce the outward hyperbolic velocity attainable.

These two

effects would greatly reduce the maximum distance that could be reached

for a given mission duration.

As a "strawman mission", it is recommended that a no-return trajec­ tory with an asymptote near R.A. 2500, Decl -15o and a flyby of Pluto be

6

90

I "11 APEX OF SOLAR MOTION RELATIVE TO NEARBY STARS

60 - BARNARD'S STAR 380,000 AU

YEAR 2000 30 AU

30-

z

1990-30 30 AU

o

CELESTIAL EQUATOR

0 uj

0 -60

INCOMING INTERSTELLAR GAS R-30GWELLER AND MEIER (1974) 2010AJErLLO (1977)

*

-2

2 34 AU

*

C

a C N UR A R Na.CN 270,000 AU

-90, 360

300

240

180 RIGHT ASCENSION

Fig. I

120 (0)

Some Points of Interest on the Celestial Map. From Sergeyevsky (1971) modified.

60

0

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considered, with a hyperbolic excess velocity of 40-90 km/s or more.

Higher velocities should be used if practical.

Propulsion should be

designed to avoid interference with scientific measurements and should

be off when mass measurements are to be made.

A number of scientific observations (discussed below) would be

considerably improved if two spacecraft, operating simultaneously, were

used, with asymptotic trajectories at approximately right angles to

each other.

Thus, use of a second spacecraft, with an asymptotic tra3ec­

tory approximately parallel to the solar axis, is worthwhile scientifically.

SCIENTIFIC MEASUREMENTS

Heliopause and Interstellar Medium

Determination is needed of the characteristics of the solar wind

just inside the heliopause, of the heliopause itself, of the accompanying

shock (if one exists), and of the region between the heliopause and the

The location of the heliopause is not known; estimates now tend

shock.

to center at about 100 AU from the sun.

(As an indication of the uncer­

tainty, estimates a few years ago ran as low as 5 AU.)

Key measurements to be made include magnetic field, plasma proper­ ties (density, velocity, temperature, composition, plasma waves) and

electric field.

Similar measurements, extending to low energy levels,

are needed in the interstellar medium, together with measurements of the

properties of the neutral gas (density, temperature, composition of atomic

and molecular species, velocity) and of the interstellar dust (particle

concentration, particle mass distribution, composition, velocity).

The

radiation temperature should also be measured.

The magnetic, electric, and plasma measurements would require only

conventional instrumentation, but high sensitivity would be needed.

Plasma

blobs could be detected by radio scintillation of small sources at a wave­ length near 1 m.

Radiation temperature could be measured with a radiom­

eter at wavelengths of 1 cm to 1 m, using a detector Kelvins.

cooled to a few

Both in-situ and remote measurements of gas and dust properties

are desirable.

In-situ measurements of dust composition could be made

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by an updated version of an impact-ionization mass spectrometer.

In-situ

measurements of ions could be made by a mass spectrometer and by a plasma

analyzer.

In-situ measurements of neutral gas composition would probably

require development of a mass spectrometer with greater sensitivity and

signal/noise ratio than present instruments.

Remote measurements of gas

composition could be made by absorption spectroscopy, looking back toward

the sun, Of particular interest in the gas measurements are the ratios

+H/H2/H+ D/i /1HH/H,Hele;tecnetofN,0adifpsbe , He/H, He3/He4; the contents of C, N, , and if possible of Li, Be, B; and the flow velocity.

Dust within some size range could be

observed remotely by changes in the continuum intensity.

Stellar and Galactic Distance Scale

Present scales of stellar and galactic distance are probably uncer­ tain by 20%.

This in turn leads to uncertainties of 40% in the absolute

luminosity (energy production), the quantity which serves as the funda­ mental input data for stellar model calculations.

Uncertainties in galactic

distances make it difficult to provide good input data for cosmological

models.

The basic problem is that all longer-range scales depend ultimately

on the distances to Cepheid variables in nearby clusters, such as the

Hyades and Pleiades.

Distances to these clusters are determined by sta­

tistical analysis of relative motions of stars within the clusters, and

the accuracy of this analysis is not good.

With a baseline of a few

hundred AU between S/C and earth, triangulation would provide the dis­ tance to nearby Cepheids with high accuracy.

This will require a camera

with resolution of a fraction of an arc second, implying an objective

diameter of 30 cm to 1 m.

Star position angles need not be measured

relative to the sun or earth line, but only with respect to distant

stars in the same image frame.

To reduce the communications load, only

the pixel coordinates of a few selected objects need be transmitted to

earth.

Cosmic Rays

Measurements should be made of low energy cosmic rays, which the

solar magnetic field excludes from the heliosphere.

9

Properties to be

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measured include flux, spectrum, composition, and direction.

Measurements

should be made at energies below 10 MeV and perhaps down to 10 keV or

lower.

Conventional instrumentation should be satisfactory.

Solar System as a Whole

Determinations of the characteristics of the solar system as a

whole include measurements of neutral and ionized gas and of dust.

Quan­

tities to be measured include spatial distribution and the other proper­ ties mentioned above.

Column densities of ionized material can be observed by low fre­ quency radio dispersion. Nature, distribution and velocity of neutral

gas components and some ions can be observed spectroscopically by fluores­ cence under solar radiation. objective will be needed.

To provide adequate sensitivity, a large

Continuum observation should show the dust

distribution.

The total mass of the solar system should be measured.

This could

be done through dual frequency radio doppler tracking.

Observations of Distant Objects

Observations of more distant objects should include radio astronomy

observations at frequencies below 1 kHz, below the plasma frequency of the

interplanetary medium.

This will require a VLF receiver with a very long

dipole or monopole antenna.

Also, both radio and gamma-ray events should be observed and timed.

Comparison of event times on the S/C and at earth will indicate the direc­ tion of the source.

In addition, the galactic hydrogen distribution should be observed

by UV spectrophotometry, outside any local concentration due to the sun.

Pluto

If a Pluto flyby is contemplated, measurements should include optical

observations of the planet to determine its diameter, surface and atmos­ phere features, and an optical search for and observations of any satellites

or rings.

Atmospheric density, temperature and composition should be measured,

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and nearby charged particles and magnetic fields. composition should also be observed.

Surface temperature and

Suitable instruments include a TV

camera, infrared radiometer, ultraviolet/visible spectrometer, particles

and fields instruments, infrared spectrometer.

For atmospheric properties, UV observations during solar occultation

(especially for H and He) and radio observations of earth occultation should

be useful.

The mass of Pluto should be measured: radio tracking should provide

this.

If a Pluto orbiter is included in the mission, measurements should

also include surface composition, variable features, rotation axis, shape,

and gravity field.

Additional instruments should include a gamma-ray

spectrometer and an altimeter.

Simulated Stellar Encounter

If return to the solar system is contemplated, as a simulation of a

stellar encounter, observations should be made, during approach, of the

existence of possible stellar companions and planets, and later of satel­ lites, asteroids, and comets, and of their characteristics.

Observations

of neutral gas, dust, plasma, and energetic emissions associated with the

star should be made, and any emissions from planets and satellites.

Choice(s)

should be made of a trajectory through the approaching solar system (recog-_

nizing the time-delays inherent in a real stellar mission), the choice(s)

should be implemented, and flyby measurements made.

The approach measurements could probably be made using instruments

aboard for other purposes.

For flyby, it would probably be adequate to

use data recorded on earlier missions rather than carry additional instru­ ments.

An alternative considered was simulating a stellar encounter by

"looking backwards while leaving the solar system and later replaying

the data backwards".

This was not looked on with favor by the scientists

contacted because the technique would not permit making the operational

decisions that would be key in encountering a "new" solar system: locating

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and flying by planets, for example.

"Looking backwards" at the solar system

is desired to give solar system data per se, as mentioned above.

Stellar

encounter operations are discussed briefly in Appendix C.

Gravity Waves

A spacecraft at a distance of several hundred AU offers an opportunity

for a sensitive technique for detecting gravity waves.

All that is needed

is precision 2-way radio doppler measurements between S/C and earth.

Measurements Not Planned

1)

Observations not contemplated include:

Detecting the Oort cloud of comets, if it exists.

No method of

detecting a previously unknown comet far out from the sun is recog­ nized unless there is an accidental encounter.

Finding a previously

seen comet when far out would be very difficult because the nrbits

of long-period comets are irregular and their aphelia are hard to

determine accurately; moreover, a flyby, far from the sun, would

tell little about the comet and nothing about the Oort cloud.

The

mass of the entire Oort cloud might be detectable from outside, but

the mission is not expected to extend the estimated 50,000 AU out.

If Lyttleton's comet model is correct, a comet accidentally encoun­ tered would be revealed by the dust detector.

2)

VLBI using an earth-S/C baseline.

This would require very high rates

of data transmission to earth, rates which do not appear reasonable.

Moreover, it is doubtful that sources of the size resolved with

this baseline are intense enough to be detected and that the re­ quired coherence would be maintained after passage through inhomo­ geneities in the intervening medium.

Also, with only 2 widely

separated receivers and a time-varying baseline, there would be

serious ambiguity in the measured direction of each source.

Advantages of Using Two Spacecraft

Use of two spacecraft, with asymptotic trajectories at roughly right

angles to each other, would permit exploring two regions of the heliopause

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(upwind and parallel to the solar axis) and provide significantly greater

understanding of its character, including the phenomena occurring near the

magnetic pole direction of the sun.

Observations of transient distant

radio and gamma-ray events from two spacecraft plus the earth would permit

location of the source with respect to two axes, instead of the one axis

determinable with a single S/C plus earth.

CANDIDATE SCIENCE PAYLOAD

1)

Vector magnetometer

2)

Plasma spectrometer

3)

Ultraviolet/visible spectrometers

4)

Dust impact detector and analyzer

5)

Low energy cosmic ray analyzer

6)

Dual-frequency radio tracking (including low frequency with high

frequency uplink)

7)

Radio astronomy/plasma wave receiver (including VLF; long antenna)

8)

'Mass spectrometer

9)

Microwave radiometer

10)

Electric field meter

11)

Camera (aperture 30 cm to 1 m)

12)

Gamma-ray transient detector

If Pluto flyby or orbiter is planned:

13)

Infrared radiometer

14)

Infrared spectrometer

If Pluto orbiter is planned:

15)

Gamma-ray spectrometer

16)

Altimeter

13

77-70

TRAJECTORIES

UNITS AND COORDINATE SYSTEMS

Units

Some useful approximate relations in considering an extraplanetary

mission are:

1 AU

= 1.5 x 108km

1 light year

= 9.5 x 1012 km = 6.3 x 104 AU

1 parsec

= 3.1 x

1 year

= 3.2 x 10 7

1 km/s

= 0.21 AU/yr = 3.3 x 10- 6 c

1km = 2.1 x 105 AU = 3.3 light years

10

where c = velocity of light

Coordinate Systems

For objects out of the planetary system, the equatorial coordin­ ate system using right ascension (a) and declination (6) is often more

convenient than the ecliptic coordinates, celestial longitude (X)

and celestial latitude (8). sin S

Conversion relations are:

= cos s sin 6- sin s cos 6 sin

a

6 cos & sin

a

Cos & Cos

a

cos 8 sin X = sin c sin 6 +cos CoS

Cos A =

where s = obliquity of ecliptic = 23.50

DIRECTIONS OF INTEREST

Extraplanetary

,Most recent data for the direction of the incoming interstellar

neutral gas are:

Weller & Meier (1974):

Right ascension

a = 2520

Declination

6 = -15'

Ajello (1977):

Right ascension

a = 252 °

Declination

6 = -17*

14

77-70

Thus, these 2 data sources are in excellent agreement.

At a = 2500 the ecliptic is about 200S of the equator, so the wind

comes in at celestial latitude of about 4' .

Presumably, it is only

a coincidence that this direction lies close to the ecliptic plane.

The direction of the incoming gas is sometimes referred to as the

"apex of the sun's way", since it is the direction toward which the sun

is moving with respect to the interstellar gas.

The term "apex", how­

ever, conventionally refers to the direction the sun is moving relative

to nearby stars, rather than relative to interstellar gas. directions differ by about 450 ascension.

These two

in declination and about 200 in right

The direction of the solar motion with respect to nearby

stars, and some other directions of possible interest, are shown in

Fig. 1.

Pluto

Table 1 gives the position of Pluto for the years 1990 to 2030.

Note that, by coincidence, during 2000 to 2005 Pluto is within a few

degrees of the direction toward the incoming interstellar gas (see Fig. 1).

At the same time it is near its perihelion distance, only 30-31 AU

from the sun.

SOLAR SYSTEM ESCAPE TRAJECTORIES

As a step in studying trajectories for extraplanetary missions, a

series of listings giving distance and velocity vs. time for parabolic

and hyperbolic solar system escape trajectories has been generated.

These

are given in Appendix D and a few pertinent values extracted in Table 2.

Note, for example, that with a hyperbolic heliocentric excess velocity

V

= 50 km/s, a distance of 213 AU is reached in 20 years and a distance

of 529 AU in 50 years.

With V

= 100 km/s, these distances would be

doubled approximately.

LAUNCHABLE MASS

Solar system escape missions typically require high launch energies,

referred to as C3, to achieve either direct escape or high flyby velocity

15

77-70

TABLE 1

Position of Pluto, 1990-2030

Position on 1 January Distance Right

from

Declination,

ascension,

sun, Year

AU

1990 1995 2000 2005 2010

29.58 29.72 30.12 30.78 31.64

227.03 238.51 249.98 261.39 272.61

2015

-1.37 -6.30 -10.89 -14.92 -18.20

32.67

283.53

2020 2025 2030

-20.69

33.81 35.04 36.31

294.02 304.00 313.37

-22.37 -23.32 -23.63

16

0

0

77-70

TABLE 2

Summary of Solar System Ballistic Escape Trajectories

Initial Condition: V. km/s 0 1 5 10 20 30 40 50 60

Circular Orbit at 1 AU

Distance (RAD), AU, for Time (T) = 10 yrs. 20 yrs. 50 yrs. 25.1 25.2 27.0 32.1 47.7 66.5 86.5 107. 128.

40.4 40.6 45.1 57.0 91.2 130. 171. 213. 254.

75.3 76.0 90.4 126. 220. 321. 424. 529. 634.

Velocity (VEL), la/s

for Time (T) =

10 yrs. 20 yrs.

50 yrs.

8.4 8.4 9.5 12.5 20.9 30.4 40.3 50.2 60.1

4.9

4.9

6.7

10.7

20.2

30.1

40.1

50.0

60.0

6.6 6.7 8.0 11.4 20.5 30.2 40.1 50.1 60.1

(See Appendix D for detail)

17

77-70

at a gravity assist planet.

Table 3 gives projected C3 capabilities

in (km/s)2 for the three versions of the Shuttle/Interim Upper Stage

assuming net payloads of 300, 400, and 500 kg.

It can be seen that as

launched mass increases the maximum launch energy possible decreases.

Conceivably higher C3'

are possible through the use of in-orbit

assembly of larger IUS versions, or development of more powerful upper

stages such as the Tug.

The range of C3 values found here will be used

in the study of possible escape trajectories given below.

DIRECT LAUNCH FROM EARTH

Direct launch from the Earth to a ballistic solar system escape

trajectory requires a minimum launch energy of 152.2 (cm/s) gives the maximum solar system V

2

.

Table 4

obtainable (in the ecliptic plane) and

maximum ecliptic latitude obtainable (for a parabolic escape trajectory)

for a range of possible C 3 .

The relatively low V

and inclination values obtainable with direct

launch make it an undesirable choice for launching of extra-solar

probes as compared with those techniques discussed below.

JUPITER ASSIST

Jupiter Gravity Assist

Of all the planets, Jupiter is by far the best to use for gravity

assisted solar system escape trajectories because of its intense gravity

field.

The geometry of the Jupiter flyby is shown in Figure 2.

Assume

that the planet is in a circular orbit about the Sun with orbital velocity VJh

=

13.06 km/s.

The spacecraft approaches the planet with some relative velocity, Vin , directed at an angle 0 been bent through an angle a.

to VJh, and departs along Vou t after having The total bend angle

a = 2 arcsin [1/(I + V. in

2

r p /p)]

where r is the closest approach radius to Jupiter and v= GMJ, the

P

gravitational mass of Jupiter. Note that VJh , Vin and Vou t need not all

18

77-70

TABLE 3

Capabilities of Shuttle with Interim Upper Stage

Launch energy C3,

(km/s) 2 for indicated payload (kg) Launch Vehicle

300

400

500

Shuttle/2-stage IUS

95.5

91.9

88.2

Shuttle/3-stage IUS

137.9

131.0

124.4

Shuttle/4-stage IUS

178.4

161.5

148.2

19

77-70

TABLE 4

Sblar System Escape Using Direct Ballistic Launch from Earth

Launch

energy, C3 ,

Maximum

hyperbolic

excess velocity,

V , in ecliptic

plane

(km/s)2

(km/s)

Maximum

ecliptic latitude,

?,Max' for parabolic

trajectory

(0)

152.2

0.00

0.00

155.

3.11

2.73

160.

5.15

4.53

165.

6.57

5.80

170.

7.73

6.84

175.

8.72

7.74

20

77-70

A

/v

/

/

/

/

~VA

Fig. 2

escape

h

Geometry of Jupiter Flyby

21

77-70

be in the same plane, so the spacecraft can approach Jupiter in the

ecliptic plane and be ejected on a high inclination orbit.

The helio­

centric velocity of the spacecraft after the flyby, Vsh , is given by the

vector sum of VJh and Vou t . 1.414 VJh

If this velocity exceeds approximately

shown by the &ashed circle in Figure 2, the spacecraft

achieves by hyperbolic orbit and will escape the solar system.

The

hyperbolic excess velocity is given by V 2 sh - 2p/r where V here is GMs,

the gravitation mass for the Sun, and r is the distance from the Sun,

5.2 astronomical units.

The maximum solar system escape velocity will

be obtained when the angle between V

and Vout is zero.

This will

necessarily result in a near-zero inclination for the outgoing orbit.

Around this vector will be a cone of possible outgoing escape trajec­ tories.

As the angle from the central vector increases the hyperbolic

excess velocity relative to the Sun will decrease.

The excess velocity

reaches zero (parabolic escape orbit) when the angle between VJh and Vsh is equal to arc cos [(3 - V2 in/V

2

Jh)/2

"2.

This defines then the

maximum inclination escape orbit that can be obtained for a given V.in at Jupiter. Table 5 gives the dependence of solar system hyperbolic

escape velocity on V. and the angle between V and Vs. The maximum

in Jh s angle possible for a given V.in is also shown. For example, for a V.in at Jupiter of 10. km/s the maximum inclina­ tion obtainable is 31.41', and the solar system escape speed will be

13.03 km/s for an inclination of 100, 10.45 km/s for an inclination of

20'.

Note that for V.in 's greater than 20 km/s it is possible to eject

along retrograde orbits. This is an undesirable waste of energy however.

It is preferable to wait for Jupiter to move 1800 around its orbit when

one could use a direct outgoing trajectory and achieve a higher escape

speed in the same direction.

To consider in more detail the opportunities possible with Jupiter

gravity assist, trajectories have been found assuming the Earth and

Jupiter in circular, co-planar orbits, for a range of possible launch

energy values.

These results are summarized in Table 6.

Note that the

orbits with C3 = 180 (km/s) 2 have negative semi-major axes indicating

that they are hyperbolic. With the spacecraft masses and launch vehicles

discussed above it is thus possible to get solar syst6m escape velocities

22

77-70

TABLE 5

Solar

System Escape Using Jupiter Gravity Assist

Approach velocity relative

6.0 to Jupiter,Vin (km/s):

10.0

15.0

20.0

25.0

30.0

Angle between outbound

heliocentric velocity

of S/C, Vsh, and

of Jupiter, Jsh (0)

0.0 5.0 10.0 15.0 20.0 25.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

Solar system hyperbolic excess velocity, V., (km/s),

for above approach velocity

4.70 4.01

13.81 13.61 13.03 12.00 10.45 8.12 3.93

21.12 21.00 20.63 20.01 19.13 17.99 16.57 12.73 6.47

27.42 27.32 27.02 26.53 25.85 24.97 23.91 21.25 17.89 13.75 8.32

33.28 33.19 32.93 32.50 31.91 31.16 30.25 28.01 25.28 22.13 18.65 14.86 10.65

38.90

38.82

38.58

38.19

37.65

36.97

36.15

34.13

31.69

28.92

25.94

22.83

19.70

Maximum angle between outbound heliocentric velocity

of S/C, Vsh , and of Jupiter, Vjh,(), for above

approach velocity

9.58

Note:

31.41

53.53

76.60

103.57

* indicates unobtainable combination of V. and angle.

in

23

143.56

TABLE 6

Jupiter Gravity Assist versus Launch Energy

Launch Energy, 2 C3 (kn/s)

Transfer orbit semimajor axis, (AU)

Approach velocity relative to Jupiter, Vin (km/s)

Angle between approach velocity and Jupiter heliocentric velocity,a, ((0)

Maximum Maximum Maximum heliocentric inclination hyperbolic to ecliptic bend for parabolic escape angle trajectory, velocity, relative to Xmax, for Jupiter, a, Vw, for flyby at flyby at for flyby 1.1 R 1.1 R at 1.1 R (0) (0)

0.0

3.23

6.55

148.96

153.85

6.59

13.66

90.0 100.0 110.0 120.0 130.0 140.0 150.0 160.0 180.0 200.0

3.82 4.63 5.82 7.74 11.38 20.98 117.43 -33.64 -9.63 -5.71

9.08 10.98 12.54 13.88 15.07 16.14 17.12 18.03 19.67 21.13

127.34 119.53 115.10 112.13 109.95 108.27 106.91 105.78 103.99 102.61

144.10 137.02 131.35 126.59 122.48 118.86 115.61 112.67 107.52 103.11

12.22 15.38 17.72 19.61 21.21 22.61 23.87 25.01 27.02 28.77

27.17 35.81 42.69 48.58 53.82 58.61 63.05 67.22 74.99 82.22

D

77-70

on the order of 25 km/s in the ecliptic plane and inclinations up to

about 670 above the ecliptic plane using simple ballistic flybys of

Jupiter.

Thus a large fraction of the celestial sphere is available

to solar system escape trajectories using this method.

Jupiter Powered Flyby

One means of improving the performance of the Jupiter flyby is to

perform a maneuver as the spacecraft passes through periapsis at Jupi­ ter.

The application of this AV deep in the planet's gravitational

potential well results in a substantial increase in the outgoing Vout

and thus the solar system hyperbolic excess velocity V..

This technique

is particularly useful in raising relatively low Vin values incoming

to high outgoing Vout's.

Table 7 gives the outgoing Vou t values at

Jupiter obtainable as a function of V. in and AV applied at periapsis.

A flyby at 1.1 R is assumed. The actual Vou t might be fractionally smaller

because of gravity losses and pointing errors but the table gives a

good idea of the degrees of performance improvement possible.

Carrying the necessary propulsion to perform the AV maneuver would

require an increase in launched payload and thus a decrease in maximum

launch energy and V.in possible at Jupiter. Table 8 gives the required

launched mass for a net payload of 300 kg after the Jupiter flyby, using

a space storable propulsion system with I

sp of 370 seconds, and the

maximum C3 possible with a Shuttle/4-stage IUS launch vehicle, as a

function of AV capability at Jupiter.

These numbers may be combined

with the two previous tables to find the approximate V. at Jupiter and

In

the resulting Vou t *

Launch Opportunities to Jupiter

Launch opportunities to Jupiter occur approximately every 13 months.

Precise calculations of such opportunities would be inappropriate at

this stage in a study of extra-solar probe possibilities.

Because

Jupiter moves about 330 in ecliptic longitude in a 13 month period, and

because the cone of possible escape trajectories exceeds 300 in half­ width for V

out

above about 10 km/s, it should be possible to launch

to any ecliptic longitude over a 12 year period by properly choosing

the launch date and flyby date at Jupiter.

25

With sufficient V

out

the

77-70

TABLE 7

Jupiter Powered Flyby

Approach

velocity

relative Jupaie to

to

Jupiter, Vin

6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0

Outbound velocity relative to Jupiter, Vo, (kn/s), for indicated AV (km/s) applied at periapsis of 1.1 R.

.50

1.00

1.50

2.00

2.50

9.66 11.03 12.57 14.22 15.96 17.76 19.59 21.46

12.30 13.41 14.71 16.16 17.72 19.37 21.08 22.83

14.48 15.44 16.59 17.00 19.33 20.86 22.47 24.14

16.38 17.25 18.29 19.50 20.83 22.37 23.80 25.39

18.11

18.90

19.86

20.99

22.24

23.61

25.06

26.00

26

77-70

TABLE 8

Launched Mass for 300 kg Net Payload

after Jupiter Powered Flyby

AV at Jupiter

Required launched mass

for S/C Is = 370 s

p

Maximum launch energy, C3 ,

attainable with

shuttle/4-stage IUS

(km/s) 2

(km/s)

(kg)

.0

300.

