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.
iii
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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.
v
77-7o
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 -----------------------------------------
18
18
18
25
25
28
28
28
30
30
31
31
32
32
32
32
33
33
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
51
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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
5
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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
77-70
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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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.
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200-217.
R. W. Bussard (1960), "Galactic matter and interstellar flight", Astronautica
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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
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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
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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
-. 711711 6.,;nnc 6.A7ar 7. 111411n 7.nnrn . r,360; n.nian 0. -;p,? ln.nAq7
17.A~ng 16.A1nA 16.Mqn3 I .47n r f4.00AA 1.UqII a1 14.0 1.6fiII 1I.POA4
.30 6.,.ibq 7.noP7
I .*,7 1=.Af7
7.44i
I M.400
7.AOn6 A Ipit; A.rAla tnr q."1
19.1mro la,Km
ln.11lo o ip.qQAR t1.o001171 11.A7An ip.nfqu
9.926q
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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
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44.2430
8.0686
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43.37Q1
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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
7.9870 7.90fq 7.8206 7.7495 7.6791
49.94p7 4P.14q 48.8690 rn.9086 9P.1321
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25.00
54.1337
7.6010
53.9363
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91.7414
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26.00
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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
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6
5.0 KM/S
V-INFINITY T - YRS
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8.90n4
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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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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.
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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
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. PAD
AU VFL
0 PAn .s;n 1*0734
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2.0477 3.6966
4P.O?"3 37.2106
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39.2663 14l.1797
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3.rrp1 9.0l63 6.49?9 7.0070 O '3.3n17
5AU VFL
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66.607P
1flOnnn
4P.415f8 37.4090
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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
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17.6 I.9e7Q 14'317q tI.62'n q3*00l7 3gp7f77 jp.4f76
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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
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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
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22.161P
331L47Q3
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11.92A9 31.48r6 31.34?7 31.2668 3l.l0 t 31.13114 31.0836 1.0340
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In.inoo 3.8080
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3n.6040
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4A.068n 9q*.4Q1 -I.q,;ni rp.Illn 94.0017
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'n.5916 Tn.q1nn
99.8388
30,50s 30.i33
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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
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60.6446 61.9304 63.2159 64.9009
30.4837 30.4737 3n.4642 30.4550
9.80
65.7856
10.00
67.0699
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57.7660
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30.5178 30.5064 30.4Q95 3n.4050 30.N4750 30.4654 30.4562
30.5163 30.5050
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11.111A
30.7piq 'o.7o16
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4.5n1
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38.1246 30.u2A0
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60.2 026
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30.UQ I0.R1I 30.47 30.4818 30.4-27
64.11I
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66.4867
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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
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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.$7Q
C0.21A
R1.9185
F2.2pl0 rn.P172
70.2?6U gl.'44'
7.80 8.00
84.0160 86.1343
50.2107 50.2056
83.8975 86.0057
50.2111 511.2059
83.704
c0.2113
8.20
88.2523
50.2006
88.123A
5f.2000
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rn.2061 K0.2011
50.2117 n.?fl5
89.u690
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83.616rR RT.75,4q
87.87P7
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8.40
90.3702
50.1a5q
8.60
90.2416
50.1962
92.487c
90.t1i5
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50.1064
92.359P
8Q.qqP4
50.1ot7
OP.265q
;0.1c1
94.4767
50.11 4
94.3834
8.80
94.6053
50.172
64.8117
66.032u 69.0529
5n.2415
7
50.p2418 c0.25fn Rf.22R6
5.3n004
6p.P74T 64.011 66, n,
68.63q
5fn.36A 'n.398 Rn.316o
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6p.1791
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5.26rI Ifn.Pq78
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9.pns
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7n.Ap'27 7p.-301 74.qr'n
5n.P9n6 q"5.111
0.1420 Kn.p560 50.2006 r0.2,3
Fn.Pi76
76.oeD$,
50.91n snt.*n0
70.n80
5n.9I9
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qnfl
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9.649
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80l.10 5
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'50.1876
04.22nP
Knf.ln7q
n4.n0480
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0
9.00
96.7226
50.1831
96.9941
50.1P33
(6.9f006
50.135
96.34P3
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96.1647
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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
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100.7146
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100.5761
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08.1046
90.1764
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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
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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
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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
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3n7.0144
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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
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PRW**
fl*'r 03W77 V-INFINITY =
T - YRS
o
0= RAn
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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
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AU VEL
n = PAn
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n = 1.0 Atl PA) VFL
1.nonn
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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
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6n.60q5
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6n.6103 60.5594
23.6441 26.1990
6n.6p?2 60.9617
PA.5710 P6.173
6n.6940 o.5r.W
64.8417
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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
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60.5101 60.4688 60.4337
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49.2448 51.7885
6n.2095 60.2848
49.133A 91.6774
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59.4162 61.9579
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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
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6.40
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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
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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
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28.A637 31.4157 33.9660
60.2382
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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
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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 $7.A577 f 0.npqi qRj.9Iqf An.np p qO6.IRIA An.nP4q3 6nA.";37 6lO.nplA Apl.qnq 600P11 614.167R fi0.0PPS f46.8?Ql 6n.nPP4 Ati..40na 6n.nP 0 67P.lr? A0.0P16 6A4.914n 6n.nP12 -6q7.475i4 An.fnPnA 71n.136A 60.npn4 7PP7Q n 6n.npni 719.49q> fin.0nI R 749.1201 A0.njQ4 76n.7814
VEL 6n.,II di 6n. t nf4 60.00fi6 60.08ql 6n.0npq An.M774 6n.176 60.0693 6n.0646 60,ft6lP 6n.n-;R1 6n*0Aqq 6nl.09Pg
5.2 AU
IP7.A87A 140,MS71 I~SPOMA 16w,.Aq n 178.n64A tOO0.T11 P01.4011 P16.06A? PPA.79Qq P t.4007 P9400 P66.73c ls P~q.4011
An.nPS 104.710 ' 6n.oM469 17.Nqvl 6n,0 44 Al0,.W'l 6n-n"Aol 14P.IP67 6n.fn416 i"s.19in 6n.n4ni1 69.n9RP 6fl.0ARq An ."I01 6.7 in3.,tqqo 6n.nIA4 406.m4Aq 60.nlql 4I8.71 n 6n.Mlu 411.17A 6in.nil 4.01A 6noiP4 4r6.AQQA 6n.O"19 4fq.NAOI0 An.0IO7 4AP.nPUq 6n.n0Q 404.AR74 60.n'Qt q07.1400 6n.nI84 900.nlll An.fti77 ql?.A744 60.n>71 qKlArfi.nK An.O61K qq7.QqA6n.n ,q -i7n.f6nu 6n.0,9 9P.IPPI An.0>4A qQ9.nA4A 66.nP4 6na.4R6 6n.no x8 API. 071 6n.noll Al3.n6AA 60.0*PQ A46.Aino 6n.oP04 fi9Q.9011 6n0nln0 671.n l~ 6n.n0>16 6n4.At" 6n.0O>IP 607.p74A 6n.npnR 7nQ.0j9A 60.flp05 7.r 4 " 6n.Mint 19.9r,Pf? 6n.o|a08 747.0|A fi0.n1o4 76n.971),
VL
fin*116O f,. I ot$
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600A61
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fin.nv"o
6AnAA4R
60nOA8
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6n.AlA6
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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
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6n.nAc;
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6"00g
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6n..plp
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r
PUBLICATION 77-70
