Military Technical College. Chair of Aircraft Special Equipment and Armament. Design of Remote Sensing Satellite Orbit. By. Maj.Eng. Ibrahim Shaaban ...
Military Technical College Chair of Aircraft Special Equipment and Armament
Design of Remote Sensing Satellite Orbit
By Maj.Eng. Ibrahim Shaaban El-Sayed Sanad Military Technical College
Under supervision of Maj. Gen. (Ret.) Assoc.Prof. Dr. Mohamed Allam El.Sanabawy Military Technical College Brig. (Ret.) Dr. Ahmed Yehia El-Raffie National Authority of Remote Sensing and Space Science(NARSS) Dr. Mohamed Ahmed Zayan Nile-Sat Ground Station
This thesis is submitted as a partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering
Cairo 2013
Military Technical College Chair of Aircraft Special Equipment and Armament
Design of Remote Sensing Satellite Orbit By Maj.Eng. Ibrahim Shaaban El-Sayed Sanad Military Technical College
Under supervision of Maj. Gen. (Ret.) Assoc.Prof. Dr. Mohamed Allam El.Sanabawy Military Technical College Brig. (Ret.) Dr. Ahmed Yehia El-Raffie National Authority of Remote Sensing and Space Science(NARSS) Dr. Mohamed Ahmed Zayan Nile-Sat Ground Station This thesis is submitted as a partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering Date of discussion
Affiliation Discussion Committee
th
2013
Name
PGS-Reviewer Lt.Col.Dr.
Tarek Abd Ellatif Elnady
Head of PGS Affairs Col.Dr.
Mohamed Aly Metwaly
Cairo 2013
Signature
Abstract One of the most important reasons of remote sensing missions in space is more and deep study of our Earth planet and its atmosphere. Remote sensing missions usually aim to image certain areas on the Earth surface, requiring these images to be obtained with certain temporal resolution. In general, the spatial resolution of the image is also a mission requirement. For this purpose, the specific operational orbit, as one of the basic component of space mission, plays a special role in remote sensing mission design. Selection of orbital parameters for Earth observation satellites is the most reflective factor upon fulfillment of the space mission requirements. Practically, straight forward approach for selection of these parameters does not exist. Therefore, it is necessary to follow a complex process that requires tradeoffs among the orbital parameters and the corresponding orbit related mission requirements. Predicting the orbit of satellite is an essential part of the mission analysis and has impacts on the power system, attitude control and thermal design of the satellite. Furthermore, it is the starting point in planning whether a proposed mission is feasible and how the satellite needs to be designed. The study of orbital dynamics concepts is very important for predicting the satellite position and velocity with time, which is known as satellite orbital propagator. This thesis provides an appropriate survey on the orbital mechanics which is the basis for the development of the satellite orbital propagator.
II
In this thesis, to clarify the concept of orbit propagation a model representing the two body propagator where the so called f and g functions is introduced. This model can be described as the basic propagator. It does not consider any perturbation so secular and periodic changes are absent. In this thesis, we developed two orbital propagator models based on two different perturbation techniques to add the effects of orbital perturbations including Earth oblateness represented in J2 and atmospheric drag perturbations. Those perturbation forces are the main source of orbital disturbances for the satellite mission under consideration. One of these models is based on a general perturbation technique and so called General Perturbation Technique Propagator (GPTP) while the other based on a special perturbation technique and so called Special Perturbation Technique Propagator (SPTP). These propagators give rapid and fairly accurate results for estimating satellite orbit in the initial phases of a mission. For verification of these propagators, the errors between the results from both Matlab orbital propagators (SPTP & GPTP) with the High Precision Orbit Propagator in Satellite Tool Kit (STK HPOP) are compared. This thesis introduces and implements three various methods for designing the remote sensing orbit based on the remote sensing mission requirements. Remote sensing missions usually need to resolve two main problems. The first problem is to put the satellite in its designated orbit, since launchers in general do not position the satellite accurately in its nominal orbit. The second problem is to maintain the nominal satellite position against disturbances; an activity known as ‘orbit maintenance’. In this thesis, orbit maintenance maneuvers are discussed.
III
Acknowledgements Thanks to Allah the creator of the universe who ordered us to study and explore his creations in order to know him better. However, as I come to understand more; I find that there is so much more knowledge to absorb and to get to grips with. I wish to express my deepest gratitude and sincere thanks to my supervisors Maj. Gen. (Ret.) Assoc. Prof. Dr.\ Mohamed Allam El-Sanabawy, Brig. (Ret.) Dr.\ Ahmed Yehia El-Raffie, and Dr. \ Mohamed Ahmed Zayan who gave me their very deep information and continuous guidance through this work. I also would like to express my gratitude to Maj. Gen. Dr.\ Fawzy El Tohamy Hassan for his helpful advices and consultant that helped during the progression of this work. I also would like to express my gratitude to Col. Dr.\Ahmed Medhat Yousif, Lt. Col. Dr.\Ahmed Mohamed Azam, and Maj.Eng.\Ashraf Desouky Abo Sekeen for their consultant and creative direction during the progression of this work. I am indeed grateful to all the members of the Aircraft Special Equipment and Armament departments for their continuous encouragement, technical supports, and efforts to complete this work. My special gratitude to my family, they were very patient and helpful. They endured a lot of effort to get this work completed.