178.4

.5

428.

157.4

1.0

506.

147.4

1.5

602.

137.0

2.0

720.

127.2

2.5

869.

114.9

27

77-70

high ecliptic latitudes would be available as described in an earlier

section.

Flight times to Jupiter will typically be 2 years or less.

Venus-Earth Gravity Assist

One means of enhancing payload to Jupiter is to launch by way of

a Venus-Earth Gravity Assist (VEGA) trajectory. These trajectories

2

launch at relatively low C3 's, 15 - 30 (km/s) , and incorporate gravity

assist and AV maneuvers at Venus and Earth to send large payloads to

the outer planets.

The necessary maneuvers add about 2 years to the

total flight time before reaching Jupiter.

The extra payload could

then be used as propulsion system mass to perform the powered flyby

at Jupiter.

An alternate approach is that VEGA trajectories allow use

of a smaller launch vehicle to achieve the same mission as a direct

trajectory.

POWERED SOLAR FLYBY

The effect of an impulsive delta-V maneuver when the spacecraft is

close to the Sun has been calculated for an extra-solar spacecraft.

The

calculations are done for a burn at the perihelion distance of 0.1 AU,

for orbits whose V ly.

value before the burn is 0, 5, and 10 lan/s respective­

Results are shown in Table 9.

It can be seen that the delta-V

maneuver deep in the Sun's potential well can result in a significant

increase in V burn V

after the burn, having its greatest effect when the pre­

is small.

The only practical means to get 0.1 from the Sun (other than with a

"super sail", discussed below) is a Jupiter flyby at a V relative to

Jupiter of 12 km/s or greater.

The flyby is used to remove angular

momentum from the spacecraft orbit, and "dump" it in towards the Sun.

The same flyby used to add energy to the orbit could achieve V

of 17

km/s or more without any delta-V, and upwards of 21 km/s with 2.5 km/s

of delta-V at Jupiter.

The choice between the two methods will require

considerably more study in the future.

LOW-THRUST TRAJECTORIES

A large number of propulsion techniques have been proposed that do

not depend upon utilization of chemical energy aboard the spacecraft.

28

77-70

TABLE 9

Powered Solar Flyby

AV (km/s)

Heliocentric hyperbolic excess velocity, V., (km/s),

after burn 0.1 AU from Sun and initial V as indicated (km/s)

0

5

10

.1

5.16

7,19

11.25

.3

8,94

10.25

13.42

.5

11.55

12.59

15.29

1.0 1.5

16,35 20.05

17.10 20.67

19.19

22.42

2.0

23.17

23.71

25.26

2.5

25.93

26.41

27.82

29

77-70

Among the more recent reviews pertinent to this mission are those

by Forward (1976), Papailiou et al (1975), and James et al (1976).

A

very useful bibliography is that of Mallove et al (1977).

Most of the techniques provide relative low thrust and involve long

periods of propulsion.

The following paragraphs consider

methods that

seem the more promising for an extraplanetary mission launched around

2000.

Solar Sailing

Solar sails operate by using solar radiation pressure to add or

subtract angular momentum from the spacecraft (Garwin, 1958).

The

basic design considered in this study is a helio-gyro of twelve

6200-meter mylar strips, spin-stabilized.

According to Jerome Wright (private communication), the sail is

capable of achieving spacecraft solar system escape velocities of 15-20

km/s.

This requires spiralling into a close orbit approximately 0.3 AU

from the sun and then accelerating rapidly outward.

The spiral-in

maneuver requires approximately one year and the acceleration outward,

which involves approximately 1-1/2 - 2 revolutions about the sun,

takes about 1-1/2 - 2 years, at which time the sail/spacecraft is

crossing the orbit of Mars, 1.5 AU from the sun, on its way out.

The sail is capable of reaching any inclination and therefore any

point of the celestial sphere.

This is accomplished by performing a

"cranking" maneuver when the sail is at 0.3 AU from the sun, before

the spiral outward begins.

The cranking maneuver keeps the sail in a

circular orbit at 0.3 AU as the inclination is steadily raised.

The

sail can reach 900 inclination in approximately one year's time.

Chauncey Uphoff (private communication) has discussed the possi­ bility of a super sail capable of going as close as 0.1 AU from the sun,

and capable of an acceleration outward equal to or greater than the

sun's gravitational attraction.

Such a sail might permit escape V's

on the order of 100 km/s, possible up to 300 km/s.

However, no such

design exists at present and the possibility of developing such a sail

has not been studied.

Laser Sailing

Rather et al (1976) have recently re-examined the proposal (For­ ward, 1962, Marx, 1966,Moeckle, 1972) of using high energy lasers, rather

than sunlight, to illuminate a sail.

The lasers could be in orbit

30

77-70

around the earth or moon and powered by solar collectors.

Rather et al found that the technique was not promising for star

missions but could be useful for outer planet missions.

Based on their

assumptions , a heliocentric escape velocity of 60 Io/s could be reached

with a laser output power of about 30 kW, 100 km/s with about 1500 kW,

and 200 Im/s with 20 MW.

Acceleration is about 0.35 g and thrusting

would continue until the S/C was some millions of kilometers from earth.

Solar Electric Propulsion

Solar electric propulsion uses ion engines, where mercury or

other atoms are ionized and then accelerated across a potential gap

to a very high exhaust velocity.

The electricity for generating the

potential comes from a large solar cell array

on the spacecraft.

Current designs call for a 100 kilowatt unit which is also proposed

for a future comet rendezvous mission.

A possible improvement to the

current design is the use of mirror "concentrators" to focus additional

sunlight on the solar cells at large heliocentric distances.

According to Carl Sauer (private communication) the solar powered

ion drive is capable of escape V.'s on the order of 10-15 km/s in the

ecliptic plane.

Going out of the ecliptic is more of a problem because

the solar cell arrays cannot be operated efficiently inside about 0.6 AU

from the sun.

Thus the solar electric drive cannot be operated

close iiito the sun for a cranking maneuver as can the solar sail.

Modest inclinations can still be reached through slower cranking or the

initial inclination imparted by the launch vehicle.

Laser Electric Propulsion

An alternative to solar electric propulsion is laser electric:

lasers, perhaps in earth orbit, radiate power to the spacecraft, which is

collected and utilized in ion engines.

The primary advantage is that

higher energy flux densities at the spacecraft are possible.

This would

permit reducing the receiver area and so, hopefully, the spacecraft

weight.

To take advantage of this possibility, receivers that can

operate at considerably higher temperatures than present solar cells will

be needed.

A recent study by Forward (1975) suggests that a significant

performance gain, as compared to solar electric, may be feasible.

Rather et al assumed an allowable flux incident on the sail of 10 6 W/m 2 laser wavelength 0.5 pm, and laser beam size twice-the diffraction limit. For this calculation, 10 km2 of sail area and 20,000 kg total

mass were assumed.

*

31

77-70

Nuclear Electric Propulsion

Nuclear electric propulsion (NEP) may use ion engines like solar

electric, or, alternatively, magnetohydrodynamic drive.

It obtains

electricity from a generator heated by a nuclear fission reactor.

Thus, NEP is not powertlimited by increasing solar distance.

Previous studies indicate that an operational S/C is possible

by the year 2000 with power levels up to a megawatt (electric) or more

(James et al, 1976).

Preliminary estimates were made based on previous calculations for

a Neptune mission.

Those indicated that heliocentric escape velocity

of 50-60 km/s can be obtained.

Fusion

With a fusion energy source, thermal energy could be converted to

provide ion or MHD drive and charged particles produced by the nuclear

reaction can also be accelerated to produce thrust.

A look at one fusion concept gave a V spacecraft weight was 3 x 106 kg.

of about 70 ku/s.

The

Controlled fusion has still to be

attained.

Bussard (1960) has suggested that interstellar hydrogen could be

collected by a spacecraft and used to fuel a fusion reaction.

Antimatter

Morgan (1975, 1976), James et al, (1976), and Massier (1977a and b)

have recently examined the use of antimatter-matter annihilation to

obtain rocket thrust. that a V

A calculation based on Morgan's concepts suggests

over 700 Ion/s could be obtained with a mass comparable to

NEP.

Low Thrust Plus Gravity Assist

A possible mix of techniques discussed would be to use a low­ thrust propulsion system to target a spacecraft for a Jupiter gravity

assist to achieve a very high V

escape.

If for example one accelera­

ted a spacecraft to a parabolic orbit as it crossed the orbit of

Jupiter, the V. in at Jupiter would be about 17.2 km/s.

One could use

gravity assist then to give a solar system escape V. of 24 ku/s in the

ecliptic plane, or inclinations up to about 63' above the plane.

Powered swingby at Jupiter could further enhance both V

32

and inclination.

77-70

A second possibility is to use a solar sail to crank the space­ craft into a retrograde (1800 inclination) orbit and then spiral out to

encounter Jupiter at a V.an of over 26 km/s. This would result in

escape V 's on the order of 30 km/s and inclinations up to 900, thus

covering the entire celestial sphere.

Again, powered swingby would

improve performance but less so, because of the high Vin already present.

This method is somewhat limited by the decreasing bend angle possible

at Jupiter as Vin increases.

With still higher approach velocities

the possible performance increment from a Jupiter swingby continues

to decrease.

Solar Plus Nuclear Electric

One might combine solar electric with nuclear electric, using solar

first and then, when the solar distance becomes greater and the solar

distance becomes greater and the solar power falls off, switching to NEP.

Possibly the same thrusters could be used for both.

Since operating

lifetime of the nuclear reactor can limit the impulse attainable with NEP,

this combination might provide higher V

than either solar or nuclear

electric single-stage systems.

CHOICE OF PROPULSION

Of the various propulsion techniques outlined above, the only

ones that are likely to provide solar system escape velocities above

50 km/s utilize either sails or nuclear energy.

The sail technique could be used with two basic options:

solar

sailing, going in to perhaps 0.1 AU from the sun, and laser sailing.

In either case, the requirements on the sail are formidable. Figure 3

shows solar sail performance attainable with various spacecraft light­ ness factors (ratios of solar radiation force on the S/C at normal in­ cidence to solar gravitational force on the SIC). mass/area ratios required to attain various V Table 10.

The sail surface

values are listed in

For a year 2000 launch, it may be possible to attain a sail

surface mass/area of 0.3 g/m2 , if the perihelion distance is constrained

to 0.25 AU or more (W. Carroll, private communication).

This ratio

corresponds to an aluminum film about 100 nm thick, which would probably

have to be fabricated in orbit.

With such a sail, a V

might be obtained.

33

of about 120 km/s

77-70

300

Jg

200-

X= 0 U, Ln

Uj LU

LU j

z

100II

U

0

01 0

0.1

0.2

0.3

PERIHELION RADIUS, AU

Fig. 3

Solar System Escape with Ultralight Solar Sails. Lightness factor X = (solar radiation force on S/C at normal incidence)/(solar gravitational force on S/C). From C. Uphoff (private communication).

34

77-70

TABLE

10

PERFORMANCE OF ULTRALIGHT SOLAR SAILS

Initial Perihelion Distance

Heliocentric Excess Velocity,

Lightness Factor X

Vw

g/m2

km/s

AU

Sail Load/ Efficiency aF T/1

Sail

Surface

Mass/Area

aF g/m2

0.25

60

0.8

2.0

0.9

0.25

100

1.8

0.85

0.4

0.25

200

5.5

0.3

0.12

0.1

100

0.6

2.7

1.2

0.1

200

2.2

0.7

0.3

0.1

300

5.0

0.3

0.14

Notes:

X

=

(solar radiation force on S/C at normal (incidence)/(solar gravitational force on S/C)

aT =

(total S/C mass)/(sail area)

p

sail efficiency

=

oF =

includes sail film, coatings, and seams; excludes structural

and mechanical elements of sail and non-propulsive portions

of S/C. Assumed here: 'IF= 0.5 aT; P = 0.9.

Initial orbit assumed: semi-major axis = 1 x 108 1cm. optimized for maximum rate of energy gain.

35

Sail angle

77-70

If the perihelion distance is reduced to 0.1 AU the solar radia­ tion force increases but so does the temperature the sail must withstand.

With a reflectivity of 0.9 and an emissivity of 1.0 the sail temperature

would reach 470C (740 K), so high temperature material would have to

be used.

Further, according to Carroll (ibid), it may never be possible

to obtain an emissivity of 1.0 with a film mass less than 1 g/m 2 ,

because of the emitted wavelength/thickness ratio.

For such films an

emissivity of 0.5 is probably attainable; this would increase the tempera­ ture to over 6000 C (870 K).

Carbon films can be considered, but they

would need a smooth highly reflective surface.

It is doubtful a sail

surface mass/area less than 1 g/m 2 could be obtained for use at 6000 C.

This sail should permit reaching V of 110 km/s: no better than for the

0.25 AU design.

For laser sailing, higher reflectivity, perhaps 0.99, can be

attained because the monochromatic incident radiation permits effective

use of interference layers (Carroll, ibid).

Incident energy flux

equivalent to 700 "suns" (at 1 AU) is proposed, however.

The high

reflectivity coating reduces the absorbed energy to about the level of that for a solar sail at 0.1 AU, with problems mentioned above.

V.'s up

to 200 km/s might be achieved if the necessary very high power lasers were available in orbit.

-Considering nuclear energy systems, a single NEP stage using

fission could provide perhaps 60 to 100 km/s V.

NEP systems have

already been the subject of considerable study and some advanced develop­ ment.

Confidence that the stated performance can be obtained is there­

fore higher than for any of the competing modes. a solar electric followed by NEP, higher V

Using 2 NEP stages or

could be obtained: one

preliminary calculation for 2 NEP stages (requiring 3 shuttle launches

or the year 2000 equivalent) gave V

= 150 km/s.

The calculation for a fusion propulsion system indicates 30%

spacecraft velocity improvement over fission, but at the expense of

orders of magnitude heavier vehicle. hibitive.

The cost would probably be pro­

Moreover, controlled fusion has not yet been attained, and

development of an operational fusion propulsion system for a year 2000

launch is questionable.

As to collection of hydrogen enroute to refuel

a fusion reactor, this is further in the future and serious question

exists as to whether it will ever be feasible (Martin, 1972, 1973).

An antimatter propulsion system is even more speculative than a

fusion system and certainly would not be expected by 2000.

36

On the other

77-70

hand, the very rough calculations indicate an order of magnitude velocity

improvement over fission NEP without increasing vehicle mass.

Also,

the propulsion burn time is reduced by an order of magnitude.

On the basis of these considerations, a fission NEP system was

selected as baseline for the remainder of the study.

The very light­

weight solar sail approach and the high temperature laser sail approach

may also be practical for a year 2000 mission and deserve further

study.

The antimatter concept is the most "far out", but promises orders

of magnitude better performance than NEP.

Thus, in future studies

addressed to star missions, antimatter propulsion should certainly be

considered, and a study of antimatter propulsion per se is also warranted.

37

77-70

MISSION CONCEPT

The concept which evolved as outlined above is for a mission out­ ward to 500-1000 AU, directed toward the incoming interstellar gas.

Critical science measurements would be made when passing through the

heliopause region and at as great a range as possible thereafter.

The

location of the heliopause is unknown but is estimated as 50-100 AU.

Measurements at Pluto are also desired.

Launch will be nominally in

the year 2000.

The maximum spacecraft lifetime considered reasonable for a year

2000 launch is 50 years.

(This is discussed further, below).

To

attain 500-1000 AU in 50 years requires a heliocentric excess velocity

of 50-100 km/s.

The propulsion technique selected as baseline is NEP

using a fission reactor.

Either 1 or 2 NEP stages may be used.

If 2 NEP

stages are chosen, the first takes the form of an NEP booster stage and the

second is the spacecraft itself. The spacecraft, with or without an NEP

booster stage, is placed in low earth orbit by some descendant of the

Shuttle.

NEP is then turned on and used for spiral earth escape.

Use of

boosters with lower exhaust velocity to go to high earth orbit or earth

escape is not economical.

The spiral out from low earth orbit to earth

escape uses only a small fraction of the total NEP burn time and NEP pro­ pellant.

After earth escape, thrusting continues in heliocentric orbit.

A

long burn time is needed to attain the required velocity: 5 to 10 years are

desirable for single stage NEP (see below), and more than 10 years if two

NEP stages are used.

The corresponding burnout distance, depending on the

design, may be as great as 200 AU or even more.

Thus, propulsion may be on

past Pluto (31 AU from the sun in 2005) and past the heliopause.

To measure

the mass of Pluto, a coasting trajectory is needed; thrust would have to be

shut off temporarily during the Pluto encounter.

The reactor would continue

operating at a low level during the encounter to furnish spacecraft power.

Attitude control would preferably be by momentum wheels to avoid any distur­ bance to the mass measurements.

Scientific measurements, including imagery,

would be made during the fast flyby of Pluto.

38

77-70

After the Pluto encounter, thrusting would resume and continue until

nominal thrust termination ("burnout") of the spacecraft.

Enough propel­

lant is retained at spacecraft burnout to provide attitude control (unload­ ing the momentum wheels) for the 50 year duration of the extended mission.

At burnout the reactor power level is reduced and the reactor provides

power for the spacecraft, including the ion thrusters used for attitude control.

A very useful add-on would be a Pluto Orbiter.

This daughter spacecraft

would be separated early in the mission, at approximately the time solar

escape is achieved.

Its flight time to Pluto would be about 12 years and its

hyperbolic approach velocity at Pluto about 8 km/s.

The orbiter would be a full-up daughter spacecraft, with enough chemical

propulsion for midcourse, approach, and orbital injection.

It would have a

full complement of science instruments (including imaging) and RTG power

sources, and would communicate directly to Earth.

Because the mass of a dry NEP propulsion system is much greater than

that required for the other spacecraft systems, the added mass of a daughter

S/C has relatively little effect on the total inert mass and therefore relatively

little effect on propulsive performance.

The mother NEP spacecraft would fly by

Pluto 3 or 4 years after launch, so the flyby data will be obtained at least

5 years before the orbiter reaches Pluto.

Accordingly, the flyby data can be

used in selecting the most suitable orbit for the daughter-spacecraft.

If a second spacecraft is to be flown out parallel to the solar axis,

it could be like the one going toward the incoming interstellar gas, but

obviously would not carry an orbiter.

Since the desired heliocentric escape

direction is almost perpendicular to the ecliptic, somewhat more propulsive

energy will be required than for the S/C going upwind, if the same escape

velocity is to be obtained.

A Jupiter swingby may be helpful.

stage would be especially advantageous for this mission.

39

An NEP booster

77-70

MASS DEFINITION AND PROPULSION

The NEP system considered is similar to those discussed by Pawlik and

Phillips (1977) and by Stearns (1977).

As a first rule-of-thumb approximation

the dry NEP system should be approximately 30-35 percent of the spacecraft

mass.

A balance is then required between the net spacecraft and propellant,

with mission energy and exhaust velocity being variable.

For the very high

energy requirements of the extraplanetary mission, spacecraft propellant

expenditure of the order of 40-60 percent may be appropriate.

A booster

stage, if required, may use a lower propellant fraction, perhaps 30 percent.

Power and propulsion system mass at 100-140 km/s exhaust velocity will

be approximately 17 kg/kWe.

This is based on a 500 kWe system with 20% con­

version efficiency and ion thrusters.

Per unit mass may decrease slightly

at higher power levels and higher exhaust velocity.

Mercury propellant is

desired because of its high liquid density, - 13.6 g/cm 3 or 13,600 kg/m 3 .

Mercury is also a very effective gamma shield.

If an NEP booster is to be

used, it is assumed to utilize two 500 We units.

The initial mass in low earth orbit (M ) is taken as 32,000 kg for

the spacecraft (including propulsion) and as 90,000 kg for the spacecraft

plus NEP booster.

32,000 kg is slightly heavier than the 1977 figure for

the capability of a single shuttle launch.

The difference is considered

unimportant, because 1977 figures for launch capability will be only of

historical interest by 2000.

90,000"kg for the booster plus S/C would re­

quire the year 2000 equivalent of three 1977 Shuttle launches.

Figure 4 shows the estimated performance capabilities of the propulsion

system for a single NEP stage.

A net spacecraft mass of approximately 1200 kg is assumed and may be broken

out in many ways.

Communication with Earth is a part of this and may trade off

with on-board automation, computation and data processing. launch of daughter spacecraft may be needed. possible.

Support structure for

Adaptive science capability is also

The science instruments may be of the order of 200-300 kg (including

a large telescope) and utilize 200 kg of radiation shielding (discussed below)

and in excess of 100 W of power. Communications could require as much as 1 kW.

40

140

140

120

120 w

"-

--V e = 100, Msc

"

=

Ve 0 u

120, M

= 0

,,

= 2000

U

e = 140,' Mps/c = 4000 ~V00 FORZ

70

_u -J

0W=\ 60 a HV

= 120, Mpc =0 = 2000

x

-60

Vz ee == 140, Mps/c = 4000

>

LU
50 BL (coherent system)

for

50 BL the

to its asymptotic value of 2 R% could be made slightly

faster by techniques employing suppressed carrier tracking loops which

utilize all the received power for both tracking and data demodulation.

However, for this study these curves are sufficiently accurate to

ascertain Pr IN

levels necessary to achieve desired data rates.

BASELINE DESIGN

Parameters of the System

For a "baseline" design we have tried to put together a system

that has a good chance of being operational by the year 2000.

Con­

sequently in certain areas we have not pushed current technology but

have relied on fairly well established systems.

In other areas, we

have extrapolated from present trends, but hopefully not beyond develop­ ments that can be accomplished over 20-25 years.

This baseline design

will be derived in sufficient detail so that the improvement afforded

by the "other options" discussed in the next section can be more

easily ascertained.

First, we assume that received carrier frequency stabilities

allow tracking with a loop bandwidth BL

1 Ez.

This circumstance

is quite likely if an oscillator quite stable in the short term is carried

49

77-70

on the S/C, if the propulsion systems are not operating during trans­ mission at 1000 AU (Doppler rate essentially zero), and if the receiver

is orbiting Earth (no ionospheric disturbance). data rates RD of at least 100 bits/s are desired.

Second, we assume

at 1000 AU or 400 b/s at 50 AU

From the discussion preceding eq. (6) and Figure 5 we

see this implies a coherent demodulation system with Pr/N

to exceed

25 dB.

As a baseline we are assuming an X-band system (X 40 watts transmitter power.

=

3.55 cm) with

We assume the receiving antenna is on Earth

(if this assumption makes BL

11 Hz unattainable, then the value of Pr IN

for the non-coherent system only increases by 1 dB) so the system noise temperature reflects this accordingly. Decibel Table and Discussion In Table 12

we give the dB contributions from the various para­

meters of the range eq. (1), loop tracking, and data coding.

By design

the parameters of this table give the narrowest performance margins.

If any of the "other options" of the next section can be realized, per­ formance margin and data rate should correspondingly increase.

The two antenna parameters that are assumed require some

explanation.

A current mission (SEASAT-A) has an imaging radar antenna

that "unfurls" to a rectangular shape 10.75 m x 2 m, so a 15 m diameter

spaceborne antenna should pose no difficulty by the year 2000. diameter receiving antenna is assumed.

A 100 m

Even though the largest DSN

antenna is currently 64 m, an antenna and an array both having effec­ tive area _> (100 m)2 will be available in West Germany and in this country

in the next five years.

Consequently, a receiver of this collecting

area could be provided for the year 2000.

OPTIONS

More Power

The 40 watts transmitter power of the baseline should be currently realizable being only a factor of 2 above the Voyager value. This might be increased to 0.5

-

1 kW, increasing received signal power

by almost 10-15 dB, allowing (after some increase in performance margin) a tenfold gain in data rate: 1 kb/s at 1000 AU, 4 kb/s at 500 AU.

The

problem of coupling this added energy into the transmission efficiently may cause some difficulty and should definitely be investigated.

50

77-70

70

60-

COHERENT

50-

BL

NON-COHERENT

10 Hz

N

z

0

L.

30­ -/ ---

BL 10 Hz

20­

BL = Hz

10-

CO-COHERENTH BL =1Hz

10 0 0

I

I

II

10

20

30

I

40

DATA RATE RD (dB bits/sec) Fig. 5.

Data Rate vs. Ratio of Signal Power to Noise Spectral Power Density

51

50

60

77-70

Table 12. BASELINE TELEMETRY AT 1000 AU

No.

Parameter

Nominal Value

1.

Total Transmitter power (dBm) (40 watts)

46

2.

Efficiency (dB) (electronics and antenna losses)

-9

3.

Transmitting antenna gain (dB) (diameter = 15 m)

62

4.

Space loss (dB) (A/47R) X = 3.55 cm,

2

-334

R = 1000 AU

5.

Receiving antenna gain (dB) (diameter = 100m)

6.

Total received power (dBm) (Pr)

7.

Receiver noise spectral density (dBm/Hz) (N0 )

kT with T = 25 K

79

-156

-185

Tracking (if BL = 1 H4z is achievable)

8.

Carrier power/total power 9dB)

-5

(100 BL/(100BL + 2 R))

9.

Carrier power (dBm) (6,+

8)

10.

Threshold SNR in 2 BL (dB)

11.

Loop noise bandwidth (dB) (BL)

12.

Threshold carrier power (dBm) (7 + 10 + 11)

13.

Performance margin (dB) (9 - 12)

-161

20

0

-165 4

Data Channel

14.

Estimated loss (waveform distortion, bit sync,

etc.)

15.

(B)

-2

Data power/total power (dB)*

-2

(2RD/(100BL+ 2RD ) ) 16.

Data power (dBm) (6 + 14 + 15)*

-160

17.

Threshold data power (dBm) (7 + 17a + 17b)

-162

18.

a.

Threshold PrT/N 0 (BER = 10- 4

b.

Bit rate (dB BPS)

3 20

Performance margin (dB) (16 - 17)*

2

*If a non-coherent system must be used each of these values are reduced by approximately 1 dB.

52

77-70

Larger Antennas and Lower Noise Spectral Density

If programs calling for orbiting DSN station are funded, then

larger antennas operating at lower noise spectral densitites should be­ come a reality.

Because structural problems caused by gravity at the

Earth's surface are absent, antennas even as large as 300 m in diameter

have been considered.

Furthermore, assuming problems associated with

cryogenic amplifiers in space can be overcome, current work indicates

X-band and Ku-band effective noise temperatures as low as 10 K and 14 K

respectively (R. C. Clauss, private communication). would increase Pr/N

These advances

by approximately 12-13 dB making a link at data

rates of 2 kb/s at 1000 AU and 8 kb/s at 500 AU possible.

Higher Frequencies

Frequencies in the Ku-band could represent a gain in directed

power of 5-10 dB over the X-band baseline, but probably would exhibit

noise temperatures 1-2 dB worse (Clauss, ibid) for orbiting receivers.

Also, the efficiency of a Ku-band system would probably be somewhat less

than that of X-band.

Without further study, it is not apparent that

dramatic gains could be realized with a Ku-band system.

Frequencies in the optical or infrared potentially offer tre­ mendous gains in directed power.

However, the efficiency in coupling

the raw power into transmission is not very high, the noise spectral

density is much higher than that of X-band, and the sizes of practical

antennas are much smaller than those for microwave frequencies.

To

present these factors more quantitatively, Table 13 gives parameter con­ tributions to Pr and N

.

We have drawn heavily on Potter et al (1969) and

on M. S. Shumate and R. T. Menzies (private communication) to compile this table.

We assume an orbiting receiver to eliminate atmospheric

transmission losses.

Also, we assume demodulation of the optical signal

can be accomplished as efficiently as the microwave signal (which is not likely without some development). Pr/N

Even with these assumptions,

for the optical system is about 8 dB worse than that for X-band

with a ground receiver.

Pointing problems also become much more severe for the highly

directed optical, infrared systems.

Laser radiation at wavelength 10 Pm

from a 1 m antenna must be pointed to 5 x 10- 6 radians accuracy.

The corresponding pointing accuracy of the baseline system is 10- 3 radians.

53

77-70

Table 13. OPTICAL TELEMETRY AT 1000 AU Parameter

Value

Nominal

1.

Total Transmitter power (dBm) (40 watts)

46

2.

Efficiency (dB) (optical pumping, antenna losses,

No.

-16

and quantum detection)

3.

Transmitting antenna gain (dB) (diameter = 1 m)

4.

2

Space loss (dB) (A/4r)

X =lO

pm,

110

-405

r =1000 AU

5.

Receiving antenna gain (dB) (diameter = 3m)

6.

Total Received power (dBm) (P

7.

Receiver noise spectral density (dBm/Hz) (N0 )

)

- 2 0 watt/HZ)

(2 x 10

54

119

-146

-167

77-70

Higher Data Rates

This mission may have to accommodate video images from Pluto.

The Earth-Pluto separation at the time of the mission will be about 31

AU.

The baseline system at 31 AU could handle approximately 105 b/s.

For rates in excess of this, one of the "other option" enhancements would

be necessary.

SELECTION OF TELEMETRY OPTION

Table 14 collects the performance capabilities of the various

telemetry options.

Table 15 shows the proposed data rates in various

S/C systems for the different phases of the mission.

In both tables

2

the last column lists the product, (data rate) x (range) , as an index

of the telemetry capability or requirements.

Looking first at the last column of Table 15 , it is apparent that

the limiting requirement is transmittal of heliopause data if DSN

coverage can be provided only 1% of the time.

If DSN scheduling is

sufficiently flexible that 33% coverage can be cranked up within a

month or so after the heliosphere is detected, then the limiting

requirement is transmittal of cruise data (at 1% DSN coverage).

For

these two limiting cases, the product (data rate) x (range)2 is, respec­ 8 8 2 tively, 2-40 x 10 and 5-10 x 10 (b/s) . AU Looking now at the last column of Table 14 , to cover the cruise

requirement some enhancement over the baseline option will be needed.

Either increasing transmitter power to 0.5-1 kW or going to orbiting DSN

stations will be adequate.

No real difficulty is seen in providing the

increased transmitter power if the orbiting DSN is not available.

If, however, DSN coverage for transmittal of recorded data from

the unpredictable heliosphere encounter is constrained to 1% of the

time (8 h/month), then an orbital DSN station (300-m antenna) will be

needed for this phase of the mission, as well as either increased trans­ mitter power or use of K-band.

55

TABLE

14

TELEMETRY OPTIONS (Data Rate) x (Range)

Data Rate (b/s) OPTIONS

Improvement Over Baseline, dB

At 1000 AU

At 500 AU

At 150 AU

1 x 102

4 x 102

4 x 103

1 x 105

1 x 108

4 x 103

4 x 104

1 x 106

1 x 109

9 x 104

2 x 106

2 x 109

2 x 10

5 x 10

5 x 109

At 31 AU

(b/s) • AU2

Baseline (40 W, 100-m receiving antenna, X-band)

----

More power (0.5 ­ 1 kW)

10-15

1 x 103

Orbiting DSN (300-m antenna) X-band (10 K noise temperature)

13

2 x 103

K-band (14 K noise temperature)

17

5 x 103

2 x 10

C)

Both more power and orbiting DSN X-band

23-28

3 x 104

1.2 x 105 1 x 106

3 x 107

3 x 1010

TABLE 15 PROPOSED DATA RATES TeleCommuni-

Misslon Phase

Cruise

Heliopause

cation Range AU 500

50-

Estimated Data Rate, b/s

(Data

Processed Data, Average

Transmitted Data

I 1.2-1.5 x 104

2-4 x 101

2-4 x 103

1 1.2-1.5

31-2 1-2 x 103

Raw Data

x 10

x 105

150

Pluto Flyby

-31

SI l 5 1-2 x 10

x 10 5

Pluto Orbiter

-31

15 11-2 x 10

*To return flyby data in 4 days.

tate x (Range)2 b/s .Au2

0.01

5-10 x 108

0.01

2-40 x 108

0.33

0.8-15 x 107

0.33*

1 x 10 8

3-5 x 104

1 11

(10 total I bits)

Fraction of Time Transmitting

(3 x 10

10

4

3-5 x 104

bits)

3x101.00*

3 x10

x 10

9-15 x 104

3-5 x10 4

0.33

9-15 x 107

1.00

3-5 x

0

77-70

RELATION OF THE MISSION TO

SEARCH FOR EXTRATERRESTRIAL INTELLIGENCE

The relation of this mission to the search for extraterrestrial

intelligence appears to lie only in its role in development and test

of technology for subsequent interstellar missions.

58

77-70

TECHNOLOGY REQUIREMENTS AND PROBLEM AREAS

LIFETIME

A problem area common to all S/C systems for this mission is that of

lifetime.

The design lifetime of many items of spacecraft equipment is now

approaching 7 years.

To increase this lifetime to 50 years will be a very

difficult engineering task.

These consequences follow:

a)

It is proposed that the design lifetime of the S/C for this mission

be limited to 20 years, with an extended mission contemplated to a total of

50 years.

b)

Quality control and reliability methods, such as failure mode effects

and criticality analysis, must be detailed and applied to the elements that

may eventually be used in the spacecraft, so as to predict what the failure

profile will be for system operating times that are much longer than the test

time and extend out to 50 years.

One approach is to prepare for design and

fabrication from highly controlled materials whose failure modes are

completely understood.

c)

To the extent that environmental or functional stresses are conceived

to cause material migration or failure during a 50-year period, modeling and

accelerated testing of such modes will be needed to verify the 50-year scale.

Even the accelerated tests may require periods of many years.

d)

A major engineering effort will be needed to develop devices, circuits,

components, and fabrication techniques which, with appropriate design, testing,

and quality assurance methods, will assure the lifetime needed.

PROPULSION AND POWER

The greatest need for subsystem development is clearly in propulsion.

Further advance development of NEP is required. higher uranium loadings and higher burnup.

Designs are needed to permit

This in turn will require better

control systems to handle the increased reactivity, including perhaps throw-away

control rods.

Redundancy must be increased to assure long life and moving

parts will need especial attention.

Development should also be aimed at reducing

system size and mass, improving efficiency, and providing better and simpler

thermal control and heat dissipation.

Simpler and lighter power conditioning

59

77-70

is needed, as are ion thrusters with longer lifetime or self-repair capability.

Among the alternatives to fission NEP, ultralight solar sails and laser

sailing look most promising.

A study should be undertaken of the feasibility

of developing ultra-ltght solar sails

(sails sufficiently light so that the

solar radiation pressure on the sail and spacecraft system would be greater

than the solar gravitational pull) and of the implications such development

would have for spacecraft design and mission planning.

Similarly, a study

should be made of the possibility of developing a high power orbiting laser

system together with high temperature spacecraft sails, and of the outer planet

and extraplanetary missions that could be carried out with such laser sails.

Looking toward applications further in the future, an antimatter propul­ sion system appears an exceptionally promising candidate for interstellar

missions and would be extremely useful for missions within the solar system.

This should not be dismissed as merely "blue sky": matter-antimatter reactions

are routinely carried out in particle physics laboratories.

The engineering

difficulties of obtaining an antimatter propulsion system will be great; con­ taining the antimatter and producing it in quantity will obviously be problems.

A study of possible approaches would be worthwhile.

(Chapline (1976) has suggested

that antimatter could be produced in quantity by the interaction of beams of

heavy ions with deuterium/tritium in a fusion reactor).

Besides this, a more

general study of propulsion possibilities for interstellar flight (see Appendix

C) should also be considered.

PROPULSION/SCIENCE INTERFACE

Three kinds of interactions between the propulsion/attitude control

system and science measurements deserve attention.

They are:

1)

Interaction of thrust and attitude control with mass measurements.

2)

Interaction of electrical and magnetic fields, primarily from the thrust subsystem, with particles and fields measurements.

3)

Interactions of nuclear radiation, primarily from the power subsystem, with photon measurements.

60

77-70

Interaction of thrust with mass measurements

It is desired to measure the mass of Pluto and of the solar system as

a whole through radio tracking observations of the spacecraft accelerations.

In practice, this requires that thrust be off during the acceleration obser­ vations.

The requirement can be met by temporarily shutting off propulsive

thrusting during the Pluto encounter and, if desired, at intervals later on.

Since imbalance in attitude control thrusting can also affect the trajectory,

attitude control during these periods should preferably be by momentum wheels.

The wheels can afterwards be unloaded by attitude-control ion thrusters.

Interaction of thrust subsystem with particles and fields measurements

A variety of electrical and magnetic interference with particles and fields

measurements can be generated by the thrust subsystem.

The power subsystem can

also generate some electrical and magnetic interference.

Furthermore, materials

evolved from the thrusters can possibly deposit upon critical surfaces.

Thruster interferences have been examined by Sellen (1973), by Parker et al.

(1973), and by others.

It appears that thruster interferences should be reduc­

ible to acceptable levels by proper design, but some advanced development will

be needed.

Power system interferences are probably simpler to handle.

Essen­

tially all the thruster effects disappear when the engines are turned off.

Interaction of power

subsystem with photon measurements

Neutrons and gamma rays produced by the reactor can interfere with

photon measurements.

A reactor that has operated for some time will be highly

radioactive even after it is shut down.

Also, exposure to neutrons from the

reactor will induce radioactivity in other parts of the spacecraft.

In the

suggested science payload the instruments most sensitive to reactor radiation

are the gamma-ray instruments, and, to a lesser degree, the ultraviolet

spectrometer.

A very preliminary analysis of reactor interferences has been done.

Direct neutron and gamma radiation from the reactor was considered and also

neutron-gamma interactions.

The latter were found to be of little significance if

61

77-70

the direct radiation is properly handled. except

Long-lived radioactivity is no problem

possibly for structure or equipment that uses nickel.

Expected

flux levels per gram of nickel are approximately 0.007 y/cm2-s.

The nuclear reactor design includes neutron and gamma shadow shielding

to fully protect electronic equipment from radiation damage. are defined in terms of total integrated dose. to 1012 nvt and gamma dose to 106 rad.

Requirements

Neutron dose is to be limited

A primary mission time of 20 years is

assumed, yielding a LiH neutron shield thickness of 0.9 m and a mercury gamma

shield thickness of 2.75 cm (or 2 cm of tungsten).

Mass of this shielding is

included in the 8500 kg estimate for the propulsion system.

For the science instruments, it is the flux that is important, not total

dose.

The reactor shadow shield limits the flux level to 1.6 x 103 neutrons

2 or gammas/cm 2 . This is apparently satisfactory for all science sensors except

the22

gamma-ray detectors. They require that flux levels be reduced to 10 neutrons/

cm -s and 0.1 gamma/cm -s. Such reduction is most economically accomplished by local

shielding.

The gamma ray transient detector should have a shielded area of

possibly 1,200 cm 2 (48 cm x 25 cm). thickness of

Its shielding will include a tungsten

8.7 cm and a lithium-hydride thickness of 33 cm.

The weight of

this shielding is approximately 235 kg and is included in the spacecraft mass

estimate.

It may also be noted that the gamma ray transient detector is prob­

ably the lowest-priority science instrument.

An alternative to shielding it

would be to omit this instrument from the payload.

(The gamma ray spectrometer

is proposed as an orbiter instrument and need not operate until the orbiter is

separated from the NEP mother spacecraft).

A detailed Monte Carlo analysis

and shield development program will be needed to assure a satisfactory solution

of spacecraft interfaces.

TELECOMMUNICATIONS

Microwave vs.

Optical Telemetry Systems

Eight years ago JPL made a study of weather-dependent data links in

which performance at six wavelengths ranging from S-band to the visible was

analyzed (Potter et al., 1969).

A similar study for an orbiting DSN (weather­

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independent) should determine which wavelengths are the most advantageous.

The work of this report indicates X-band or K-band are prime candidates, but

a more thorough effort is required that investigates such areas as feasibility

of constructing large spaceborne optical antennas, efficiency of power conver­ sion, feasibility of implementing requisite pointing control, and overall costs.

Space Cryogenics

We have assumed cryogenic amplifiers for orbiting DSN stations in order

to reach 4-5 K amplifier noise contributions.

Work is being done that indicates

such performance levels are attainable (R. C. Clauss, private communication;

D. A. Bathker, private communication) and certainly should be continued.

At

the least, future studies for this mission should maintain awareness of this

work and probably should sponsor some of it.

Lifetime of Telecommunications Components

The telecommunications component most obviously vulnerable to extended

use is the microwave transmitter.

Current traveling-wave-tube (TWT) assemblies

have demonstrated 11-12 year operating lifetimes (H. K. Detweiler, private

communication; also, James et al., 1976) and perhaps their performance over

20-50 year intervals could be simulated.

However, the simple expedient

measure of carrying 4-5 replaceable TWT's on the missions might pose a

problem since shelf-lifetimes (primarily limited by outgasing) are not known

as well as the operating lifetimes. solid-state transmitters.

A more attractive solution is use of

Projections indicate that by 1985 to 1990 power

transistors for X-band and Ku-band will deliver 5-10 watts/device and a few

watts/device respectively with lifetimes of 50-100 years (J. T. Boreham,

private communication).

Furthermore, with array feed techniques, 30-100

elements qould be combined in a near-field Cassegrainian reflector for

signal transmission (Boreham, ibid).

This means a Ku-band system could

probably operate at a power level of 50-200 watts and an X-band system

could likely utilize 0.2 - 1 kW.

Other solid state device components with suitable modular replacement

strategies should endure a 50 year mission.

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Baseline Enhancement vs.

Non-Coherent Communication System

The coherent detection system proposed requires stable phase reference

tracking with a closed loop bandwidth of approximately 1 Hz.

Of immediate

concern is whether tracking with this loop bandwidth will be stable.

Moreover,

if the tracking is not stable, what work is necessary to implement a non-coherent

detection system?

The most obvious factors affecting phase stability are the accelerations

of the SIC, the local oscillator on the S/C, and the medium between transmitter

and receiver.

If the propulsion system is not operating during transmission,

the first factor should be negligible.

However, the feasibility of putting on

board a very stable (short term) local oscillator with a 20-50 year lifetime

needs to be studied.

Also, the effect of the Earth's atmosphere and the

Planetary or extraplanetary media on received carrier stability must be

determined.

If stability cannot be maintained, then trade-off studies must be

performed between providing enhancements to increase Pr IN

and employing

non-coherent communication systems.

INFORMATION SYSTEMS

Continued development of the on-board information system capability

will be necessary to support control of the reactor, thrusters, and other

portions of the propulsion system, to handle the high rates of data acqui­ sition of a fast Pluto flyby, to perform on-board data filtering and compres­ sion, etc.

Continued rapid development of information system capability to

very high levels is assumed, as mentioned above, and this is not considered

to be a problem.

THERMAL CONTROL

The new thermal control technology requirement for a mission beyond the

solar system launched about 2000 A.D. involve significant advancements in ther­ mal isolation techniques, in heat transfer capability and in lifetime extension.

Extraplanetary space is a natural cryogenic region (_3 K).

64

Advantage may be taken

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of it for passive cooling of detectors in scientific instruments and also

for the operation of cryogenic computers.

If cryogenic computer systems

and instruments can be developed, the gains in reliability, lifetime, and

performance can be considered.

However, a higher degree of isolation will

be required to keep certain components (electronics, fluids) warm in extra­ planetary space and to protect the cryogenic experiments after launch near

Earth.

This latter is especially true if any early near-solar swingby is

used to assist escape in the mission.

A navigational interest in a 0.1 AU

solar swingby would mean a solar input of 100 suns which is beyond any

anticipated nearterm capability.

More efficient heat transfer capability from warm sources (e.g., RTG's)

to electronics, such as advanced heat pipes or active fluid loops, will be

necessary along with long life (20-50 years).

The early mission phase also

will require high heat rejection capability, especially for the cryogenic

experiments and/or a near solar swingby.

NEP imposes new technology requirements such as long-term active heat

rejection (heat pipes, noncontaminated radiators), and thermal isolation.

NEP also might be used as a heat source for the S/C electronics.

Beyond this, the possibility of an all-cryogenic spacecraft has been

suggested by Whitney and Mason (see Appendix C). priate to missions after 2000 but warrants study.

This may be more appro­ Again, there would be a

transition necessary from Earth environment (one g plus launch, near solar)

to extraplanetary environment (zero g, cryogenic).

The extremely low power

(-1 W)requirement for superconducting electronics and the possibility of

further miniaturation of the S/C (or packing in more electronics with low

heat dissipation requirements) is very attractive.

Also looking ahead, the

antimatter propulsion system mentioned above would require cryogenic storage

of both solid hydrogen and solid antihydrogen using superconducting (cryo)

magnets and electrostatic suspension.

Table 16 summarizes the unusual thermal control features of an extra­ planetary mission.

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TABLE 16

T-HERMAL CONTROL CHARACTERISTICS OF EXTRAPLANETARY MISSIONS

Baseline Mission

1. Natural environment will be cryogenic

a) b)

Good for cryogenic experiments - can use passive thermal control.

Need for transitien from near Earth environment to extraplanetary

space. •

i. Can equipment take slow cooling?

ii. Well insolated near sun.*t

iii. Cryogenic control needed near Earth?*t

2. 'NEP

a) b)

Active thermal control - heat pipes - lifetime problems.*

Heat source has advantages & disadvantages for S/C design.

Not Part of Baseline Mission

3. Radioisotope thermal electric generator (RTG) power source provides hot

environment to cold S/C

a) b)

Requires high isolation.*

Could be used as source of heat for warm S/C.

c)

i. Fluid loop - active devices will wear - lifetime problem.*

ii. Heat pipes.

Must provide means of cooling RTG's.

4. Close Solar Swingby - 0.1 AU*

a) b) c)

*

*

100 "suns" is very high thermal input - must isolate better.*

Contrasts with later extraplanetary environment: almost no sun.

Solar Sail requirements 0.3 AU (11 suns), Super Sail 0.1 AU.*

Significant technology advancement required. Not part of baseline mission.

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COMPONENTS AND MATERIALS

By far the most important problem in this area is prediction of long-term

materials properties from short-term tests. other problems noted.

This task encompasses most of the

Sufficient time does not exist to generate the required

material properties in real time.

However, if in the time remaining we can

establish the scaling parameters, the required data could be generated in a

few years.

Hence development of suitable techniques should be initiated.

Another critical problem is obtaining bearings and other moving parts with

50 years lifetime.

Effort on this should be started.

Less critical but also desirable are electronic devices that are inherently

radiation-resistant and have high life expectancy.

DOE

has an effort under­

way on this looking both at semiconductor devices, utilizing amorphous semi­ conductors and other approaches that do not depend on minority carriers, and

at non-semiconductor devices, such as integrated thermonic circuits.

Other special requirements are listed in Table 17.

SCIENCE INSTRUMENTS

Both the problem of radiation compatibility of science instruments with NEP

propulsion and the problem of attaining 50-year lifetime have been noted above.

Many of the proposed instruments have sensors whose lifetime for even current

missions is of concern and whose performance for this mission is at best uncer­ tain.

Instruments in this category, such as the spectrometers and radiometers,

should have additional detector work performed to insure reasorvable-performance.

Calibration of scientific instruments will be very difficult for a 20-50 year

mission.

Even relatively short term missions like Viking and Voyager pose

serious problems in the area of instrument stability and calibration verifica­ tion.

Assuming that "reliable" 50-year instruments could be built, some means

of verifying the various instrument transfer functions are needed.

Calibration

is probably the most serious problem for making quantitative measurements on a

50-year mission.

The major problems in the development of individual science instruments

are listed below.

These are problems beyond those likely to be encountered

and resolved in the normal course of development between now and, say, 1995

or 2000.

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TABLE 17

TECHNOLOGY REQUIREMENTS FOR COMPONENTS & MATERIALS

1.

Diffusion Phenomena

1.1 Fuses

1.2 Heaters

1.3 Thrusters

1.4 Plume Shields

1.5 RTG's

1.6 Shunt Radiator

2.

Sublimation and Erosion Phenomena

2.1

Fuses ­

2.2 2.3 2.4 2.5 2.6 2.7 2.8

Heater

Thrusters

Plume Shields

RTG's

Polymers

Temperature Control Coatings

Shunt Radiator

3.

Radiation Effects

3.1 Electronic components

3.2 Polymers

3.3 Temperature Control Coatings

3.4 NEP and RTG Degradation

4.

Materials Compatibility

4.1 Thrusters

4.2 Heat Pipes

4.3 Polymeric Diaphragms & Bladders

4.4 Propulsion Feed System

5.

Wear and Lubrication

5.5 Bearings

6.

Hermetic Sealing and Leak Testing

6.1 Permeation Rates

6.2 Pressure Vessels

7.

Long-Term Material Property Prediction from Short-Term Tests

7.1 Diffusion

7.2 Sublimation

7.3 Wear and Lubrication

7.4 Radiation Effects

7.5 Compatibility

7.6 Thermal Effects

8.

Size Scale-Up

8.1 Antennae

8.2 Shunt Radiator

8.3 Pressure Vessels

9.

Thermal Effects on Material Properties

9.1 Strength

9.2 Creep and Stress Rupture

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Neutral Gas Mass Spectrometer

Designing a mass spectrometer to measure the concentration of light gas

species in the interstellar medium poses difficult questions of sensitivity.

Current estimates of H concentration in the interstellar medium near the

solar system are 10 --10

atom/cm

and of He contraction about 10

atom/cm

(Bertaux and Blamont, 1971; Thomas and Krassna, 1974; Weller and Meier 1974;

Freeman et al., 1977; R. Carlson, private communication; Fahr et al., 1977;

Ajello, 1977; Thomas, 1978).

On the basis of current estimates of cosmic

relative abundances the corresponding concentration of C, N, 0 is 10 - 4

10

atom/cm

3

-

and of Li, Be, B about 10 10 atom/cm

to

3 .

These concentrations are a long way beyond mass spectrometer present

capabilities, and it is not clear that adequate capabilities can be attained

Even measuring H and He at 10- 2 to H- 1 atom/cm 3 will require a con­

by 2000.

siderable development effort.

Included in the effort should be:

Means of collecting incoming gas over a substantial

a) Collection:

frontal area and possibly of storing it to increase the input rate

and so the S/N ratio during each period of analysis.

b)

Source:

Development of ionization sources of high efficiency

and satisfying the other requirements.

c)

Lifetime:

Attaining a 50-year lifetime will be a major problem,

especially for the source.

d)

S/N:

Attaining a satisfactory S/N ratio will be a difficult

problem in design of the whole instrument.

Thus, if a mass spectrometer suitable for the mission is to be provided,

considerable advanced development work-will be needed.

Camera Field of View vs. Resolution

Stellar parallax measurements present a problem in camera design because

of the limited number of pixels/frame in conventional and planned spacecraft

cameras.

For example, one would like to utilize the diffraction-limited reso­

lution of the objective.

For a 1-m objective, this is 0.'12.

To find the

center of the circle of confusion accurately, one would like about 6 measure­ ments across it, or, for a 1-m objective, a pizel size of about 0'02 or 0.1 vrad.

(Note that this also implies fine-pointing stability similar to that for earth­

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But according to James et al. (1976) the number of

year 2000 is 106

elements per frame expected in solid state cameras by the orbiting telescopes).

for a single chip and 107 for a mosaic.

With 107 elements, or 3000 x 3000,

the field of view for the case mentioned would be 30O0 x 0.02 = 1 minute of

arc.

At least five or six stars need to be in the field for a parallax

Thus, a density of 5 stars per square minute or 18,000 stars

measurement.

per square degree is needed.

To obtain this probably requires detecting

stars to about magnitude 26 near the galactic poles and to magnitude 23

near galactic latitude 45' .



This would be very difficult with a 1-m telescope.

A number of approaches could be considered, among them:

a)

Limit parallax observations to those portions of the sky having

high local stellar densities.

b)

Use film.

c)

Find and develop some other technique for providing for more

pixels per frame than CCD's and vidicons.

d) Sense the total irradiation over the field and develop a masking

technique to detect relative star positions.

An example would be

the method proposed for the Space Telescope Astrometric Multiplexing

Area Scanner (Wissinger and McCarthy, 1976).

e) Use individual highly accurate single-star sensors, like the Fine

Guiding Sensors to be used in Space Telescope astrometry (Wissinger,

1976).

Other possibilities doubtless exist.

A study will be needed to determine

which approaches are most promising and development effort may be needed to

bring them to the stage needed for project initiation.

The problems of imaging Pluto, it may be noted, are rather different than

those of star imagery.

For a fast flyby, the very low light intensity at Pluto

plus the high angular rate make a smear a problem.

Different optical trains

may be needed for stellar parallax, for which resolution must be emphasized,

and for Pluto flyby, for which image brightness will be critical.

Besides this,

image motion compensation may be necessary at Pluto; it may be possible to provide

this electronically with CCD's.

It is expected that these needs can be met by

the normal process of development between now and 1995.

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ACKNOWLEDGEMENT

Participants in

this study are listed in Appendix A, contributors to

the science objectives and requirements in Appendix B.

Brooks Morris supplied

valuable comments on quality assurance and reliability.

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REFERENCES

0

0

J. M. Ajello (1977), "An interpretation of Mariner 10 He (584 A) and H (1216 A)

interplanetary emission observations", submitted to Astrophysical Journal.

J. L. Bertaux and J. E. Blamont (1971), "Evidence for a source of an extra­ terrestrial hydrogen Lyman Alpha emission", Astron. and Astrophys., 11,

200-217.

R. W. Bussard (1960), "Galactic matter and interstellar flight", Astronautica

Acta, 6, 179-194.

G. Chapline (1976), "Antimatter breeders?", Preprint UCRL-78319, Lawrence

Livermore Laboratory, Livermore, CA.

H. J. Fahr, G. Lay, and C. Wulf-Mathies (1977), "Derivation of interstellar

hydrogen parameters from an EUV rocket observation", Preprint, COSPAR.

R. L. Forward (1962), "Pluto - the gateway to the stars", Missiles and

Rockets, 10, 26-28.

R. L. Forward (1975), "Advanced propulsion concepts study. Comparative

study of solar electric propulsion and laser electric propulsion",

Hughes Aircraft Co. D3020, Final Report to Jet Propulsion Laboratory,

JPL Contract 954085.

R. L. Forward (1976), "A programme for interstellar exploration", Jour.

British Interplanetary Society, 29, 611-632.

J. Freeman, F. Paresce, S. Bowyer, M. Lampton, R. Stern, and B. Margon

(1977), "The local interstellar helium density", Astrophys. Jour., 215,

L83-L86.

R. L. Garwin (1958), "Solar sailing - A practical method of propulsion

within the solar system", Jet Propulsion, 28, 188-190.

J. N. James, R. R. McDonald, A. R. Hibbs, W. M. Whitney, R. J. Mackin, Jr., A. J. Spear, D. F. Dipprey, H. P. Davis, L. D. Runkle, J. Maserjian,

R. A. Boundy, K. M. Dawson, N. R. Haynes, and D. W. Lewis (1976), A

Forecast of Space Technology 1980-2000. SP-387, NASA, Washington, D.C.

Also, Outlook for Space 1980-2000. A Forecast of Space Technology, JPL

Doc. 1060-42.

J. W. Layland (1970), JPL Space Programs Summary 37-64, II, 41.

W. C. Lindsey (1972), Synchronization Systems in Communication and Control,

Prentice-Hall, Englewood Cliffs, N. J.

E. F. Mallove, R. L. Forward, and Z. Paprotney (1977), "Bibliography of

interstellar travel and communication - April 1977 update", Hughes

Aircraft Co. Research Rt. 512, Malibu, California.

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A. R. Martin (1972), "Some limitations of the interstellar ramjet", Space­ flight, 14, 21-25.

A. R. Martin (1973), "Magnetic intake limitations on interstellar ramjets", Astronautics Acta, 18, 1-10. G. Marx (1966), "Interstellar vehicle propelled by terrestrial laser beam",

Nature, 211, 22-23.

P. F. Massier (1977a), "Basic research in advanced energy processes", in

JPL Publ. 77-5, 56-57.

P. F. Massier (1977b), "Matter-Antimatter", Symposium on New Horizons in

Propulsion, JPL, Pasadena, California.

W. E. Moeckel (1972), "Propulsion by impinging laser beams", Jour. Space­ craft and Rockets, 9, 942-944.

D. L. Morgan, Jr. (1975), "Rocket thrust from antimatter-matter annihila­ tion. A preliminary study", Contractor report CC-571769 to JPL.

D. L. Morgan (1976), "Coupling of annihilation energy to a high momentum

exhaust in a matter-antimatter annihilation rocket", Contractor report

to JPL, P.O. JS-651111.

D. D. Papailiou, E. J. Roschke, A. A. Vetter, J. S. Zmuidzinas, T. M.

Hsieh, and D. F. Dipprey (1975), "Frontiers in propulsion research:

Laser, matter-antimatter, excited helium, energy exchange, thermo­ nuclear fusion", JPL Tech. Memo. 33-722.

R. H. Parker, J. M. Ajello, A. Bratenahl, D. R. Clay and B. Tsurutani

(1973), "A study of the compatibility of science instruments with the

Solar Electric Propulsion Space Vehicle", JPL Technical Memo. 33-641.

E. V. Pawlik and W. M. Phillips (1977), "A'nuclear electric propulsion

vehicle for planetary exploration", Jour. Spacecraft and Rockets, 14,

518-525.

P. D. Potter, M. S. Shumate, C. T. Stelzried; and W. H. Wells (1969), "A

study of weather-dependent data links for deep-space applications",

JPL Tech. Report 32-1392.

J. D. G. Rather, G. W. Zeiders, and R. K. Vogelsang (1976), Laser Driven

Light Sails -- An Examination of the Possibilities for Interstellar

Probes and Other Missions, W. J. Schafer Associates Rpt. WJSA-76-26

to JPL, JPL P.D. EF-644778, Redondo Beach, CA.

J. M. Sellen, Jr. (1973), "Electric propulsion interactive effects with

spacecraft.science payloads", AIAA Paper 73-559.

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A. B. Sergeyevsky (1971), "Early solar system escape missions - An epilogue

to the grand tours", AAS Preprint 71-383. Presented to AAS/AIAA Astro­ dynamics Specialist Conference.

D. F. Spencer and L. D. Jaffe (1962), "Feasibility of interstellar travel",

Astronautica Acta, 9, 49-58.

J. W. Stearns (1977), "Nuclear electric power systems: Mission applications

and technology comparisons", JPL Document 760-176 (internal document).

G. E. Thomas and R. F. Krassna (1974), "OGO-5 measurements of the Lyman

Alpha sky background in 1970 and 1971", Astron. and Astrophysics, 30,

223-232.

G. E. Thomas (1978), "The interstellar wind and its influence on the

interplanetary environment", accepted for publication, Annual Reviews

of Earth and Planetary Science.

A. J. Viterbi (1967), "Error bounds for convolutional codes and an asymp­ totically optimum decoding algorithm", IEEE Transactions on Information

Theory, IT-3, 260.

C. S. Weller and R. R. Meier (1974), "Observations of helium in the inter­ planetary/interstellar wind: The solar-wake effect", Astrophysical

Jour., 193, 471-476.

A. B. Wissinger (1976), "Space Telescope. Phase B Definition Study. Final

Report", Vol II-B, "Optical Telescope Assembly, Part 4, Fine Guidance

Sensor", Perkin Elmer Corp. Report ER-315 to NASA Marshall Space Flight

Center.

A. B. Wissinger and D. J. McCarthy (1976), "Space Telescope Phase B Defini­ tion Study. Final Report", Vol. II-A, "Science Instruments. Astrometer",

Perkin Elmer Corp. Report ER-320(A) to NASA Marshall Space Flight Center.

J. M. Wozencraft, and I. M. Jacobs (1965), Principles Engineering, Wiley, New York.

74

of Communication

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APPENDIX A

STUDY PARTICIPANTS

Participants in this study and their technical areas were as follows:

Systems

Paul Weissman

Harry N. Norton

Space Sciences

Leonard D. Jaffe (Study Leader)

Telecommunications

Richard Lipes

Control & Energy Conversion

Jack W. Stearns

Dennis Fitzgerald

William C. Estabrook

Applied Mechanics

Leonard D. Stimpson

Joseph C. Lewis

Robert A. Boundy

Charles H. Savage

Information Systems

Charles V. Ivie

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APPENDIX B

SCIENCE CONTRIBUTORS

The following individuals contributed to the formulation of scientific

objectives, requirements and instrument needs during the course of this

study:

Jay Bergstrahl

Robert Carlson

Marshall Cohen (Caltech)

Richard W. Davies

Frank Estabrook

Fraser P. Fanale

Bruce A. Goldberg

Richard M. Goldstein

Samuel Gulkis

John Huchra (SAO)

Wesley Huntress, Jr.

Charles V. Ivie

Allan Jacobson

Leonard D. Jaffe

Walter Jaffe (NRAO)

Torrence V. Johnson

Thomas B. H. Kuiper

Raymond A. Lyttleton (Cambridge University)

Robert J. Mackin

Michael C. Malin

Dennis L. Matson

William G. Melbourne

Albert E. Metzger

Alan Moffett (Caltech)

Marcia M. Neugebauer

Ray L. Newburn

Richard H. Parker

Roger J. Phillips

Guenter Riegler

R. Stephen Saunders

Edward J. Smith

Conway W. Snyder

Bruce Tsurutani

Glenn J. Veeder

Hugo Wahlquist

Paul R. Weissman

Jerome L. Wright

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APPENDIX C

THOUGHTS FOR A STAR MISSION STUDY

The primary problem in a mission to another star is still propulsion:

obtaining enough velocity to bring the mission duration down enough to be

of much interest.

The heliocentric escape velocity of about 100 km/s

believed feasible for a year 2000 launch, as described in this study, is

too low by two orders of magnitude.

PROPULSION

A most interesting approach, discussed recently in Papailou in James

et al. (1976) and by Morgan (1975, 1976) is an antimatter propulsion system.

The antimatter is solid (frozen antihydrogen), suspended electrostatically

or electromagnetically.

Antimatter is today produced in small quantities

in particle physics laboratories.

Chapline (1976) has suggested that much

larger quantities could be produced in fusion reactors utilizing heavy-ion

beams.

For spacecraft propulsion, antimatter-matter reactions have the great

advantage over fission and fusion that no critical mass, temperature, or reac­ tion containment time is required; the propellants react spontaneously. are "hypergolic").

(They

To store the antimatter (antihydrogen) it would be frozen

and suspended electrostatically or electromagnetically.

Attainable velocities

are estimated at least an order of magnitude greater than for fission NEP.

Spencer and Jaffe (1962) showed that multistage fission or fusion systems

can theoretically attain a good fraction of the speed of light.

To do this,

the products of the nuclear reaction should be used as the propellants and

the burnup fraction must be high.

The latter requirement may imply that

fuel reprocessing must be done aboard the vehicle.

The mass of fusion propulsion systems, according to James et al. (1976)

is expected to be much greater than that of fission systems.

As this study

shows, the spacecraft velocity attainable with fusion, for moderate payloads,

is likely to be only a little greater than for fission.

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CRYOGENIC SPACECRAFT

P. V. Mason (private communication, 1975) has discussed the advantages

for extraplanetary or interstellar flight of a cryogenic spacecraft.

The

following is extracted from his memorandum:

"If one is to justify the cost of providing a cryogenic environment, one

must perform a number of functions. The logical extension of this is to

do all functions cryogenically. Recently William Whitney suggested that an

ideal mission for such a spacecraft would be an ultraplanetary or interstellar

voyager. Since the background of space is at about 3 Kelvin, the spacecraft

would approach this temperature at great distances from the Sun using only

passive radiation (this assumes that heat sources aboard are kept at a very

low level). Therefore, I suggest that we make the most optimistic assumptions

about low temperature phenomena in the year 2000, and try to come up with a

spacecraft which will be far out in design, as well as in mission. Make

the following assumptions:

1. The mission objective will be to make measurements in ultraplanetary

space for a period of 10 years.

2. The spacecraft can be kept at a temperature not greater than 20 Kelvin

merely by passive radiation.

3. Superconductors with critical temperatures above 20 Kelvin will be

available. All known superconducting phenomena will be exhibited

by these superconductors (e.g., persistent current, Josephson effect,

quantization of flux, etc.).

4. All functions aboard the spacecraft are to be performed at 20 Kelvin or

below.

I have been able to think of the following functions:

I. SENSING

A. Magnetic Field

Magnetic fields in interstellar space are estimated to be about

10-6 Gauss. The Josephson-Junction magnetometer will be ideal for

measuring the absolute value and fluctuations in this field.

B. High Energy Particles

Superconducting thin films have been used as alpha-particle detectors.

We assume that by 2000 A.D. superconducting devices will be able to

measure a wide variety of energetic particles. Superconducting magnets

will be used to analyze particle energies.

C. Microwave and Infrared Radiation

It is probable that by 2000 A.D. Josephson Junction detectors will

be superior to any other device in the microwave and infrared regions.

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II.

SPACECRAFT ANGULAR POSITION DETECTION

We will navigate by the visible radiation from the fixed stars, especially

our Sun. We assume that a useful optical sensor will be feasible using

superconductive phenomena. Alternatively, a Josephson Junction array of

narrow beam width, tuned to an Earth-based microwave beacon could provide

pointing information.

III. DATA PROCESSING AND OTHER ELECTRONICS

Josephson Junction computers are already being built. It takes very

little imagination to assume that all electronic and data processing,

sensor excitation and amplification and housekeeping functions aboard

our spacecraft will be done this way.

IV. DATA TRANSMISSION

Here we have to take a big leap. Josephson Junction devices can now

radiate about one-billionth of a watt each. Since we need at least

one watt to transmit data back to Earth, we must assume that we can form

an array of 10+9 elements which will radiate coherently. We will also

assume that these will be arranged to give a very narrow beam width.

Perhaps it could even be the same array used for pointing information,

operating in a time-shared mode.

V.

SPACECRAFT POINTING

We can carry no consumables to point the spacecraft--or can we? If we

can't, the only source of torque available is the interstellar magnetic

field. We will point the spacecraft by superconducting coils interacting

with the field. This means that all other field sources will have to be

shielded with superconducting shields.

It may be that the disturbance torques in interstellar space are so small

that a very modest ration of consumables would provide sufficient torque

for a reasonable lifetime, say 100 years.

Can anyone suggest a way of emitting equal numbers of positive and negative

charged jarticles at high speed, given that we are to consume little power,

-and are to operate under 20 Kelvin? These could be used for both attitude

control and propulsion.

VI.

POWER

We must have a watt to radiate back to Earth. All other functions can

9

be assumed to consume the same amount. Where are we to get our power

First try--we assume that we can store our energy in the magnetic field of

a superconducting coil. Fields of one mega-Gauss will certainly be feasible

by this time. Assuming a volume of one cubic meter, we can store 4 x 109 joules.

80

77-70

This will be enough for a lifetime of 60 years.

If this is unsatisfactory, the only alternate I can think of is a

Radio Isotope Thermal Generator. Unfortunately, this violates our

ground rule of no operation above 20 Kelvin and gives us thermal power

of 20 watts to radiate. If this is not to warm the rest of the space­ craft unduly, it will have to be placed at a distance of (TBD) meters

away. (No doubt we will allow it to unreel itself on a tape rule

extension after achieving our interstellar trajectory.) We will also

use panels of TBD square meters to radiate the power at a temperature

of TBD."

LOCATING PLANETS

ORBITING ANOTHER STAR

Probably the most important scientific objective for a mission to

another star here would be the discovery of planets orbiting it.

What

might we expect of a spacecraft under such circumstances?

1)

As soon as the vehicle is close enough to permit optical detection

techniques to function, a search must begin for planets.

Remember,

at this point we don't even know the orientation of the ecliptic planet

for the system in question.

The vehicle must search the region around

the primary for objects that

a)

exhibit large motion terms with respect to the background stars and

b)

have spectral properties that are characteristic of reflecting

bodies rather than self luminous ones. When one considers that

several thousand bright points (mostly background stars) will be

visable in the field of view and that at most only about a dozen of

these can be reasonably expected to be planets, the magnitude of

the problem becomes apparent.

Some means of keeping track of all these candidate planets or some

technique for comprehensive spectral analysis is in order.

Probably a

combination of these methods will prove to be the most effective.

Consider the following scenario.

When the vehicle is about 50 AU from

the star, a region of space about 10 or 15 AU in radius is observed. the radius referred to is centered at the target star.

Here

This corresponds

to a total field of interest that is about 10 to 15 degrees in solid angle.

Each point of light (star, maybe planet) must be investigated by spectro­ graphic analysis and the positions of each candidate object recorded for future

use.

As the vehicle plunges deeper into the system, parallax produced by its

81

77-70

own motion and motion of the planets in their orbits will change their

apparent position relative to the background stars.

By an iterative

process, this technique should locate several of the planets in the

system.

Once their positions are known then the onboard computer must compute the

orbital parameters for the objects that have been located.

This will result

in, among other things, the identification of the ecliptic plane.

This plane

can now be searched for additional planets.

Now that we know where all of the planets in the system may be found, a

gross assumption, we can settle down to a search for bodies that might harbor

life.

If we know the total thermal output of the star, and for Barnard we do, we

can compute the range of distances where black body equilibrium temperature

ranges between 00 C and 1000C.

This is where the search for life begins.

If one or more of our planets falls between these boundaries of fire and

ice, we might expect the vehicle to compute a trajectory that would permit

either a flyby or even an orbital encounter with the planet.

Beyond obser­

vation of the planet from this orbit, anything that can be discussed from this

point on moves rapidly out of the range of science and into science fiction and

as such is outside the scope of this report.

82

77-70

APPENDIX D

SOLAR SYSTEM BALLISTIC ESCAPE TRAJECTORIES

The listings which follow give distance (RAD) in astronomical

units and velocity (VEL) in km/s for ballistic escape trajectories

with perihelia (Q) of 0.1, 0.3, 0.5, 1.0, 2.0, and 5.2 AU, and hyper­ bolic excess velocities (V) and 60. km/s.

For each V

of 0., 1., 5., 10., 20., 30., 40., 50.,

output is given at 0.2 year intervals for

time (T) less than 10 years after perihelion, and one year intervals

for time between 10 and 60 years after perihelion.

For higher V

and long times, the distance (RAD) can be scaled as

proportional to V. and the velocity VEL V.

83

PRW**

nATr 03in77

V-TNFINITY T - YRS .00 .20 On0

.60 .80 1.00 1.2n 1.40 1.60 1.80 2.00 2.20

2.4o 2.60 2.80 3.00 3.20 3.4n 3.60

3.80

O 4.

0O

4.00 4.20 4.40 4.60 4.80 5.00 9.20 5.40 9.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.2o 7.40

7.60 7.80 8.00 8.20 8.40 A.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00

nA*1

I

.0 KM/S

0 PAD

.1 AU VEL

.1000

131.201A 31.1952 P.9552 24.s0P9 3.0016 21.3290 4.7466 19.3330 55233 17.Q9p0 6.2496 16.64q3 6.q365 19.9032 7.5914 19.2879 8.P19% 14.60P2 A.A?47 14.1794 9.4100 11.7313 q077q 13.3349 11.5302 P.9805 11.0684 I.6609 11.5940 IP.3706 12.1081 lP.1092 12.6115

11.861t

13.1052 13.5898 14.0660 14.5343 14.9952 15.4492 15.8967 16.3380 16.7734 17.2033 17.6279 18.0475 18.4623 18.8725 19.2784 1Q.6800 20.0776 20.4713 2n.1612 21.2476 21.6305 22.0101 22.3664 22.7596 23.1298 23.4971 23.8615 24.2232 24.5822 24.9386 25.2925 25.6440 25.9931

11.6355 11.4262 11.2311 11.0487 10.6776 in.7165 10.5646 In.4210 10.284B 10.1555 10.0329 q.9192 q.8031 q.6060 q.5934

1.8279

q.4Q50

Q.4009 9.3007 .2223 Q.1380 Q.0968 .9784 8.96P6 8.8203 A.7583 8l.6898 A.6230 R.5584 8.4957 8.4347 8.3755 8.3179 8.2619

0 = PAD .30on 1.6741 2.7133V' 3.7226 4.563 5.3381 6.06p7 6.7483 7.14021 8.0294 8.6330

.3 AU VEL 76.q041 3p9*,5;q

n = PAn

.rnl0n

21.819 1Q.7172 18.2312

.'7Ap ?.F,1*4 3.9666 4.306 9.166

I7.1n71

.8Q

P.21*84

.5 AI VFL

D = 1.0 Slt QAn VFL %1.710n

P.0nn p.Ifls

po.7aI47 PA.41I

q.pnn 5.9n2

P6.q07

P.6410

95r.Qn05

PP.3n 314 PO.OnI1 1A.';77

!93*23A14 Pn.Ag°n 10.IA66

3.P1 .A466 4.u7jn

.45 P1.476M 10.0149

9.11=1 tfl.9'06 ;.QitS;u I 1o.fl'p j,&l40 1 '.'.7

C.P71n

1."nfl

17.3 06P

r9A16

-. 0P39)

16.4104 1R.6718 1S.9041 4.4AR1 14.012 11.r031 13.2191 1p.8P27 I2. 77P 1p.20A6

17.02RA

6.19

6.1qn4 6.P31? 7.448P A.04o A.6214 01896 C.79POt 10.6P4 70.7835 1102n16

18.66"

i,.orn7 16.1161 19.411J4 14.PR17 14.496 iI.OflnO 3.n3 13.14A7 12.A971 .saol

17.6115 16.7019 16.m067 15.44An 14.Onsq

I'.l"q

-.70n 6.P'Q~P 6.A7o 7.414r 7.QAls A.928 n*O n' Q.9660 jo.n7po n.1;6a6

6." 6.71A 7.nI 7.141 7.7067 A.670 A.tW4'; P.Opal q.'l10

I. 9; 1.

jt.n9i

12.Ar67P

P9.q1?;

12.417q

I1.9912

Ip.p30a

11.7pP9 11.5nf7 11.3oqr 11.1234 10.01488

IP.01449

11.7019

12.7P30 13.P07A 11.6A34 14.1!1 14.6115 1.065 1f 1-.51]20 IS.cq2q 1(.3A79 16.8175 17.9*17

11.8116 11.50f 11.3871 11.107; 11.0199 1.sR3 I0.68g i.51*6n I0.4051 1n.2714 10.144? Io.O3 0.0079 Q.7Q07 Q.6015 q.9qq

ip.pe';s

Ip:P.A4f 13.7n1 141.1637 14.6196 19.0612 19.q007 19.0144 16.3627 16.7850 h7.O41 tt.6176 18.0266 In.411 1A.17

19.0fllP 11.743 11.57AC5 137Al l1.l9P3 1l1.07Q

13.S717 14.3308 14.8006 15.2544 15.7017 16.1420 16.q782 17.o8n 17.432' 17.852n

18.2667 IR.676A 1q.n829 19.4841 19.0816 20.P752

jo.7847 10.6300 In.4A38 10.3492

1n.2137 10OS5 Q.603 0,995

17.66in

j9.7657 tV.p3o2

12.nfn

14.0nnI 13.61Al I.P71q lp,.o; A

o,70 n~nnflf

19.4n1

ln.fAn-

19.1

1n.n7nn

iA.'tA6

g.pi7fl %.1lt7

jC.npq3 I(.9t; .tamn1 n j~fl0.nm7f j.8n~f) j,."3 '.0Ann 1S'''1 9.7750

0.0pq Q.81114 0.7nf

17.00rP

q."06

16.16r9

n.6nQ

If.38n3

1q.6210

0.';n3

1A.7777

0.8*po o.7lnr

16.Pf t6..ao0

nA f.*ao6

q.30Q3

20.0100

0.163 1Q.5461 1o.093 P0.1014 20.674' 21,0441 21.4114 21.77r.7 PP.137' P2.496e 22.AS?'A 23.P064 23.t570 P3,9fl7fl 24,253A

17.1>477

In.I14

20.359

0.41r4 0.3270 Q,*4np Q. I7A 0.17779 Q.0nnn RA.Q91I AR.599 8.7893 R.7141 81.61*8 8.583q .P16 R.4611 8.40P2

06991

q.292p

q.5p7r 0.4164 Q.34146 0.?6A30 .Ini 0.1030 0.0966 R.029r 8.R888 8.8113 A.7430 A.6784 8.614 8.30

17.6041* 17.0-Af 18.'112 18.6616 lo.nnn 1Q.3'56$ 10.7000o 9fl.nl44 Pa. APl1 po p 71.090A pj.1qf 2I.MP'4 , P2.0680

iA.lnp2 o.nfol,

C.74A7 0.6499 0.94P6

100021

a.44F

6.4027

p.3946

1Q.6807 2n.031

1n.P953

q.3p

20.6651

0.269q

P0.47PO

21.0514 21.434P 21.013A 22.1900 22.563P 22.9333 23.3005 23.6649 24.0269 2'4.385c; 24.74lq 25.0957 25.4471 25.7962

q.1s05 0.00 2 q.0167 8.9e.1Q 8.8676 A.7958 9.7P62 A.6588 A.5934 A.599 8.4692 8.4083 8.3500 8.2934

2n.Aon 21.6911 21.907'5 22.3703 2P.7403 P3.I074 2.4717 P3.833P 24.1021 24.9484 24.90n2 25.2934 25.6024

1.i371

14.47q

1A.l,17 1P.,,n3

Ip.473A11.96 Ij,> iP.311 11.7135 19.Af7n 117.9144 1?.nl'" 131.A7R 11.3p76 1patO 14.966A 11.1';19lp.nnp6 14.7001 In.Qn6 13i.a" 1.128 1n.89QA 1-.q6t t!.';t in.6Q1 1i.n 9. ij.0607 i.uaO 14.'lj 1 .. 38v1 i0.46' 1±.AQ1A 16.7Q,9 I.9790 1s;.n!Rfs 17.1Q?7 1f.1q'2 '.4398 17.rqAl i.fl0q 15.ann1

IA.n075 1q.4094 1 .Rl0

21.P417

5.2 AU vrl

u9.1"i

0.7860 1.337A 10.1757 11.4010 11.014A

3.3998

A Ar)

1.r6'; ?.""1l 3.P87t9 4.077A 4.8107

A.7P3 7.P94fl 7.A45 P.q2A .n6p Q.6n95 10.i153 In.6900 It21" 11.7'R3

12.0114

.O All 1 EL

i.nnno

ro.r-Qfi 33.98po

I6.214R 1).4821 14t.8651 14.3399 1I.871 11.4650 1.1.nO7 19.7726 IP.47q lP.?ol0

0.2186

0 PAM

30 W.O.8A 8.9p1o 8.On9 A.8331 8.7626 8.6043 .6PA3 A.q630 8.0n1 8.4400 8.3A20 8.3247

20.777; 21.1569 21. 5In 21.004p 22.9737 22.64113 23.0040 23.3650 21;7P34 *4.0791 24.U326 24.7A35 25.1320

j0n.fl37

111.609 In.';9l 1inA.1Al 1P.27n0

In.1';3 0.3lq4

11 I'9r

11>01109 . ji.flq I.'7', r'.6n C 1 1.'vAq !leg" 1'. 118 lo.q0A3

O.8l' .l."I9 jn.9nAq "f.41A5

0.8ij

0.'Cfl7 0.6fnq 074f

0.U4'0 o.btnA9 0.1"A ',s0e 'o.In7 O.InA5 Q.,f 4 A.462

PRW**

nAT! 0I3077

V-INFINITY

T - YRS

:

't

0

0 = RAD 25.Q931 27.7048 29.3653 30,Q803

14.00

32.9544

18.00 19.00

34.0914 35.5946 37.0667 38.5103 39.q274 41.3199 42.6892 44.0370 45.3645 46.6730 47.9633 49.2366

.1 AU VEL

25.796P 27.5077 29.16R1 30.7820 3P.3568 33.8937 35.3g68 36.8680 38.3124 3q.7294 41.1?17 42.4911 43.8388 45.166 46.474*7 47.7690 4q.38? 50.?99 3 51.r36S 52.7637 53.Q766 55.1761 56.1627 57.9371 58.6996 59.8508 60.q9ll 6P.1209 63.0409 64.1504 69.4508 66.9421 67.6245 68.6984 69.7640 70.A216 71.8713 72.Q135 73.9483 74.9760 75.P966 77.0105 78.017A 79.0187 80.0133 81.0017 81.84P 82.0609 83.q318 84.9972 85.8572

51.7353

2c)O0

52.9622

5.7880

30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00 34.00 40.00 41.00 42.00 43.00 44.00 45.00 46.00 47.00 48.00 49.00 50.00 51.00 52.00 53.00 54.00 55.00 56.0n 57.00 58.00 59.00 60.00

54.1751 59.3746 56.5613 57.7357 58.8983 60.0495 61.1898 62.3196 63.4393 64.5491 65.6496 66.7409 67.A233 68.8973 6q.9629 71.0204 72.0702 73.1124 74.1472 75.1749 76.1956 77.2095 78.2168 79.2177 80.2123 81.2007 82.1832 83.1599 84.1309 85.0963 86,0562

9.7p2a 9.6605 5.6008 5.5435 5.48A8 5.4397 5.3848 5.3398 5.28A5 r.2428 5.1987 5.1560 5.1147 5.0747 5.0359 4.9982 4.9617 4.9262 4.8917 4.8582 4.8255 4.7937 4.7628 4.73P6 4.7031 4.6744 4.6464 4.6190 4.5923 4.5662 4.5406

50.4937

G = RAD

8.2619 AoOn26 7.7730 7.5677 7.3825, 7.2142 7.0602 6.9186 6.7877 6.6661 6.5528 6.446Q 6.3475 6.2519 6.1696 6.0821 6.0029 9.9277 5.8962

20.00 21.00 22.00 23.00 24.00 25.00 26.00 27.00 28.00

2

.0 KM/s

10.00 11.00 12.00 13.00 15.00 16.00 17.00

PArF

.3 AU VEL

8.2q34

q = PArl

.9 AU VEL

(4 PAn

25.6024 P7.3139 PP.Q?36 30.5ARt 10.1619 31.6989 39.2 4 36.6733

8.3P47 A.0qq7 7.8p54 7.6161 7.4P74 7?261 7.0oq9 6.9556

PS.1120 p6.A41P IA4QQ7 10.11pq 11.6893 33.P2n9

6.805P 6.69P7

38.1166

6.5686

4n.QP96 49*q4A 41.6425 411.960Q 4A.PA1 47.9684s 4A.AR19 90.0OA4 91.314a qP.9A6A 53.77q6 91.0790 56.1656 57.1 QQ 9n.5,03 5q.6935 60.7q37 61.q959 63 .0431 64.1929 65.2q3? 66.344q 67.4269 6A.9o0 60.5661 70.6238 7t.6736 7P.7157 73.7905 74.77R1 7q.7087 76.8126 77.81Qq 78.8P07 79.8153 80.8037 81.7A62 SP.7628 S3.7137 84.6092 85.6590

6.8p2A 6.6n09 6,SP.3 6.4769 6.3761 6.2813 6.2I1 A.n73 6.0P72 r.~Q.l 9.8787 9.8007 9;.749 5.60nA0 9.69n r.5626 ;.5n71 9.4c37 9.4023 *.392A 9.3052 9.2990 9.2144 9.1714 9.IpW7 5.0893 5.0902 9.0122 4*q.54 4.9396 4.9049 4.8710 408381 4.8N61 4.774q 4.7449 4.7148 4.6P85 4.6977 4.6'01 4.6032 4.5760 4.591P

37.6364 ".09P9 40.4441 41.8I17 43.1 "R 44.4R66 49.7n44 47.n842 48.3970 4q.6139 5O.P947 92.fl 11 S3.?Q36 r4.4 Q7 59.6740 96'A.30 98.019p 90.1661 60.3061 61.4356 69.9590 63.6646 64.7648 69.8958 66.0381 68.0118 6Q.0771 70.1345 71.I41 72.P?61 71.2607 74.8RP 79.30N7 76.32P4 77.3209 78*.303 7q.3P47 80.3130 qt1.qS4 82.7tq 93.2427 A4.0080 85.1678

8.0312 1.79q3 7.9o20

7.4no0

7.2352 7.07qQ A.937j

6.4619 6.1618 6.2676 6.1797 6.0947 6.0191 ,0304 9.8674 9.79A8 r,.7V3 9.6706 9.6206 5.5531 9.4q7 9.4447 9.3Q36 9.3443 9.296A r.2509 5.2066 9.1617 9.122 r.O8O 9.0430 9.0052 4.9686 4.932q 4.8983 4.8646 4.A318 4.790q 4.768 4.735 4.700 4.6802 4.6520 4.6246 £.5077 4.5715 4.'5499

3q9.9134

3T.7P22

36.103Q

1=. AU VEL

8.4022 8.2303 7,Rqnp 7.67I 7.4A31l 7.3Al 7.14A3 7,0019 6A.660 6.74n4 6.6P14 ,.St4j r0,419' 6.4116 631C3 6.PP49 6. I;6 6.0r73 RO l 9.9q67 *.83A7

'.7e6q r.706t *.6490 5.90A64 9.532 9.4761 5.424 r.1740 9,3p7 9.97Pj 9.P141 9.1oo 9.14R4 9.2n76 9.06A1 ;*nn7 4.QQ?5 4.Q963 4.021P 4.8871 4.8R548 4.8219 467Q00 4*71O3

4*7PO4 4.7n02 4.6717 4.643q 4.6167 4.9Q02 4.643

0 = P.0 All PAD VEL

n = 9.2 AU PAn Vr I

24.P51P pq.q5j 27.A06 pq.P14* 3fl.7M 9 3P.31PO 33.pl9 3.P77q

R.5930 A.P67Q A.0169 7.70,1 7.9021t 7.4101 7.P441 7.ft018

Pp.n6n p3.6031 Psi IPAAA P6,4A PR.'6'11 2q.p6n0 31.'p' 32.7603

m.6f.p

36.7171

6.Ql4 6.*214 6.7009 6.5o76 6.4818 A.3n2r A.IQAO 6.Pn09 6.1169 A.i7r r.qAp1 9.*ofl s.Ra>17 S.796P 5.6nl3 r.635 9.9790 .9on0 9.4671 r.4161 9i.ls66, 5.110 o 5.2730 5.ppA9 5.19i9 9.143% 9.In35 5.n644 9.;064 4.qQ98 4.qWi7 4.0lg 4.8R91 4.A891 4.*800 4.7A88 4.793 4.7*06 4.6q6 4.61'3 4.6437 4.61A7 4.50l3

34.17n 19.96nn 36.0*6, 3.1712P

'.'97 '.0636 A.01 7 *l

3O.nin

s.eo'q

4n.Q0l7 -4p.101i 41.t690 44.729 45.0641 47, 3I 4A.4046 4q.6007 r n' 91.0671 r9.13nA 94.*R' r5.4246 9.9s96 57.676R 9A.7817 q.A8Q9 60.09p* 6p.n661 63.1419 64.2086 69.>617 66.X1P 67.1697 6A.000 69.4p" 7n..494 71.e60 7P.4747 7A.477P 74.4711 7r.463 76.44'3 77.4P9 7R*39fnl 7q.164.0 80j32I4 81.2826

6.CnAI 9.1147 6.900 6o.*n6 6.O19 o.i 17 A.nr43 .qpr6 913

3A.Iln4 Q0.910o 4P.?01 41q94n 44A.6n7 6.124r6 47.4q17 48.67a6 4q0141 t.133q

S.As0 93.94RI 54.7134 q5.qn6e 9r7.0674 9A.P173 5q.3561 60.484Q 61.6014 Ap. 7 1pi 61.8115 64.OIA 6.q39 67.0562 6P.l0O 6q.1776 70.P2e9 71.P67q 72.3fll 73.3288 74.34A8 79.3620 76.3686 77.3688 78.162A 79.3906 80.133 81.3n6 P2.P7q0 38143 84.2033

*.At36 P.Wi 0*ItQQ '.ftqA 7.7fA4 7.5001 '.303

s.Rfq1

p.77 8 0 .i1 .6c79 .6n1 ',.t44 q,4fl97 9.44l0 C* fn3q g.'a6 9.Im0q .*r67 ,'i'q C.1794 9. A* C*.10 3 1 g.0 9 9, .n 04 4.qnA6 4.047A b.014n 6A*810 a.014q O.0176 U.707(0 .Tg72 .7'R2 O.6098 4.671

-

PRW**

n rlp njiN77 V-INFINITY :

T - YRS ,00 .20 .4 0

q = PAD .1000 1.8283 2.056;)

-1 AU VEL

0 = PAD

.3 AU VEL

0 = P~n

111.2090 11.1677 24,51119

,30nn 1 .674 ' 2.784R

76,9tn3 "9661 2-;.263

. , nnn 1.. ;,7 P.6439

.5 Alt VFL_

n = t.n Alf PAn VFL

n = 2,0 All! PAn Vrl

A = SP Atl mAr) Vrl

90.577A 1.902A P9.QO6P

J~nnoln 1.96in 2.41IP

up.11AR 13.7p n P6.0712

P~nnnn 2.11 61 2,64rp

PO.Anic PA .cn6P Pr.01Al

t;,prnn S.pa PI " .Tlnrt

lAar4PI

4.APIA

lompnliq

4.u7AA

1q.*.>o

r,.?m A711

11 16.IIQA Io

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11.2236

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4P.4176 NI.047P

13.7334 1'.4323 13.1r09 12.9108 12.6R28 I.47P6 IP.2780 12.0)71 11.02A4

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27.658A 29.6187 31.5343 33.4104

q.441A Q.243 9.0147 n.8377

14.00

35.4493

8.6632

35.0527

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19.00

37.2600 39.0423

17.00 18.00

40.7989 42.5318

A.5216 8.3931 8.2797 8.1680

37.0633

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40.6020 42.334A

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20.00 21.00 2,.200 23.00 24.00

45.9341 47.6066 49.2616 50.Q00 52.5242

7.9766 7.8911 7.8113 7.7368 7.6668

45.7370 47.4q094 49.0644 50.703P 52.326Q

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25.00

54.1337

7.6010

53.9363

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91.7414

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26.00

55.7297

7.5390

55.5322

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7.4250 7.3725 7.32P6 7.2751 7.2298 7.1866 7.1454 7.1059q 7.0681 7.0319 6.9970 6.9636 6.9314 6.9004 6.8706 6.8418 6.8I40 6.7872 6.7613 6.736a 6.7119 6.6884 6.6696 6.6435 6.6221 6.6012 6.5810 6.5614 6.5423 6.5P37 6.5056 6.4880 6.4709

58.6868 60.046A 61.796Q 63.3350 64.864P 66.3841 67.8951 69.1977 70.8g21 72.3787 73.8578 75.3298 76.7944 7A.2533 7Q.7053 81.151P 82.9911 84.025P 89.4538 86.R77 88.2951 89.7081 91.1163 92.5107 93.9189 95.312q 96.7030 98.0880 9Q.4707 100.1485 102.2224 103.59P7 104.0592

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9A.0149 iq.,i744 61.P133 62.661q 64.10n7 65.7103 67.2210 68.7233 70.174 71.7n03 73.1R7 74.6544 76.110 77.9774 7q.flP Ag.474q 81.q146 83.3486 84.7770 6.ao0 R7.6179 R9.008 o0.4988 ql.R4PO q3.P407 Q4.6190 q6.024q 97.4107 qR.7923 100.700 n.543* 1oP.9140 104.28n4

28.00 29.00 30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.OC 38.00 39.00 40.00 41.00 42.00 43.00 44.00 .4500 46.00 47.00 48.00 49.0O 50.00 51.00 52.00 53.00 54.00 59.00 56.00 57.00 58.00 59.00 60.00

6

5.0 KM/S

V-INFINITY T - YRS

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9pen307 4n.15

8.90n4

4P.4AA

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44.175 4.98491 47.497l 4q.I335 S0.79,47

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57.1064 98.6647 6n.t1 p 61.74q6 61.077N 64.799 66.30ss 67.R06A

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133.5761

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6.0618 '.a46

P6.'7AS 9.4t04

27.nQ44 9.16±1

P7.A009 f.n5AJA

28.1231 29.7706

2p.RSSR P.7963

pq.147fi lp.An1s

P.*5 9.Aa1

V-INFINITY =

T - YRS

la b.

o

%

Q = RAD

.1 AU VEL

G = RAI)

.3 AU VEL

0 = PAD

.5 At VFL

0 = 10 RU VFL RAD

1P.4pn 1109.6 IP.1IIR 11.9q66 11.88RR 11.7928 11.706q 11.6p93 ti.5990 11.404R 11.4361 ii.3R'o 11.3,Nt 11.28%q 0 11 11.?030 11.1696

3P.507 3lQq 17.671q '0.P11 42.7p79 4.?P2 47.6089 90.1580 52.6n17 %.f 1 97.448P 59.833 6.P2475 64.631 67.0067 69.37?9 71.7111

1P.4131 lPP698 12.128' 1p.0O51 11.8064 11.7097 11.7131 11.6,5% 11.964P 11.4096 11.4409 11.3A61 11.1ra

11f.V96 11.1998 11.1626

32.693P 39.0918 37.859P 40.39q3 42.q157 45.4108 47.8070 50.3463 52.7901 55.2198 57.6368 60.042n 62.4364 64.R?0' 67.1957 69.5621 71.9201

11o168

lpn67A 14,6644 37. 0'O 39.7687 42.P83n 44.777s 47.Pr3n 4q.7113 5P.1943 4.' 31 56.QOq6 59.4nP 61.7qAO 64.181A 66.9=6 68.0 p2 71.PI1

74.46559

11.1277

74.P710

il.1lfl5

74.0817

11.1;3,1

71.6103

28.00

76.0ql

11.0950

76.6146

1i.0O77

76.4P9P

11.103

7q.q7l6

29.00

79.1461

11.0642

11.0667

81.4767 83.8014 86.1205 88.4343

11.0352 11.0078

7R.7A2 81.nq?6

11.n69P 1l.0'9q

78,3101

30.00 31.00 32.00 33.00

78.Q519l 81.0821

A1.4171 A9.7163 S8.Oro0

11.0121

A0.6404 AP.0648

10n.961

R5.PA6

10.9573

83.606A 85.925A 88.0396

34.00

90.7430

10.9340

90.5483

35.00 36.00 37.00 38.00 39.00 40.00 41.00 42.00 43.00 44.00 45.00 46.00

93.0470 95.3464 97.6415 99.324 102.2194 104.5027 106.7823 I0Q.0584 111.3313 113.6009 115.8676 115.131?

I0.9118 10.8908 10.8707 10.8515 10.8332 10.8156 10.7Q89 10.7899 10.7674 10.7526 10.7384 10.7?47

92.P523 95.1516 97.4467 99.7376 102.0246 104.3078 106.5874 108.9636 111.1364 113.4060 115.6726 117.9361

47.0o

120.3921

10.7116

48.00 4q.00 50.00 51.00 52.00 53.00 54.00 55.00 56.00

122.6502 124.9057 1?7.1587 129.4093 131.6579 133.9034 136.1471 138.3887 140.6282

10.6989 10.6867 10.6749 10.6635 10.6525 10.6419 10.6316 10.6217 10.61P1

57.00 58.00

142.8658 145.1014

10.602 10.5q38

5q.00

147.3351

60,00

140.9670

12.4077 IP.p474 2P.10A9 11.9878 11.8810 1.7P58 11.7005 11.6235 11.5936 I1.48qq 11.4315 11.3778 11.3PS2

24.00 25.00 26.00

27.00

23.00

C C

10.0 KM/S

32.8864 3t4n5P 38.f527 40.5930 43.1094 4r.6047 48.0810 50.9403 52.9842 55.4140 57.8311 60.2363 62.6307 65.0151 67.3901 6q.7565 72.114

10.00 11.00 12.00 13.00 1M.00 15.00 16.00 17.00 18.00 19.00 20.00 21.00 22.00

a

OArr

OATw 01307'

PRW**

11.2B?3

1P.p2q8 11.0463

11.61

*Q.AR3 lp3,IQ7A '4."'If 37.91R iq.Aq06 42.19 R 44.ROO 47.n311 49.a56

79.1941

77.4898

ii.fnn9

7*.45'-7

7a1qn 82.14p't A4.460 p6.77PO

j .nls' 11.*27' 1i.fl.n3 I0q'4q

31.pg26 JARAfn A6.44o 3A.083I 41.4941 43.ql44 46.4561 4A.0116 51.390 y.77 r6.1q9 7 CfR,9qq 6f.o0Q71 F 63.A6 04 6.742p 6.fl6A 70.463'

l1.791 i1.4r5

7P.PI23

I1.9613

87.9q71

11.0179 in.9o11 in.9661

p0.3987

Io.9'79

pq.on9R

t.q4?3

89.0l0q

io.9ro7

q9.6p6 Q4.9619 97.?96Q 4q.9479 101.8148 104.1179 106.l975 10R.67A6 110.9464 11N.216n 119.4R26 117.7463

10.q199 10.804P .10.A740 10.8 46 10.816P 10.8185 I1.8n17 I1.7P-S 10.7700 10.7q91 1n.740o in.7?70

qp.PfQ2 04.5084 96.P0n3 q.0nq9q 101.3R07 103.6637 109.Q43P 108.Pi91 110.4qt1 112.7613 11i.0277 117.?q13

n.QIA ln.,RQA I.P779 10.85 4 in.slOR In.PPf2 In.R050 nI.7F7 1f.7713 in.717Rn lfl74'6 1n.?p97

q1.38'9 93.61' aq.076 9.661 loo.99p2 I0l.A346 105.135 101.NR88 no.e61n 11.3nn 114.1990 116.4900

120.1971

10.71P7

lP0.0071

I0.7138

119.920

10.7164

118.710'

122.4551 124.7108 126.9637 129.2141 131.462r 133.7084 135.P521 138.1937 14n0.433P

10.7000 10.6877 10.67"Q ln.6645 10.6935 10.64P8 ln.63?5 10.6226 1.619

1P.2652 124.9P06 326.7736 1P9.024! 131.2723 113.518P 155.7619 138.034 14n.P4P9

I1.flAnq 10.7010 IP4.0693 10.6P87 10.6760 1P6.3182 10.6654 '128.9686 130.8166 10.6944 In.6437 133.0624 10.6334 11.1060 117.9479 10.6P34 in.6137 139.786

i .7039 I.6912 0.67Q2 10.6677 10.6qA6 In.6458 i0.61q l0.6P94 In.S17

1po.076A P1i3.317 lpSt.449 1p7.7349 2PO.QRln I32.PP7 134.4706 116.7117 138.Q9nA

1n.QP77 I0.9nq 10.891 .R.i I.A464 l0o894 10.8111 in.7n4 ln.77PS I0.7634 In.7ua8 lo.74A I 0.7 9 10.70? 10.6097

142.6707

10.6036 if.9945

14.4A04 144.7160

10.6063 io.9071

141.180 143.4P3

10.5e09

1o.585

146.94q97

jO,98A3

14;.669

10.5769

149.3720

I0.977?

14q.1916

10.6044 1n.R3S 10.9A6S l0.9rO

14P.P44

144,9061 147.1400

10.97n7

147.A888

144.29~9 146.4q9,

148.7P93

1%.An01 10.4941 22.tA7 I.tIR4 1p.n09 l.n.'02 jl.ft00q 11.7196 I1.rq96 6 AW.4 II j1.10I9 %4.601 11.4909 6.A47A 1 1.0043 Ro.n2 1l.ArN4 41.09R7 1."'o6l 61.971 11.', 6.11"' 11.1i 6°4 74

lP.0174 10. lip l9.tflf ip.062p 11.04AP 1t.8464 11.79t 11.677 11.006 p.5 I 11.47n06 11.414n 11.10 l1!.I6 1l.pisq 11.097, 1i.lnq4 li.1i,0 11.117)

10.4611 2.pO7 I.114 P.0pr6 II.Q147 11.8162 11.7PA 11.64A7 11.9767 1j. jI.1II 11.4911 11.3A09 1l.14 1j°PQ*0 11.?42P 1.115 11.17'9 i1.1"99 11.1065

11.0376 11.0101 In.9840 ij.9593 10.939Q 1n.9137 10.8Q09 10.87P3 10.8r91 10.8347 In.8171 10.W3 10.7A4? 10.7687 1o.753a 10.7396 10.7259

10.9819

r.2 AU VFI

n RAn

G = F.0 Atl VFP PAD

7n.7Q79 71.l

n3

il.1n31 1.1413

11.11'6

l.fnfl 7 7 .717fl 99 1.099 ef.0 l1.nl9I np.nAo O.0959 84.71A? 0.0703 A7.MIOM fn.nfl*A3 8q.3lp2 n.0'6 r ql.,O1 M. n .*AOit I f.oqh 4 q6.702 nQA6'7 98.60n7 Ifl.0u40 100.71n7 nI"1. j. l1 .0o*2847 jO.R08 jO.7n04 107.9910 In.7776 1nq.A1AP in.7t4 11.nn, l.7479 114.' 4n'

116.9Q7P

i0.711Q

1l.6710 in.66n7 0,640A 1o.613o In.6oil n.6103

1A1M? A 1pI.l0,% *193°'31 0.A03 l 97.f4qA 130.0 ..RPI 13?.3P29 134,9670; lIA.Anl

1n.7'n9 l0.'n 5 In.6o"O n.Anin In.6714 106f n.61.03 j.6fA tn.oon7

ln.6no'

13c.r.VnV

In.696

i0.6n05 1l1.1>" l0.9016 1413 0!4 .fln13 4.739 Io.9pn9

ln.619 I.60n4 jO.np

I

PRW**

DA'P 0130l77 V-INFINITY =

T - YRS :00 .20 :40 .60

0 = PAD

I Au VEL

.1000 1. 005 3.3546 4.575q

114.6943 15.9357 30.4778 PA.0667

5.7225 6.8217

0 = PAD

.3 AU VEL

= vAn

70.461q 36.8R97 3n.0006

p6.6467 P9.6922

4.4004 S.5592q 6.6499

20.3263 26.8242 p2.8230

7.8875

24.9n89

7.7137

8.9283

94.4688

8.7534

Q.a497

p4.04A3

jo0.q554

797495

21.4200 23.1780 pP.97o0

13.7241

21.0061

2.60 2.80 3.00 3.20

11.9481 12.929Q 13.q023 14.8667 15.24n 16.7751 17.7207

9.7730 10.7780 11.7710 12.7921

25.180W 24.54CA P4.114q

pP.7R01 22.6302 22.4s03 P2.3634

14.6883 19.645 16.596P 17.9419

22.82n9 ?P.6qA4 2P.5146 PP.363

Q.6196 10.6931 11.5141 IP.5044 13.9696 14.5PA l.4A3 16.4156 17.3P04

3.40

18.6612

22.2503

PP.2711

3.60

jQ.5973

22.1480

3.80

20.5293

22.05I

18.481A 19.4177 2004q90

4.00

21.4576

P1.9701

21.P776

4.20

22.3825

pt.9?

22.2024

4.4o 4.6o 4.80 9.00 5.20 5.40 5.60 5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40 7.60 7.80 8.00 A.20 8.40 8.60 8.80 9.00 9.20 9,40 9.60

23.3043

21.8205 p1.7542 21.6928 p1.6357 71.5824 21.9326 21.4860 21.4422 21.4o10 21.3621 21.3254 21.2907 P1.2579 21.2267 21.1970

1.00 1.20 1.40 1.60 1.80 2.00 P.20 2.40

10.00

q

20.0 KM/s

.30(0 1.8471 3.1945

.0

nArr

24.2231

25.1393 26.0531 26.9645 27.8737 28.7810 29.6863 30.5899 31.4918 32.3921 33.290Q 34.1883 35.0844 35.9791 36.8727 37.7651 38.6564 39.5467 40.4359 41.3242 42.2116 43.0981 43.9837 44.8685 45.7526 46.6359 47.5185 4.90 48.4003

21.16A8 pl.1419 P1.1163 21.0ooa 21.0684 P1.0460 P1.0246 21.0040 ?O.QS43 20.9653 PO.9471 20.9295 20.9126 20.8964

Onn 1.7ROA 9.fl7?P 4.273Q -;.410r 6.51i24

.5 Atl VFL 6P.8A7P 17.q?61 11.265P PS.Sns .qn07 pq.q"06

0 = 1.0 All RAI VFL t0nno 1.7614 p.0177 40nq7p q. 1'07 603rno

0 = 2.0 Al VA iAn

hA,.6pe 1.7g06 P2.O363 P7.274)

n = 5.2 AU nAn vri

2.0Nnn PT.q1"0 3.ItR

A.A7AA

c.pnnn

3(4.02,00 1340n

'%,)

11.177

l,9A'7

p.0in p'.11n4 pA.In',

4*,lr0 ;. oll6 6.0211

P9.A.3A P7.4116 P6.3t540

#.o00o9 6.r6'A 7.'*l

pA.177 pcqA pt r.10',4

26.1A77 p5.171

7*01

7.n" qu

pb.*ni4

P4.77p9

7.Qqpl

24.966

A.A7r

91.5n06

94.3nn

A.Q763

24.U471

0.11665

pl2,AA

0.047A jn.lp'

P4001

I.98PI

ol.fA1 23.6C61

np

21.4fl7 p3.P2P6

IA F lp.2pn

2'.'nA4

1.6AAU 14.A5l

pI.M143 99.0ftg

71.0110 p2.2968

7.p774j 8.30q q.3143 10.311p 11.0067 IP.7P

p3.01n

tI.Pfoo

PI1.Of6 l

p.A2 c

P:.8*Qo 2P.6A04 PP.gT37f P2.4072

I4.Inno '19. 913 t6.In13 17.043o

99.0117 pp.7Aq vp.9PS7710 P2.45pp

13.771n 14.71;A 15. o 16.8s6n

pp."nA9 PP.0164

18.3n3

2p.2oo1

lq.pqrA

22!.843

pp.flo 22216

17.5164

22.1669

17.0Rjp 10,0155 "

PP.nTP7

P20.IP73

pp.02

21.1151

Pn.?Al

PP.117A3

10.011

P9.6ouo

Ptj*4or

p1.2062

pl.

P4

20.'110

23.124n

2P.A00

PP.O06 pI.fl 04 2.8O66 "

np.lpn pp.0lp2

10.3670

P1.9A6n 21.0q06Q P1.8341

IO'.S4 4 20.771A

2P.3no pP22.275 pp.172p

22.615n

"1. .1

6

P.21A

:1.0136

1>1goo

24.0427

21.7660

?39.704

t1.7714

P3.r%34

2p,.At'

21.70145 21.6466 21.9Q27 21.5423 P1.4050 21.407 21.4090 21.3697 21.3327 21.2q76 21.2644 22.232q 21.2029 21.1744 21.1473 21.1P14 21.0Q67 21.0731 21.0505 21.0p89 21.OO8 20.9882 20.96q] 20.9508 20.331 20.9161 20.8997

2'.705 P.7187 P6.610R P7.5pAS 28.4357 q.13n0 30.P4P 31.11t4 32.n460 52.9'146 31.R1A 14.7177 35.6p3 36.9057 37.4i0

P1.7191 21.6q67 21.6021 p2.5;11 21.5034 P1.4q86 21.416S 21.3768 21.3191 21.3n30 21.2704 71.018 21.2n8 21.1706 P1.1922 21.1261 21.1p 21.0774 PI.09;47 21.0120 P1.0120 p2.9Olq lPA.Q727 pl.-q4p 2f.ql64 8.9tp 20.9027

24.471 Pq.lq97 26.2700 27.17pt pA.n044 28.qAS7 2Q.q14 31$TQps 31.6Q'n 3P. qOn 31.4f67 34.'AP1 .'2P76P 36.1602 17.06j1 37;0918 1P.841R 30.733 40.6181 41.sflO 4P.300 41.2763 44.1607 45.fl444 45.P73 4A.80o5 47.6910

23.03q0 p3.9450

Pt.Attn0

24.9580 25.8729 26.783A 27.6q2 O 28.6001 29.9054 30.408A 31.3107 32.2100 33.10q7 34.0070 34.9030 35.7977 36.691p 37.5836 38.4748 39.1691 40.2543 41.1425 42.0pq8 42.0163 43.801q 44.6867 45.5707 46.4540 47.3365 48.2184

P9.0036 2i.719R

2l.67A6 P1.6227 p .q704 91.9219 21.4797 91.43P6 p .c90 21.3530 P1.1176 P1.PA0" P1.2ifl P1.2202 21.1000 P1.1610 21.11AS

24.854A p5.761' 26.,666 A 9 p7.q nl pR.471A p0.371

P1.7717 21.7114 21.6R34 P2.5004 P1.50p9 21.9njS P1.4971t

P.'6" 94*q9l l5.19i4 26.0101 P6.onq 27.'Rn6 P9.A60

p1.317qq 21.3386 PI.314 P1.27o0 I.PII PI.P2n6 21.1706 21.123 21.1963. 21.1 21.077 pl.0ql 21.033 PI.fllP4 PO.QQP4 P0.QVP pO.q47 20.0169 Pfl.9j98

lo."'P 31.X1I7 p*10 lp7qp 33.'S 34.34A js.713o 36. Q0A 37.U7fl8

21.7614

P1.4677 pl.21Q2

7.5636 .6O0q

P?.n30q

3P,9fl2o

3Q.Iq3 *10.nAA4 4n.4766 41.q630 42.7502 43.6358 44.N05 45.4044 46.2876 47.1701 48.0519

P5.I00Q 24.6P2Q 4.175P Pl.81P1

Pi.OjRn

P .npl 13.3361

],P

p1.111t p,1)RA6q P1.0637 21.n416

p1.023 1.no 2fl.Q804

p0616 pM.0439 P0.o262 P8.904

7

,

10.!43

38.270A

1.167p 3P2n63A 30.OAtf 93.Rqp 34.7441 19.6156 36.5p2q 37.411S 38.3033 30.10 ufl.n771 4n.q6pn 41.9476 42.7316 41.615n 44.4Q~7 45.3704 46.2607 47.141p

6

ll.

9.6574

21.0i

A

P1.4t1

tR.,pol

29O.Am

16.'ngp t.5161

p9.Mo5

17.18A 1A.069A t 1n.01n

P,'.U'' pp.AIf7 ;". ao 29.1939 pP.ni

s.55"

3p.340A

3Q.P2 40.102PA 4n.07o0 41*.A5 p7 f3o 43.60A1 44.1t9i1 4'S.3T54 46.204

l.oc7p. 01.,0*-t p1.0PAJ,

21.'3 0 P1.Amn p1.A'77 , .qos pl.gx73 pi1.tnl6 21.148

pt.dnn PI06 p4.3n3 p1.o>npq p1.9f62 p1.pqp .9n57 V1.1'75 2i.11)7 21.1R0 21.100 21.0,1 p1.n056 p9.0i3 p1.01p2 l.an096 pR"."'3 pf.alP 2f.075

0

PnW**

A1? 011077

In

PA9W

V-NFNTY = 20.0 KM/S

T - YRS

0 '

0

Q = RAD

.1 AU VEL

. 3AU VEL n.997

: RAn 46.0911

.5AU VEL PO.9027 20.8289

4R.2184

2

52.61A0 57.0036

20.8p59 20.7636

5P.4513 r6.366

61.3770

20.7101

l.nqR

Pf.765A 70.712n

?0.6619

65.7400

20.6637

69.~7pR

Pfl.6f654

20.6215 20.5858 pn.5541 20.5256

70.0940 74.4400 78.7790

20.6231 2n.5872 ?0.5R53

6q.qp66 74.27P5 7A.6113

p0.6246 20.5P88

P0.5268 2n.5010 20.4777 P0.4565 2n.41371 20.4103 pn.40 '9

R2.q43q

pn.5000 20.478 p0.4556 20.4363 p0.41A5 Pn.4022 p0.371 2n.3711 P0.3601 P(.3480 20.3366 2(.3260 p0.3161 20.3067 20.279 Pn.28Q9 ?Q.2817 2n.2742 P0.2672 20.2605

93.1116 87.4386 91.7604 96.n779 100.3904 104.6Q94 109.0048 113.3070 117.606n 121.Q02P 126.1958 130.486q 134.7797 139.0621 143.346q 147.6296 1sl.io5 156.1897 160.4673 164.7433 169.017q

?n.3737 20.36n6 20.34q85 2n.3371 20.3264 ?0.116' p0.3n71 20.2082 2n.2Aqq 20.2APn 20.2745 2n.2675 ?0.2607

97.P707 ql92.r.5 q9.qq9 I00.P224 104.5113 108.R367 11.1337 117.4574 912.733A 6.f79 130.318ti 134.6n73 1.930tARi 141.1789 147.4611 16 .74Pn 156.0211 160.Pq8' 164.5747 168.R492

10.00 11.00 12.01

48.4003

13.00

61.5593

p0.7612 20.7080

14.00

69.9224

15.00 16.00 17.00 18.00

70.2765 74.6226 78.9616

52.8001 57.1857

G = RAD

20.8964 Pn.8231

20.sq65 Pq.9M7 P0.9npo P0.4786 20.4R73 p.4378 P0.41CQQ 20.403q p0.3A83

0 = 1.0 AU VEL RA

0 = 2.0 AU VEL PAD

po.q0q4 pO.894P po.77fl6

47.1419 5t.63sp 5s.9q16q

Pn.qlqA P0.f42q pn.771

6.ppa 50.rql 5400

I.QA5 pn .A.zA3 pn.7*1q6

60.8460

p0.7162

60.0851

pn.'FY7

sq.0QA7

pn.vq165

65.2082

P0.66qn

64.644A

p.6748

63.A6n4

2A.68

69;9614 73.0068 78.PW.1

,n.epR pn.9q14 'n.qol

ia.aQ57

pn.expq

73.1331

pfl50qq

77.675f

P.5631

607.0794 7p.flO0 76.P0)

pn.lp >A.n43 pO.t6M'7

82.nn61 70.0;301 56.3311 9f.i0.I1 Qne.195j pn.4805 q4.06a7 pn.4qqo qq.p7p' pn.4104 fl3.50q ?0.4PI4 ,OS&0h8 '1O7.R9O2 11p.1fl1 Po.8q"5 116.4nn 90.1754 12n.7843 n.W36p ?n.3419 jp.n770 I2.167' pn,33S5

20.2748 2n.P677 20.2610

19.0 20.00 21.00 22.00 23.00 24.00 25.00 26.00 27.00 28.00 29.00 30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00

39.00

173.4742

20.2541

173.2911

P0.2943

173.1P?4

Pn.P46

40.00 41.00 424.00

177.7461 182.0168 186.2863

P0.2480 20.2422 20.2367

177.*6D 181.8337 186.1031

20.2493 2n.242S 2n.2360

177.3Q43 1P1.664Q 1P85 344

p0.pusra .pn.P4P7 20.2172

43.00

190.5546

20.2314

190.3714

20.2317

1Qo.P027

44.00 45.00

194.821g 199.0881

20.2264 20.2216

194.6387 1Q8.Q44

20.PP66 20.2218

46.0n 47.00

203.3533 207.6179

P0.2169 20.2125

203.1701 207.4343

48.00 49.00 50.00 51.00 52.00 53.00 54.O0 55.00 56.00 57.00 58.00 59.00 60.00

211.8809 216.1434 220.4050 224.6658 228.9258 P33,1851 237.4436 241.7015 ?49.9587 250.2152 254.4711 258.7264 262.9811

20.2083 ?0.2042 pn.2002 P0.1965 20.1928 20.1R93 ?0.1859 p.1827 pO.17q5 20.1765 20.1736 70.1707 20.1680

211.6977 215.9601 220.021A 224.4826 228.7426 233.0010 237.2604 241.6183 245.7754 250.0319 P94.2878 258.5431 262.7978

5.2 AU VrL

479 rl

20.2084 P0.2n43 20.2004 20.1966 20.1930 2o.1;q5 p.1P61 20.1828 2n.17)7 2n.1766 20.1717 20.1708 20.1681

221.580 215.7Q13 220.0520 224.3137 PP8.5737

20.2(86 20.Pn4 20.?06 p0.106A 2.1031

706.8q94 211.tr74 215.42Q 219.6814 223.Q421 2P8.P0(1

20.1806

235.4613

237.0015 ?41.3493 245.6069 P4Q.8630 ?94.1189 298.1742 262.6288

p0.186P 2(.1APQ P0.179A 20.1767 20.173A 2n.'t70Q p2.168P

236.7107 P40.q775 245. 346 P2q.4I t 253.7469 258.0022 262.2q6

P10.5686 P14.307 plq.0qpi 223.359A PP7.61P3 231.A714 P36.1297 40.387 P44.644* P24.qoq 23.156P 297.4111 961.66q57

Pn.?noq po.Pn4 20.01n4 20.1076 P0.lo3q pqj.o4 n.l 7fl p0.tA37 pn.inqo pn.t'74 pn.7?45 P0.1716 0.68A.

rq.'.O30

232.8"3

,o.?Oqn Pn.Pn4 On.pnn p0.1971 P0.1934 )n.jgQq 20.IRA 2f.1A"2 p0.ISn1 20.1770 pn.1740 0.1712 9.164

pn.9,W7 20.'fl6 Pn.nO ?0.1087 pfl.loOQ P2.n1 4 pfl.1i9 p0.I046 Pn.104 p0.17A3 pm.17r3 4 Pn.j9 9n.IA6

20.3877

2n.374?

20.5611 P0.34R80 p0.337% P0.P6q ?0.116A p0.374 Pn.PO86 20.P009

P0.2A23

213.6596 17.nI9 ?PP.1716 226.4301 ?3.6878 234.Q4A

P3q.OflIA 2'&.a'7n ?47.71P PSi.n6fA PS6"*pna P60.4741

*

fATP Olin0

PRW**

V-!NFINITY =

30.0 KM/S

4

T - YRS .00 .20 .40 .60

.80 1.00 1.20

11

nAr

PAD .1000

2.1796 3.8036 5.3147

1.40 1.6n

6.769q Ft. t00 9.9886 10.9694 IP.337P

1.8n 2.00

13,6947 19.043q

2.20

16.3862

2.40

2.60

.11U0 VEL 116.5378 41.40fl7 36.9657 35.1260 34.0803 31.4 19,1

. PAD

AU VFL

0 PAn .s;n 1*0734

.3nn0

AP.5491

2.0477 3.6966

4P.O?"3 37.2106

5.16P

39.2663 14l.1797

6S.6142 8.033 9.42P97 jO.AO04

3.rrp1 9.0l63 6.49?9 7.0070 O '3.3n17

5AU VFL

0=2.0 AU otn Vrr

0=1.0 AU pn VrL

66.607P

1flOnnn

4P.415f8 37.4090

r.ORq 3.4340

11.3770 14.Pr31'

4.P70n A.PunR9

7.6n73 qCln707

RI.7 IP a?.3It54

p.nnnn

UP.P244 Iin.flh6

C;onnn r.~n

Pa.pfn7

17.2A72

5.nPS3

All.AA13

4."n08 6.2117 7.r7l R.Q10A n.*40 1I.5R5A 1P.0170

At.vIpq 14.4107 II.6n I.159o 3P.7q'> 3P.4192 .4p.:n1

6.8A3 7..;61Rl R~n7 q.7flAn 1n.0ArC Ip.n1 13.P7'S

14.'4"A

.nnA 31.1844 31.7n2

15.7nn

I9.1506 3t1r57 3I.n16 I.A 91

17.n?

31.0n1I

p*rp 9 0Qr .6P

17.6 I.9e7Q 14'317q tI.62'n q3*00l7 3gp7f77 jp.4f76

1Sn.A77

12.176c

3P.6212 3P.3,;79

51 33.nr65 3P.Aq17

1P.0453

IP.3W0

10.4403 t1.8085

3p.1108 31.9p9P

3p.100 11.0021

13.1903 14.rni0

11.7534

16.224n

31.77n4

11.714A

5.A4n7

1.A1A

1

17.7226

51.6P46

17.9601

31.63.2

31.67M

16.8%9

133.5138

31.6 lq 31.53I72

17.1714

19.0541

18 .8QtA

1A3.4n1 14.74R 18.0oq 17.14P94

lp.1688

31.909P

13.9334 14.A821

2.80 3.00 3.2) 1.40 3.60 3.80 4.01

20.1813 21.7047 23.0247 24.341A 25.6563 26.q684 28.2783

31.4174 1.3328 31.257q 31.1912 31.1313 31.0772 31.0PA1

20.218P 21.9414

1.41PQ I1.3 11

R."150 1 q*pgqo P1.1469

qt;~7A I .iAp 1.367?p

PP.7P47

1.074P

9P.IA47

AI.2886

24.178P 29.49PS 26.8044 28.114P

31.2098 31.1t4st I.08ol 31.0390

4.20 4.40 4.6n 4.80

20.5863

30.9834

29.4221

P4.0411 25.355(1 26.667n P7.0766 2C.fA4P

3f.0033

pl.770Q Pq.fQ97 P6.4n3p P7.71y7 20.01854

30.A924

10.94P4 310.9048

'0.9001

3n.016

30.3P24

IA*0QO04

Mj.A041

A0.0133

5.00 5.20 5.40 5.60 5.80

34.8016 36.1019 37.4010 38.6900 3q.0959

30.83A0 30.80R2 10.78n5 30.7546 30.7305

30.7281 32.0326 3.3355 34.6370 35.0373 37.236' 38.534P 39.8311

11.71A8 Tj.1A, t1.rlA 31.nellqt I1.0n3 If.0R90

3n.8743 in.8419 n.A110 3.7835 30.7578 3n.7334

33.197t 34.4qA5 9.T7ff 37.n075 38.3q93 30.6920

3n.f770 3n.R493 30.pirn 3n.7A6p 10.760 30.7160

31.6,60 32.QP28 ;4.PPQ6 19.qPot

6.00 6.20

41.2919 42.9869

30.7078

30.6A69

41.127n 42.422n

30.71M06 3n.6802

40.0878 4P.PA27

6.40

43.R811

45.1744 46.4670

43.7161 45.0094

3n.6298

46.301Q 47.-937

3n.6600 3n.6500 30.63P0 3n.6150

41.9767

6.60

10.6669 30.64176

48.8848

0.lqRg

50.1751 51.465P 52.7544 54.0431 55.3313 56.619n

3n.5837 30.5692 3n.5994 3n.5423 3n.5pq8

32.197n 33.5000

12.9309

32.5844 3P.3081 'V.0867

i0.87n1

22.161P

331L47Q3

3?.qp~?

11.92A9 31.48r6 31.34?7 31.2668 3l.l0 t 31.13114 31.0836 1.0340

i0.pP8 30*9474

1A76 p0.nqp 21.4092

In.inoo 3.8080

i0.o676 In.6203

4?.m6ni 43.410 45.12".

3n.6040

4R.11P8

IO.?nOS

47.r887 1

In,.1IR

in.q5A5 fn.738 n.5 O 3n.54A4 3n.q337

40.401r *8.rA0Q to.077R 53.p69p 94.52P1

An.op7 3n.577 n.3c8,6 3n.55n '0.9373

4A.068n 9q*.4Q1 -I.q,;ni rp.Illn 94.0017

jm. n00 n.S00R 3n.m0q 3t'.qM$ 30.SulR

'n.5916 Tn.q1nn

99.8388

30,50s 30.i33

%6.9P6

3M.91C01

60.4791 61.764q 63.0504 64.3394

6n.388 61.6P46 62.OIOO 64.1q50

30.507A 31.4066 f.l.tA6t '0.4761 30.4664 30.4972

56.p033 97.4qnp 98.7766 60°0826 61.3UR2 6P.6334 63.Q1P

30.4462

65.6200

30.4471

65.4796

30.4483

30.4377

66.9043

30.4388

66.7639

30.I497

5q.3583

30.4q41

59.1q28

Q.00 9.20 9.40 9.60

60.6446 61.9304 63.2159 64.9009

30.4837 30.4737 3n.4642 30.4550

9.80

65.7856

10.00

67.0699

f.fl26

3rkan8 -j1 n.,;70 CD

4 1 .9 1 1

57.7660

8.80

-l

3n.6qnn 30.6811 '0.6496 n.8o99

5A.478

57.0061

l

I0.09

4P.09n7 44.?4pt 49.932 46.823n

30.5178 30.5064 30.4Q95 3n.4050 30.N4750 30.4654 30.4562

30.5163 30.5050

.,16 n1."73

*0.67R 3

qP.6149 93.0n31 99.1013

58.0715

v1.nAnQ

3n.6711

91.0 0A 5P.3307 53.A81 r4.016n

8.60

31.l7*07

3q000;1

3n.97n7 3n.r60 3n.5437 3n.9311

10.5537 3n.5406 3n.528

'0.77p8 3ff.747r

31.q6 14.0S'0 16.1400 17.a0qn 3A.1141

11.111A

30.7piq 'o.7o16

4A.4713 4q.7613

51.6304 52.9197 54.2084 55.4066 56.7843

O.Afn2 3n.Aon

3.9IIfnq

4f.3A9A ut.A5A6

A.6n6 3n.5891

7.60 7.80 R.O 8.20 8.40

n.804n

3Y.'Ill

in.7j77 30.609R

4A.7451 50.03n 52.393

90.5069 10.5818 30.5674

3p.r%0f7

Jj.fl9O0 lp.An

3I.Ian0

40.7162 4P.0107

n0.6R20

40.0500 50.340

3fl*03fl?

11." 3 ,isrl9A1 I1.if,7

A.7130 10.6014 In.6'3Q 10.616A

7.20 7.40

11.pQ1,q

1n.906 Pn.pnnnl 9P.07TA 23.471 74.AP4 i.nnoI 97.101' 01.461P 90.74 4

3.An02

30.7659 '0.7410

4A.16P4 47.4941

30.6129

I IP23j(,6F 31.9~1f n.q3n' 11.4777 Pf.449 31.3866 p 9 .15 6 c 11.3n6o 31.pI(7 P3.4669 p4.7749 11.1708 31.113' 26.n80 ;1.nr1n p7.'PRA pA.6RAO 11.0136 pqofQl7 f.07f l

4.5n1

3a. i 104 IN.Anu3 II.I'p 19.on7

38.1246 30.u2A0

36.AP74

44.A600

47.7589

in0A209 i0.Aqn

.7pn

*"~nA

33.A8qn 3s.1860 36.1$A84 37.7777 Ko.07p,

43.3043 44.9' 71 45;88P 47.10r,

6.80 7.00

o1.074n

5;.2 All Vr)

ovn

30.AqIA m0.ApII

flx7oo

In.e6q9

if.490f

97.0P47

3f.70o0

9.17*"

30.03*4

IV.AnM7 30."7 o qn.7quA 9f.mni

At.8A71

10..1103 36.4np .86

3f.

04

3 n.9q"5 30.nAp

;P.41n,

3f.90nl

57.0132

in.4AA4 3,.4712 n0.46R5 10.4liql

9q96q" 6n.q6n4 62.2640 63.4n

"Q.PtPf 6n.40p7 61.17P4 63.091Q

60.2 026

ft.4501

64.8 3 PA

30.UQ I0.R1I 30.47 30.4818 30.4-27

64.11I

1A.ne6p

66.4867

A0.4415

66.116P

I0.4440

65.616

3n.474

30.4n

3".11q8 n.41q 3n.4054

nATF 011077

PRW**

V-INFINITY =

T - YRS 10.00 11.0n 12.0n 13.00 14.00 15.00 16.00 17.00 18.00

1q.00

Un

20.00 21.00 22.00 23.00 24.00 25.-00 26.00 27.00 2.00 29.00 30.00 t.00 32.00 33.00 34.00 35.00

36.00 37.00

38.00 39.00 40.00 41.00 42.00 43.00 44.00 45.00 46.00 47.00 48.00 49.00 50.00 51.00 52.00 53.00 54.00 55.00 56.00 57.00 58.00 59.00 60.00

PArr

12

30.0 KM/S

0 = RAO 67.0699 73.41165 79997 86.298R 92.6965 99.0897 105.4788 1lL.864 11R.2468 124.6264 131.0035 137.3783 141.7510 150.1218 156.4908 162.A589 169.2241 175.9887 181 .Q519

.1 AU VEL 90.4377

30.39q7 30.3619 30.3407 10.3173 90.2970 30.2791 30.263? 30.24q0 30.2363 30.224q 30.2145

30.2050

289.c924 296.342? 302.6914 309.0403 315.3887 321.7367 328.0844

90.Iq63 n.1884 10.1811f 30.174 I0.167) 30.1621 30.1566 30.1515 30.1467 n0.1422 30.13n0 30.1340 A0.1303 30.1267 30.1234 3n.1202 3n.1172 30.1143 30.1116 30.1089 30.1065 30.1041 30.1018 30.09q6 30.0975 30.0q55 30.0q36 30.0918 30.0900

334.4317

30.0183

340.7786 347.1252 353.4714 350.8174 366.1630 372.5084 37A.8534 385.198?

30.0866 '0.0851 30.0815 30.0821 30.0807 30.0793 30.070 30.0767

18.3140

194.6750 P01.0349 p07.3939 P13.7518 220.1090 226.4654 232.8209 239.1758 245.5300 251.8835 259.2364 264.5886 270.q404 277.2916

283.642?

: RAD 66.90q3 73.320A 79.7300 86.132c 92.5306 98.9237 105.3128 111.6984 118.080 124.4604 130.8374 137.212P 143.594A 149.q556 156.3246 162.60,0 16n.057q 175.4224 181.7857 188.1477 194.q087 200.A0A6 207.2279 213.5855 219.0427 226.2990 232.6546 23q.00q4 245.3636 251.7171

?8.0700 264.4223 270.7740 277.12)2 283.4758 289.8260 296.1757 302.5290 308.873A 315.P223 321.9703 327.Q179 334.2652 340.6121 346.q07 353.3090 359.650q 365.9966 372.3419 378.6970 385.0318

.3 AU VEL

0 t RAn 66.763 73.1101

30.4398 30.406 I0.3696 30.3414 3n.317q 30.2Q79 30.27q5 30.2636 3O.244 3n.2367 3n.225' 30.2147

P5.Q0?O Q.1896 q.7826 10.1716 111.9971 117.qq4 124.3t10 130.6q5 137.0706

30.2oS2

143.41933

7c%.589A2

3.1066 149.9t40 156.lnpq 3N.A8n6 I0.lpp l 16.9sol 3n.1744 16P.Q16P l7q.P07 In.1681 181.6439 30.1622 1oAR.00Q 30.I68 194.3669 30.1516 9n.146Q Pn.7P67 207.0n57 n.1424 P13.437 3n.1381 Plq.Rfl0R I0.1341 30.1304 P26.1571 232.5127 '0.1268 30.1235 P19.8675 30.1P03 ?4'.P2?16 30.1172 P91.5751 257.0200 30.1144 3n.1116 264.2803 27n.692n 30,1fl0 7,6.q9j1 3n.1069 283.333R 30.1041 30.1flQ 28q.6840 30.oqo7 P6.ni37 30.0q76 IO.A829 30.0956 308.7328 30.0937 315.0o0P 30.0q18 321.42P 327.7'98 3n.0on 334.1231 In.O83 30.0867 940.4700 346.0166 30.0i51 30.0636 I91.162q 30.08219n5.l088 365.8R44 30.080' 3n.0793 372.lq*q 30.0790 37P.5448 984.0896 30.0767

vj AU VFL 3fl.419q7 I0.4014 I0.3,649 10.3410 30.3184 I0.27Q A0.27qQ 30.269q 30.P4o7 30.p?6Q n.?p254 90.2150 30.205t 30.1o67 3n.1887 I0.I124 I0.174A In.1682 '0.!624 'o.is6q 30.191A An.1470 In.145 0.j8 30.1'4P If0.13l 30.1260 in.1p2q 10.1203 I0.1173 30.1144 I0.1117 90.1OQI I0.1066 10.104P i0.jO11 9n30.097 90.0076 30.056 ln.037 30.Ooq In.0c0I 30.0084 10.0867 90.0851 30.0A36 n.0n21 An.OQn7 30.0719 90.0?70 10.0767

0 = 1I) RAD 66.4867 7?.Q0pp 7Q.1fl 85.7Pq q?.!100 qq.RnP6 104.913 111.2764 117.6585 12.0377 130.4145 116.7AQ0 1413.1614 14Q.5320 15%.a0A 16'.P2600 16A.637

I74.nn61 181.361P 1n7.7PI3 194nAICQ P00.4437 P06.806 213.16A5 219.5175 229.8738 ?P2'2PqI 28.840 P44.qI31

251*2n15 257.6443 263.Q965 P70.342 276,9Q03 PA3.04qq Po.40o01 P5.7407 3gp. qAa 308.4477 14.7961 3P1.1441 397.4Q17 393*0'Aq 340.1~qR 946.324 352.8716 359.P49 36a.q7ni 371.I914 318.P604 384.609P

VFL

OAP All 0 = 2.n VEt PAn

*An

RU Vrl

Af.474 6R.A1nfA r.ft'n~q ?2.nou I".140 78.394130.'4A6 84. 7l Ift.N,*5 01.16r6 1.0,16 q7.-4A7 90.p29 103.0259 In.'#q 110.o16 3065 I. 1l6.A 7' 30,211 n9Ifl*9' 3n.pipp 1'3.nQ' 30.96 190.4191 n.2566 30.91l 135,70 in.2160 3n.*07 1'J°.l5l An.o64 %n.lnA4 14.F10A 10.1n76 in.n10n 14.A4P 'An. In06 Ift~ 0S I0.102I1l6l.P4'fl 0* ?nt0 167.An0" n.l'r3 3n. 6"5 179.n7np o.16Wn 30.1635 l8N.'301 30,1630 30.1~0 1A6.A0n 3n.1q74 7 30n'.hI A l'qj.n4 9n.19p3 it 0. 17q 'n.1475 Ia."10i 1fh414 I 2n.76n 0.1*p 9n.I"1 0 9n.liP7 P12.lA0 3fl.13 n.1146 Pla.A709 90. P4.21 30.tinq 225.4810 n. '6 1; P11.1706 90.1573 I3IR36' In.lo4p P37.5315 90.'l39 P38.1008 nn. sl0 P3.D030 'n.ln7 P44.S446 q 30.1t' P2O.5'q6 3n.1176 P0.8q7A in.110 ?56.986R I0.1147 257.2504 30.1153 90.1120 p6p.037 P63.6P4 '.1o06 26Q.?9877 l0.1no3 PAQ.QF30 In.107i 97 5 .g975 un.tceR 916.90n4 9n.l047 Pl.0A06 I 0.1044 P2A.655' 3n.tnI4 gAn.33R7 30.i021 PA8.0059 Nn.lfnp PQ4.6819l no.lno 9O5.394A 9f.nnnl 3010.n12P 90079l 301.7n3n Rnn6 9n.T7Q 9n.no5 908l.n5p5 98.nn t 913.7p79 3n.0a9 1j'.unon 38.0QP9 99fl*740 300.lot 3p0.74AA 3f.ntn 996.09n 3n.90n9 9P7.n96n n.nn7 992.7671 30.flAS f.00nA4 13.4439 90.n*71 9.mA6q A99.1131 I9Q.?7qQ 30.0A86 0n.nqRS i0.0n 3 3q4.490q 146.13611 m0.0852 q Ifn.el 351.A0ll9 n.nAA 90.037 91P.4PR 30,0095 'R8.140A 9n.0493 358g.289 0.009 A0.nflo 164.4Q41 90.00q In.0A08 165.173 370tIN 6 ift.0906 9fl.m7ns 971.5190 3fl.0704 Rf%.nR'i 177,1859 .f7pi l3?.77 jq639 '0.0789 30.n77(l '0.076Q 983,5jP 984.086 .90.07F Ift.44195 A,46q 'fl.'1fl 3l.l4fll 0 An.I1 3 9N.?qR7 'n.fnn6 30n.646 30.P03 in.PI75 30n22pq I0.' 54 A3oPn5q 30.1071 in.IACl In.1817 In.1748 ln.1695 in.1626 No.lq7' in0I,.f In.147' i n.14'7 'n, 0 13 4 in.1944 30.1306 3N.12P1 30.1297 i0.1905 90.1174 30.1146 30.1110 In.l0QP In.1067 3n.1043 i0.1000 In.OqR n.Oa7 in.nq07 '0.0q9' 90.0lq i0.0nP

66.1162 7?.9PRQ 78.cflSn X 89. ql.79l7 QoI.I 104.900Q 1j00939 117.0741 123.69PA 13fl.flR 116.4n5' 14p.7740 14Q.1410 isS.lPl i6i.87AA 16A.P441 174.'6nn 1Pn.q7n7 IP7.A3 10.6P7 P00.5pl 206,41n6 912.765 210.12c5

10.4140 mn.4nnn In.,%'pl '0.144q 3on.N7 Ifl.poo 30.Pq16

MATP 1111171

PRW**

0 RAD

.1 AU VEL

23.617P 25.3620 27.085 28.804 30.9230 3.P40n 33.09( 35.6693 37.3821

4n*9p79 40.8651

2.60

23.7822

2.80 3.00 3.2n 3.40 3.60

25.5072 27.2298 28.,502 30.668A 32.3898 34.1012 35.8151 37.5281 39.23Q8

40*0506 42.6603

40.53110 40.5169 40.4q68

4.00 4.20 4.40

4.60 4.80 5.00 5.20 5.40 5.60 5.80 6..0n 6.20 6.40 6.60 6.80 7.00

44.3692 46.0774 47.7847 49.4914 51.I75 5P.902q 54.6078 56.3121 58.0160 5.7194 61.4223

7.20

63.1240

7.40 7.60 7.80 8.00 8.20 8.40 8.60 8.80 9.00 9.20 9.40 9.60 9.80 10.00

64.8270 66.5288 68.2302 60.9312 71.6320 73,3324 75.0326 76.7324 78.4320 80.1314 81.8305 83.5293 85.2279 86.9264

VFL

40.8602 40.8064 40.7580 40.7167 40.6740 40.6452 40.6145 40.5867 40.5613

20.3234 22.nr44

41.1758 41.0768 40.9933

3.80

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40.9219

18.9886

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30.0937 40.A044 42.5141

44.223n 45.0310 47.6383 49.3450 9t.0510

52.7564 54.461P 56.1699 57.8603 50.5727 61.2756 62.0781 64.680P 66.1810 6.08.33 69.7844 71.4851 73.1859 74.8856 76.5859 78.2890 79.9844 81.6834 83.3823 85.0809 86.7793

43,430

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40.6u79 40.617n 4n.5S'9 41.5613 4n.9109

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37.2680

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40.61 0 40."007

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un.6194 on.9q3 an.967I on.9441

35,13Q7 v6.0441 1A(n0.9'1 40.P6n06 4J.0671

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40.2543 40.2318 40.2129 40.1969 40.1831 40.1711 40.1606 40.1513 40.1431 40.1357 40.1290 40.1229 40.1174 40.1124 40.1078 4n.1035 4n.0906 40.0959 40.M025

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3n.=119 9M.91V7 lp.Alft9 ;n.%nn 14.7171 nl.=qn2 301A."49 qnn3 3.0401 90.495 41,n ?n A.t4inA 4A,.lf,16F Ff*ftlf4 4R.P79A ;f.vnw4 47.IA64 mn,t'3n 40.1107r mnl. 5p Ro.aAAMIA0j fl.rgf6 9%"21' 9 a2 5Ffl3A5 qn.'iAA 57.04o1f ;nfl.nl3 6 0 0. n046

3.40 3.60 3.80 4.0f) 4.20 4.40 4.60 4.80 5.00 5.20

35.0651

37.1950 39.323

it

5n.704p

-

4,1706

90.4?

41 .in,11 47.4P6n 40.949c '1.67nq 93.'1 q5al3 9A S.n141 611.194A

50.nn0l gn.17p7

9.40

58.5753

90.3113 rn.3?Oo

r8.lq45

5.60

0.0ft3

60.6973

58.1006

Mft.no

i0.2q15

60.9690

90.2)21

60.4764

50.202q

60.3911

0.2l, 3

5.80

62.188

5n.21P6

62.44PI

9f0.2P3

64.71A9

c'l.P734

64.5631

n.P71t

6.20 6.40

67.0608 69.1812

50.2Ap2 5n.2730 51.2644 90.2963

62.078

64.0400

90.2816 50.27P5 50.2635 50.2558

62.6009

6.00

66. r'6 6A.q600

qn.2A47 50.2966

66.636 A An.n37

n.965 =0.PR72

6.60 6.80 7.00 7.20 7.40

71.3013 73.4211 75.5406 77.6599 79,7788

50.24A2 50.2411 50.2343 50.2279 90.2219

71.1720 73.2q27 75.4129 77.5314 79.650A

511.2497

rin.pilq

50.2347 50.2283 5f.2p23

71.0n00 73.1007 75.1lat 77.41 3 70.597P

on.040 =f.943 -n.9"q9 5O.Pol

70.79P6 7p.S714 7?.oRQO 77.1083

qf.2?25

70.0215 71.0431 75.16P3 77.PP13 7*40flO0

7.60

81.8975

50.2162

81.76911

50.216S

PI.$7Q

C0.21A

R1.9185

F2.2pl0 rn.P172

70.2?6U gl.'44'

7.80 8.00

84.0160 86.1343

50.2107 50.2056

83.8975 86.0057

50.2111 511.2059

83.704

c0.2113

8.20

88.2523

50.2006

88.123A

5f.2000

A9.0305

rn.2061 K0.2011

50.2117 n.?fl5

89.u690

P9.Q12*;

83.616rR RT.75,4q

87.87P7

qO.P015

8.40

90.3702

50.1a5q

8.60

90.2416

50.1962

92.487c

90.t1i5

Q00.2I4

50.1064

92.359P

8Q.qqP4

50.1ot7

OP.265q

;0.1c1

94.4767

50.11 4

94.3834

8.80

94.6053

50.172

64.8117

66.032u 69.0529

5n.2415

7

50.p2418 c0.25fn Rf.22R6

5.3n004

6p.P74T 64.011 66, n,

68.63q

5fn.36A 'n.398 Rn.316o

n.3n4 I;6n.Pi,4 no1

n.?Wot

q0.p-v90 9n.A7nlq 9n.>l

rn.66A01 5.A,,Al

6p.1791

5n.1006

9n.2-4

64A9.A'

'n5f.*Iqp

5.26rI Ifn.Pq78

A6.10", 68.r191

9.pns

o00.9t Cl.9sfl3

7n.Ap'27 7p.-301 74.qr'n

5n.P9n6 q"5.111

0.1420 Kn.p560 50.2006 r0.2,3

Fn.Pi76

76.oeD$,

50.91n snt.*n0

70.n80

5n.9I9

.1iOU4 83.nRnfl

5nA Pfl 100n.19

AR.57q6

Kno1p9 n.2n6q

A9.4918cP.

qnfl

s7.6Q6o

So.2Iq

A7.53K7

9n.0no3

50.I16

Rq.141

02.107q

n.17P

9.649

q0.1093

ot01311

80l.10 5

n.10P6

Ql.611

5fl.

'50.1876

04.22nP

Knf.ln7q

n4.n0480

R.1p03

q3,A771

10,10A6

9f.1our,

0

9.00

96.7226

50.1831

96.9941

50.1P33

(6.9f006

50.135

96.34P3

fO.IAIA

96.1647

'oI 44P

95*qonq

9.20

98.8397

90.1792

98.7111

9.40

50.17q4

100.0567

9A.6177

50.1754

50.176

09.45Q3

100.8210

t0.1797

If.17n9

100.7146

Q8.2"11

0.17158

q0.I102

100.5761

sn.1761

08.1046

90.1764

100.p1'

;A.177

9.60

103.0735

50.1718

102.9448

1 0 0 .3 47 7

50.1721

112.1514

50.1722

102,6928

9f0.17P5

102.5140

n.172P

9.80 10.00

102.313'

105.1902 107.3067

5A.11

50.1684 50.1651

105.0619 107.1780

50.1686 50.1653

104.9680 107.0845

50.1687 50.1694

104.8093 106.9257

90.1600 so.16q7

104.630P 106.7461

*0.1603 90.1699

1f4.b4g; 106.9504

qf.IKa6 If.1A62

;".Ifvs

0

9ATF 033077

PRW**

V-INFINITY = T - YRS

h. .

16

50.0 KM/S

Q = RAD

.1 AU VEL

0 = PAD

.3 AU VEL

ID.O0 11.00 12.00 13.00 14.00 15.00 16.00

107.3067 117.8874 128.4652 L39.0406 149.6140 160.1856 170.7556

90.1651 50.1503 q0.1379 50.1274 50.1184 90.1106 90.1038

107.17R 117.7586 128.3364 138.9117 149.4851 160.0566 170.6267

17.00

181.3243

90.0978

181.1954

18.00 19.00

191.8918 202.4583

191.7628 202.32Q9

20.00

213.0237

212.0947

5f.0833

21.00 22.00 23.00 24.00 29.00 26.00 27.00 28.00

221.4593 234.0231 244.586? 2S5.14A8 265.7104 27602717 286.8324 297.3n27

gn.07q3 9O.07q8 90.07'5 50o0095 50.0667 5n.064? 90.0618 90.056

5n.0576

307.0525

qn.0576

30.00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00 39.00 40.00

223.5883 234.1521 244.7152 ?55.?777 269.8395 P76.4008 286.9619 297.218 508.6816 318.6410 32q.20o0 339.7587 350.3170 360.8750 371.4327 381.c901 392.5472 403.1041 413.6607 424.2171

90.0924 50.0876 90.0832 r0.07Q3 50.0757 r0.0725 rs1.0695 90.0667 5fl.0642 50.0618 90.05Q6

50,1653 5n.1504 S0.1381 9n.1276 50.1186 5fl.1107 51.1039 sn.0o7n 500Q24 5f0R76

90.0557 9n.0539 q0.0922 50.0506 50.0401 50.0477 50.0464 990.0492 50.0440 90.0429 90.0418

41.00

434,7733

q0.0408

42.00 43.00 44.00 45.00 46.00 47.00 48.00 49.00 50.00 51.00 52.00 53.00 54.00 55.00 56.00 57.00 58.00 5).00 60.00

445.3293 455.8851 466.4406 476.9961 467.5513 4Q8.1063 508.6613 519.2160 5i29.7706 540.3251 550.8794 561.4336 571.9877 582.9416 593.0955 603.6492 614.P028 624.7563 635.3098

9n.0398 50.0389 50.0380 9n.0372 50.0364 90.0356 50.0349 90.0342 50.0335 50.0328 50.0322 50.0316 90.0310 rn.0304 50.029 50.02q4 50.028q 50.0284 50.0279

318.9119 329.0700 339.6296 350.187q 360.7498 371.3035 381.860q 392.4181 402.q74) 413.9316 424.0880 434.6441 445.2001 455.759q 466.3115 476.866) 487.4221 497.9772 508.5321 519.0868 529.6414 540.1959 550.7502 561.3044 571.8589 582.4124 592.0663 603.5200 614.0736 624.6271 635.1805

5g0l957 50.093q 50.0522 50.0596 5n.0492 5.07 6 50.0464 50.0492 50.044n0 5004 q 5.0a418 50.0408 50,l038 5,OAR9 50.0380 50.037? 90.0364 50.n056 50.01;49 5n.034P 5n.0335 90.03P8 90.0322 50.0316 50.0310 90.035 5n.0?p9 09.0?q4 50.0289 5n.024 50.0270

29.00

DArr

0 ± RAn

.5 AU VEL

rO0.26% 107.0n45 50.1506 117.6650 S.158P 128.2427 Sf.1P7S 13R.Rt0 50.1186 149.3911 s9.1108 150.0628 50.103Q 170.912A 50.8e70 181.0t14 5n.0029 141.6680 50.0877 PO0.P353 gflOfP3 21?.8007 9.0-q4 I PP3.3659 .079P 233.q2gO 0.fl7? P44.4021 S*n.rAqq Prt*.'cs. q0.0668 P69.6161 90.064P ?74.1779 0.f1618 P86.7982 5n.0q6 247.PO25 'n.fl76 t07.8RB 50.0 597 318.4177 90.0l q 3P2.9767 50.0522 x30.5353 q0.0907 390.fl36 90.049P 1%6n.6516 g0.0478 371.2003 50.0465 R1.7667 Sf.O0Sp 370PP38 51.044n 402.06 9n.042q 413.4173 90.041A 4P3.q37 50.408 434,5.4q 50.019R 445.1098 50.0980 459.6616 0.0980 466.2171 90.017P 476.7725 50.0364 87.327A 509(.056 447.8828 50.O340 50P.4377 50.0342 5g.qQ2p5 50.033-5i 9P?.5471 540.I015 S0.01PR 90.0322 R50.6r5P r0,0316 561.2100 50.0310 571.7641 50.0305 rA .9lA1 g0.olqQo 59P.8720 Rn.Oq4 6n0i.4Pqi 50,0280 613.979P 50OP4 64,.9p7 90.027Q 635.0861

0 = 1.0 AU VFL PAD 106.0q57 117.5058 IP8.08911 13.6982 14q.P312 159.An25 170*3723 10.0407 lq.9OA P22.0743 212.636

2P2.2040 P93.7677 ?44.1 07 P94.AQIn P69.4947 276.0150 286.5766 ?47.167 3l17.6q69 S1Al2558 3PR.814R 31q.37.4 34f.9316 360.48F6 371.047p 381.6049 q02.1616 402.7185 413.P79n 4p3.R1 434.I876 444.0435 495.4C)P 466.n'F34 476.6102 4A7.16'4 4q,7P04 508.2793 918.83n0 fi.3846 53q.q0 550.4933 r61.0479 571.6016 2,1555 0p.?flo S8.26in 6138166 6,4.9701 614.q239

0 = 2.0 All VFL PAD

gs.0QP6 sn.A77 FO.0R14 F.0l74 K0.f7RI r0.n726 50.nQ6 g0.0668 FO.64? rn.061q Rn5,0507

106,7461 17.2qo 1p7,qOn 13P 474C 149.n47n 19q.617qs 170,186$A 10.'54g 101.321P P01807n 212. 5gI Pi.n15" ,9*57Q9 244.1418 554.7090 96.P6s9 ?79.?6 PR6.9O66 P,6. 0 46,

rn.nrl76

n7.906i

rnfl69t7 SfllflA f.13I ;0.127 g1.Iflg qo.Ilq q0.1040 n.Iq08

9iR.n65t '2P.6P4n i5q.1Sp5 3q.74n6 f60.qA4 370.P 381.4111 lq1.07nn 40P.5P67 13.0890 4P3.A30n 434.1455 qN.°4fl8 444.7914 fnln09Q0 ) 455, 070 5;n.0 465.0628 sq.f3R3 476.417' f.n07P7 5n0.Oa4 4g6. 0nThP q0.nl~'6 407.5278 n.np6 fn.94q 5n.142 518.6373 ?O.tqiP s5lq3 qn.0i9g K9q.7469 n.n0pn 530O W0.R549 g50n.16 n.n2n r71.4n85 50.0309 581.q624 Kn .n2gQqp. AP ,03l6qR R),1PQ04 qo.nPq 613.6234 50.P24 624.176R 07q 694.73nP qn.n 50.n57 50.nn9q r(.nfln3 nn907 n.fln4 8.0479 n.0469 O.n459 qn.N440 5ffnlpq 50.04l18

n = S.2 AU Vri PAD

90 .nt6Aqlft6 ,rt 4 917.12T4 sn,1s10 P7.6046 Sl.1'AS nI.,1R0 11s8.e61 Sn.ItRg 14Po.2A7 n.1110 l5g.qQ17 16q.o5q 50.1nI4 lAn*." lOt 0.OfqRl gn.ip7 Iq0.nRp9 50.88A7A 201.A446

9fl1,;Ap .n,q71 50.1%88 gn.1oAp sf.!1i1 5n.1112 cfl.ln43 n gn. o0

5fn.nlo

qf.fA14

7IP.fl4

5n.n'q nf%.nn

K°.f70 g0.0'50 Ko.0"A '(.06A6 rn.n668 .fl64' qn.0A1Q sn.noQ7

pp.777 P13.pat 741.AAR 7 PS4.nu4A p6q.nnl 75.567' PR6.1Pra P06.AR'a'

°nf.n'6 sf.n'6A 9n.n'7 sr.ns$7 rn.nA6q qnlnu9 5n.nO gnoncnA

gn.fl77

3n7.0144

qnnR7 90.n0.n­

n.nq58 317.non O8.A5.7? 90fl4fl nA s(.0523 3llp.9 '4.4710 9(1.fMt5' 5(.0it4p 360.o207 .7 8.A '7 0.5 9 r0.0465 381.1414 1I.A0.S075 5l.f45 n.n441 U02."3'4 'i0n:,OQ 412,Pn0nl qnfl.4lq 4P9.646 OQ 50.04A18 43.Q 5e.fl0Qg 444.47-0 4gR.nmn 5n(.Oxq qn.nAt 465.caq4 U76.1'M6 0.07 5n.n64 46.Aq4i1 075A4n5 50.nx56 n°.fl'49 c7.nP n.O34P 91P.197n 50.n395 9PR.lln 50n.nxpQ 59.464q 90.0322 550.n187 5n.0316 q6n07l4 571.1PAn qn.OxAl1 ;R1.67n4 50.Minr 50.02OQ qOp. ,Ip 50n.nq4 6nP.7A1 5O.0Aq 61I.39i' 50.n094 6P3.8994 qon507Q 6340U 4q4

R".nsfnt go n"9 Onnrnfl7 0 g0*nn03 q sn.on'I

fn.niAg

on.nu53 qn.nil6 0,n0itl 5fnlnrlq 5n0,14nq

tfl*030 q 5n~nfO 5n.nl 50.0'2? sn.nje's 5fnln07

rn.n14q 50M.04P 50.n839 '3.n9 5n.n39 5n.n116 Fn.n 11 5n.nxnK sr'.n Q gn.09Q4 50.0n0q nn,f04 gn.non

PRW**

fl*'r 03W77 V-INFINITY =

T - YRS

o

0= RAn

.1AU VEL

8.3199 10.910( 13.4926 16.0656 18.6325

146.oQfo 64.7005 6P.5413 61.7524 61.340l 61.0860 60.9134 60.7884

1.60

21.1940

1.80 2.00 2.20

23.7538 26.3099

2.60 2.80 3.00 3.2n

.1000 3.0269 5.6979

q = RAr)

.3

AU VEL

n = PAn

.5 AU Vft.

n = 1.0 Atl PA) VFL

1.nonn

.300f 2.9354

07.54n7

5.5061

69.5863

8.110l 10.A043 13.3R4q 15.057P 18.5236

61.7714 61.3R'2 61.0047 60.q2'n5 60.7Q30

A.1477 lo.7177 1s.t3e1 1S.8872 jA.lrp7

64.004t pfln A,6124.63 24q76 A1.7P00 8.07o0 61.361 tO.Agqo %1.1flnn 1.502c 60.0op'g 15.7O014 0.7aA0 IP.I1r7

60.6q36

21.0895

6n.6072

Pjn130

6n.60q5

?r,.nnoo

6n.6103 60.5594

23.6441 26.1990

6n.6p?2 60.9617

PA.5710 P6.173

6n.6940 o.5r.W

64.8417

.rnnn 51 2.A~4

4.r4A

71.3o0q 04.486 APA17

0.nnnn 6A.anAn 3.13u1 F4.Pn R F,56o

S.Pnol 7.r Qt11171,

F9t,-no AI.o.4 61nnpQ 61.5RA7 Al.Aq0

6n.9168

5nptS A

i, 6 33.6604

An.31.1206 n-ins; 6n.t'95 -4, 7

An.4746 An.14'8

-tpo; 3.9 5R

An.q1 n AA0.471 An.-4,Ao

AOtq A1u1

6n.4n8

16.,un

An.flnAA

6fl1I 6n.°9? A.'370

3A.'611 41,I-Afln

An.,fnlp sMIn 71

60.5101 60.4688 60.4337

28.753f 31.305 33.8559

6n.510 60.47n,5 6n.413r

P.6n05 61.9131 11.93I6fl.4' 31.751iq A0.461

36.5150

6n.4036

36.4044

6n.4048

36.3031

6n.4nti f;

3Q.0628

60.3773

38.9521

60.3784

38.8780

61.370

38.76A7

Ae.'n?

41.6096

R8.66P4

6n.3543

41.407

60.3592

41.P4t5

6n.3590

414j31n

60n.'60

u1.pnrq 7

44.1554

60.3330

44.0445

61.3348

UI.Q0f

An.315A

43.q41U

A1."A62

46.7005

60.3158

46.580

6n.3165

4A.5151

60.3170

4fA.37qA7

6rfjl.1A

3.80 4.00

49.2448 51.7885

6n.2095 60.2848

49.133A 91.6774

60.3002 6n.2Rq4

'gf.nql 510An27

60.30A6 A6.2n8n

4RA04p3 51.4A94

4.20

54.3316

6n.2719

54.2204

60.27P1

911.11456

6n.272Z;

4.40

56.8742

59.4162 61.9579

56.762P 5P.3o5

6n.29q 6n.2408

56.6p8f 9inf °1.7719

611.2603

4.60 4.80

60.2594 60.24A3

5.00 5.20 5.40 5.60 5.8n 6.00

60.2P88 61 .22Nt 60.2121 60.207 60.1)77 60.IQ12 60.1851 60.1704

64.3R77 66.q0R2 6. 4 60 0 72.0092 74.9412 77.0885 79.627A 82.166q

e0.P2QP

6.40

64.4991 67.039q 69.r804 72.1206 74.6605 77.2001 70.7394 82.2784

6n.22n9 6n.Pi29 60.2050 6O.10O 6n.1915 60.1A54 6n.17q7

64.1126 66.A533 6303417 71.031R 74.4736 77.n31 70.5p4 n2.024

6.60

84.173

60.1741

84.7057

6n.1743

6.80 7.00 7.20 7.40 7.60 7.)30 8.00 8.20

87.3559 59.8Q43 92.4325 94.9706 97.500.4 100.0461 102.5837 105.1210

60.16q0 60.1643 60.1597 60.1559 60.1514 60.1476 60.1440 60.1405

87.2441 8.7827 92.3200 94.8580 97.096A 99.9344 102.4720 105.0091

6n.1692 6P.1645 6n.15sQ9 60.197 60.1516 60.1478 61.1441 6n.1406

8.40 8.60 8.80 9.00 9.20 9.40 9.60

107.6583 110.1954 112.7324 115.2692 117.8060 120.3426

60.1372 60.1340 60.1310 60.12R1 60.1254 60.1227

107.5466 110.0837 112.6206 115.1579 117.694P 120.2308

122.8791 125.4155 127,9518

60.1202 60.1178 60.1154

122.7673 125.3037 127.8400

61.8466

s.Pnrn

P3.4654 9A.nn8 28.97n0

28.A637 31.4157 33.9660

60.2382

6p.ov7q

5.p fU VVl

PAMn

61.7AAe e1.37n

3.60

9.80 10.00

a = 2.0 MI PAn VEL

AI..nO A.14l1 A1.P'o n.67or I3.94061,1non 61.1A . 6fl.Q;'O J-.1N 00.8113 IR.infn A.7'nn 20.A467 O9.Apt p 43,Q 30 An.c66 pr.03A 6.5103 p.4tr5

3.40

6.20

7

60.0 KM/S

00 -20 .4nl .60 .80 1.00 1.20 1.40

2.40

nArr

IAJ6.1o 4

#,n.031 6n0.S6

i1,*55

1 3 .flW s Ie.rl

Ai.nIft, 6mnn An.7017

14"Ut '1,1fn P%,An I

AnSnSn

60.6"P7 60.56'

P6°10PI

An.Afl' An.crtQ

A.7nq1

n

6n.3A' A,'.'a An.1 1 An,.9?

An.32A

4A.Tl n

n1.13 A0.PA5

u3.T a A6.Pqnc 4A.P9p* t.37v

fAn.Inn An.2871

4n

94.0979

An. P7?'0

r%3.044

611.P716

ri3. npi

An.r7%6

96.6qq 50.11j9

An.p6np 6".P406

R6.45n 58.o'53

An.2613

6fn,9613 An.nl

A6.p295 61.29oA Sn.pypV 6n.pn0p 60.1ORP 60.1017 61n.186 61.1708

64.1035 66.73140 6q.'hl 71.140 74.3S35 76.gP8 7q.4 n

A6.2paq An.P1 An.931 60.n15 Anlpq An.0

p,07fl7

Anln01

64°nr 66.6145 Aq,1537 71.64P7 74.P31" 76.7600 70.368' l.P46"

R6."5hn q.no A,=IA Aq.nq4n 6e.gna 6o.119n 71.6455 74. 17I 76.711R 7q.P4k7 ct.77!

A4.Ao

6n.1745

A4.9n

Af.1747

A4.314U

sn.styn

Av.iAv 80.7071 Op.452 9u.79*83 Q7.3plO

87.0477 A0.q8Q P,12P4 04.6618

60.1AO

80.4500 q *q07#

0q,737 102.P744 104.8116

An.1A06 A0.16Aa An.lAn3 6n1.1560 An. 191 a 60.14I1 A0.1444 n.14nq

pA.QP99

10P.3%62 ln4.335

60.16qu 6.IA46 no.1601 60.1558 An.l.Ir17 6fn.1470 6f8.144P 6n.ln7

4.5147 07071n oq.AOqo lp.146ln tnu.ARPn

68.160 A An*.A19 6n.lq6 6.11spl 60.14A A0.1446 An.1411

An.1 -J An1 7 0 6- 191A 6n."n6n 6n.lno APOM1 61.18nl 60.inn A4.lll An.19i 86.R451 6 .17n0 09.17A7 6n.1Aqp 01.015 6".1An6 040MA4*A, 6.158 Q68nn finICD3 qqRQ 611.1140 102.047 Aflfta7 104.81c7 Af.1012

6n.1373 60.1342 60.1311 60.12R3 60.1255 60.1228

107.4707 130.007A 11P.q447 115.0A81 117.6183 120.19;q

0n.1374 60.1141 6.131P 60.128p3 6n.1256 60.1P20

107.3487 10.857 112.4PP5 1j4,q* 3 117.49qq 120.03P4

An.1W76, 6n.1144 6n.1314 6n.IP9 60.1,57 60.1231

107.?105 loq.7961 ll2,2q2A 11,P n 117.3653 xo.001

61.1177 60.1146 6n.1 tq 6.IPA6 60.158 60.1039

I07.1157 IQ.A4*A 112.1838 114.7176 117P9916 11Q.T899

A Aflt.1 An.1%4 en.i'I7 An,1 4 60.19 0 6n,1943

60.1203 60.1179 60.1155

12P.6013 125.2277 127.7640

60.lpo4 6001180 0.1156

122.i60 An 6p125 125.1051 A0f11 1 127.6413 60.1157

12p.4376 124,0736 1p7.,0q6

6n.1006 60.11R2 60.11RA

1P2.1t5 124.0519 127,181

61n,l9 60.1183 An1O

6n.2386

Qq.8597

6fn.2qj 6n.2'980

61.6P7

07.1)09

An.PQI

6I0.t85q

e1.35i

6.9R n.9109 61.2311 6n.pois A1.P1I4 A.9nq 69.t1A0 An.10o

60.1n61 A.1n14

41.in1 7

5I*

9n o

,6m

Q

PRW**

DATF 011077

PArr

Is

V-TNFINITY =60.0 KM/S

T - YRS

RAD

S=.1 AU VEL

10,00

127.9518

60.1154

11.00 12.00 13.00 14.00 15.00 16.00 17.00 19.00 19.00 20o00 21.00 22.00

140.6320

6n.1050

153.3102 165.Q866 178.6617 191.3355 204.0082 P16.6800 229.3510 242.0212 254.6907 267.3596 280.0280

60.0964 6n.0890 6n.08P7 60.0772 60.0724 60.0682 60.0644 60.0611 60.0980 60.0553 60.0528

24.00 29.00 26.00 27.00 28.00 2c).00 30-00 31.00 32.00 33.00 34.00 35.00 36.00 37.00 38.00 39.00 40.00 41.00 42.00 43.00 44.00 4S.00 46.00 47.04 48.0o 49.00 50.00 5t.00 S 52.00 530 54.00 55.00 2 56.00 - 57.00 Ir 58.00 2 59.00 S 60.00

305.3632 318.0302 330.6969 343.3630 356.0289 368.6944 381.3597 394.n247 406.6895 41g.3940 432.0183 444.6824 457.3462 470.0099 482.6739 495.3368 508.0000 520.6630 533.3259 545.9886 558.6513 571.3138 583.9761 596.6364 609.3005 .621,9625 634.6245 647.2863 659.9481 7.07 685.2713 697.9327 710.5941

723.2555 735.9167 748.5779 761.2390

Q = RAO

.3 AU VEL

Q RAD

127,8400 140.9201 153.1483 165.8747 178.5497 191.P?3S 203.896P 216.568n 229.P389 241.90q1 254.';786 267.2479 279.915Q

6n.11SS 6n.10 I 6n.0964 6n.0891 6n.08PA 6n.0773 6n.07P9 6n.0692 6n.0645 60.0611 6n.0qRl 6n.0953 6nl.O9PA

IP7.7640 14n.4441 193.IP21 169.7999 17A.4739 101.147P Pn3.9199 P1fi.4417 Ppq.16?6 P41.8127 ?94.rQPP P67.1711 27Q.6394

60.0484 305.2911 60.0469 317.q1ni 60.0447 330.9846 6n.0410 343o?5nA 60.0419 355.9167 60.0401 368.5821 60.0388 381.2476 60.0175 393.q126 6n.0363 406.5773 6 00192 419.2ulP 6n.0342 431.Q061 6n.0332 444.9i70 60.0323 457.2341 6n.0314 469.R97A 6n.0106 482.9613 60.0298 499.2246 60.0291 507.887A 60.0284 920.950A 60.0277 533.2137 60.0P71 545.8769, 60.0269 598.5391 60.0P59 571.P016 6n.0P53 583.863q 60.0248 59)6. 1262 60.0243 609.1881 60.0238 621.R501 60.0233 634.5121 60.02P8 647.1741 60.0224 699.8358 6.?0672.4979 60.0216 68q.159n 60.023P 697.820r, 60.0208 710.4819 6n.0204 723.143P 60.0201 735.8049 6n.0197 748.4656 6n.0194 761.1267

6n.0484 6n.0469 6n.0447 6n.0411 6n.0419 6n.04n1 60.0i g 6n.0379 6n.0i64 6n.0353 60.0147 60.0332 6n.0123 6n.0115 6n.0306 6n.0298 6n.0291 6n.0P84 60.0p77 6n.0271 6n.0269 6n.0299 6n.0293 60.024a 6n.0243 6n.n238 6n.0213 6n.0228 6n.02P4 6n.0P20 6n.02t6 6n.02t2 6n.0208 6n.0?n4 6fl.0?01 6n.0ign 60.0104

30n9,1746 117.9416 lln n] A41.1743 19.940P 36A.rin97 IR1.1710 391.8136n 406.9n07 41q.1652 411. 95 44.Q36 457.t975 46Q9211 USP.4A46 4q9.1480 n7.811p ;Pn.474P 911.1371 9;49.7998 9qA.4624 r71.IP4q qA3.7871 5Q6.44995 6n9.1116 6pi.7717 614.4'$6 647.nq74 6rQ.7591l 672.4P08 6A9.n824 607.743A 71g.409P 7P3.066t; 71q.7P7A 748.3A89 76|.A900

.5 AU VEL

0 = 1.0 AU RAO VFL

68.11S6 IP7.6411 fip.10nP 140.PI0 600%K6 1920"s~q 60.0891 169.6790 fin.OAPA 17A.349A 6n.077?? la1.0P33 60.0?pq Pnl.6Q$4 6n.0683 P16.1679 60°064 P?4,fnl83 60o061t] P41,?0pl 60.0981 294.1777 6n0,93 P67.fl46r, 6n0,0PR 78 .T147 6n.0484 6P.046i5 6n.044? 6n.0431 6n.nulq 6An4nl 6n.nARP Afl.037 6n.0164 6n.0193 6n.0142 60.0133 6n.0121 An.0319; 6n.0 0O6 A0.07qq4 60.0?91 An.0P94 6n.0777 6n.nP71 60.DP6r 60.0?59 60.0P"3 6n.nP4S 6n.nP43 60.nP3P 60.0P31 60.0P2A 60.0?24 60.npp0 60.0?16 60.0pip 6n.o n8 6n.0p04 60.0701 fin.nlqA 6n.0194

l0fin4QA 317.7167 33n.183? 143.04ql 359.7191 368.l06 3st.n4'!0 3Q3.7108 4n6.3799 419.n4no 411.7n4l 444.16A3 4-i7.0321 46g.fi9Rf 482.lqg3 Q90226 507.6857 5PO.14R7 513.nI16 945.6743 Sr,31An 870.Q04 53.6617 950.3P30 608.9A6n 6pt.6461 614.310O 646.o71A 69q.6339 672.PQ91 694.q567 6Q7.6181 71n.P709

7p2. QnA 735.6021 749.263P 760.OP43

A0e11S7 fin.tftv Afl.0n 6in.ARQ2 60.048 Afl.0774 Aq.n7P9 A"003 An.0649 A6006 60.09A| An.,n5l An.nqps

0 = 2.0 AU

a

An

Olin

1P7.580 14WA. 8 ll;P.864n 165.5400 179.214P 10O.A871 P03. 5I P16.?0P PPS.9nn6 1 .I*7?P P 4.I$ QI P66.q077 P79o57q?

AiN.n44 304.01060.fn465 317.%76q Ann447 l30,0441, 6n.04ll X4P.qnqi An.n416 iq-;,q74A An.n0n01 6A.P4ni Anl.03PA '3Po.qOiP. An.n375 9 .T0 6n.n364 406.P34A 6n-nlq3 418.PqAQ 60,034P u31.9611 6n.0lll 444.PP7 fi.0n03 49fi.Ago An.nII 469.9ri41 An.0WM6 UAP0.177 An.04g Uq4.PRnn An.0p t qn?.943n 60.nPA4 9pn.PO0 60$0P77 ';3P.A6Q6 6n.0p71 r4;.91PI 60.0PA5 q58.194A O60.n~qq $7.A577 f 0.npqi qRj.9Iqf An.np p qO6.IRIA An.nP4q3 6nA.";37 6lO.nplA Apl.qnq 600P11 614.167R fi0.0PPS f46.8?Ql 6n.nPP4 Ati..40na 6n.nP 0 67P.lr? A0.0P16 6A4.914n 6n.nP12 -6q7.475i4 An.fnPnA 71n.136A 60.npn4 7PP7Q n 6n.npni 719.49q> fin.0nI R 749.1201 A0.njQ4 76n.7814

VEL 6n.,II di 6n. t nf4 60.00fi6 60.08ql 6n.0npq An.M774 6n.176 60.0693 6n.0646 60,ft6lP 6n.n-;R1 6n*0Aqq 6nl.09Pg

5.2 AU

IP7.A87A 140,MS71 I~SPOMA 16w,.Aq n 178.n64A tOO0.T11 P01.4011 P16.06A? PPA.79Qq P t.4007 P9400 P66.73c ls P~q.4011

An.nPS 104.710 ' 6n.oM469 17.Nqvl 6n,0 44 Al0,.W'l 6n-n"Aol 14P.IP67 6n.fn416 i"s.19in 6n.n4ni1 69.n9RP 6fl.0ARq An ."I01 6.7 in3.,tqqo 6n.nIA4 406.m4Aq 60.nlql 4I8.71 n 6n.Mlu 411.17A 6in.nil 4.01A 6noiP4 4r6.AQQA 6n.O"19 4fq.NAOI0 An.0IO7 4AP.nPUq 6n.n0Q 404.AR74 60.n'Qt q07.1400 6n.nI84 900.nlll An.fti77 ql?.A744 60.n>71 qKlArfi.nK An.O61K qq7.QqA6n.n ,q -i7n.f6nu 6n.0,9 9P.IPPI An.0>4A qQ9.nA4A 66.nP4 6na.4R6 6n.no x8 API. 071 6n.noll Al3.n6AA 60.0*PQ A46.Aino 6n.oP04 fi9Q.9011 6n0nln0 671.n l~ 6n.n0>16 6n4.At" 6n.0O>IP 607.p74A 6n.npnR 7nQ.0j9A 60.flp05 7.r 4 " 6n.Mint 19.9r,Pf? 6n.o|a08 747.0|A fi0.n1o4 76n.971),

VL

fin*116O f,. I ot$

An.nOA?

600A61

6f).OAN

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fin.nv"o

6AnAA4R

60nOA8

6n*.n

6n.nq p

6n ,0 -q

An.nql

Aft.W

6n.AlA6

6A.M44

6M.nl

An.nh16

6n.naop

6 n R ­ A n?6 ­ An.nMmA 4

fio.n l C>

6ft.nl l

6n.nl l

6m.qI0

Aft*t 15

6n.nmn7

finnoaq

An.nio1

An.n A4

Fn.ni 8

n°oV 1

6n.nAc;

6in*.n-Q

6n.n o~

An.A 4A

6n.no4N

Aft.nOle

fitn0ll

6"00g

An.n*4

Aft°ni9

An.n 16

6n..plp

6ft.noAR 6A.nln';

6n.q,>A

6n~nlqn An.nin4

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PUBLICATION 77-70