Finally, I would like to thank my reading committee for taking the time to review my thesis and attend my final presentation; I really appreciate their helpful comments. Maj. Eng. \ Ebrahim shaban El-Sayed Sanad Cairo 2013
IV
Table of Contents Abstract .............................................................................................................I Acknowledgements ....................................................................................... III Table of Contents .......................................................................................... IV List of Figures .............................................................................................. VII List of Tables.................................................................................................. XI Nomenclature ............................................................................................... XII Chapter 1 Introduction ................................................................................... 1 1.1 Overview ........................................................................................... 1 1.2 Problem Statement ............................................................................. 4 1.3 Work description ............................................................................... 5 1.4 Thesis Organization ........................................................................... 6
Chapter 2 Background and Literature Review ............................................ 7 2.1 Orbital Selection and Design Process................................................ 7 2.2 Review on Orbit Design .................................................................. 10 2.3 Thesis Objectives ............................................................................. 16
Chapter 3 Space Missions and the Associated Spacecraft's Orbits ......... 17 3.1 Space Missions and Space Systems ................................................ 17 3.2 Mission Development Process ........................................................ 20 3.3 Orbit Geometry ................................................................................ 24 3.4 Orbital Parameters ........................................................................... 26 3.5 Satellite Orbits Classification and Their Applications .................... 32 3.5.1 Classification Due To Orientation of the Orbital Plane .......... 32 3.5.2 Classification Due To Eccentricity of the Orbit...................... 33 3.5.3 Classification due to distance from Earth ............................... 34 3.6 Special orbits characteristics ........................................................... 38 3.7 Satellite Ground Tracks ................................................................... 42
Chapter 4 Payload Requirements for Remote Sensing Space Missions 44 4.1 Remote Sensing Process - An Overview ......................................... 44
V
4.2 Classification of Remote Sensing Systems ..................................... 46 4.2.1 Optical Remote Sensing Systems............................................ 47 4.2.2 Thermal Infrared Remote Sensing Systems ............................ 48 4.2.3 Microwave Remote Sensing Systems ..................................... 48 4.3 Remote Sensing Satellite payloads .................................................. 49 4.3.1 Classification of Sensors ......................................................... 50 4.3.2 Sensor Parameters ................................................................... 52 4.4 Major Remote Sensing Missions ..................................................... 54
Chapter 5 Orbital Dynamics and Orbital Propagation............................. 57 5.1 Two Body Problem .......................................................................... 57 5.1.1 Law of Universal Gravitation and Equation of Motion .......... 58 5.1.2 The Trajectory Equation ......................................................... 61 5.2 Reference Coordinate and Time Systems........................................ 64 5.2.1 Coordinate systems ................................................................. 65 5.2.2 Time Systems .......................................................................... 72 5.3 Kepler’s problem and satellite orbit determination ......................... 76 5.3.1 Kepler’s problem ..................................................................... 76 5.3.2 Two body propagator using f and g functions ........................ 80 5.4 Orbital Perturbation ......................................................................... 84 5.4.1 Third-Body Perturbation ......................................................... 86 5.4.2 Earth Oblateness or Non-Spherical Earth perturbation........... 87 5.4.3 Atmospheric Drag ................................................................... 91 5.4.4 Solar Radiation Pressure ......................................................... 92 5.4.5 Perturbation Techniques.......................................................... 93 5.5 Satellite Orbit Propagator models ................................................... 94 5.5.1 STK propagator models .......................................................... 95 5.5.2 Orbital elements from 5.5.3 and
and
................................................ 98
from the orbital elements ........................................... 99
5.5.4 Orbital propagator based on special perturbation technique . 100 5.5.5 Orbital propagator based on general perturbation technique 110
VI
5.6 Summary ........................................................................................ 117
Chapter 6 Orbit Selection for Remote Sensing Satellites ........................ 118 6.1 Basis of Orbital Selection .............................................................. 118 6.1.1 Orbital Parameters Regards................................................... 121 6.2 First Method .................................................................................. 124 6.2.1 Orbit Selection Process ......................................................... 124 6.2.2 Results of Calculations .......................................................... 128 6.2.3 First Method Conclusion ....................................................... 129 6.3 Second Method .............................................................................. 130 6.3.1 Method of Calculation ........................................................... 132 6.3.2 Lifetime Estimation with STK .............................................. 135 6.3.3 Results and Altitude Selection .............................................. 137 6.4 Third Method ................................................................................. 143 6.4.1 Introduction ........................................................................... 143 6.4.2 Selecting Orbital Altitude ..................................................... 144 6.4.3 Selecting the nodal position .................................................. 150 6.4.4 The Use of Frozen Orbits ...................................................... 150
Chapter 7 Orbit Maintenance .................................................................... 151 7.1 Introduction ................................................................................... 151 7.2 Station Keeping (SK) .................................................................... 152 7.3 Orbital transfer ............................................................................... 158 7.3.1 In plane maneuvers................................................................ 158 7.3.2 Out of plane maneuvers ........................................................ 161
Chapter 8 Conclusion and Future Work .................................................. 162 8.1 Conclusion ..................................................................................... 162 8.2 Future Work ................................................................................... 164
References .................................................................................................... 165 Appendices ................................................................................................... 169 Appendix A: Derivation of the Gaussian VOP Equations .................. 169 Appendix B: The Condition of Earth-Sun Synchronous Orbits ......... 173
VII
List of Figures Fig. No.
Title
Page No.
1.1
Area Seen from the Satellite on The Earth Surface
3
3.1
Space System Elements
18
3.2
Space Mission Life Cycle
20
3.3
Conic section geometry
25
3.4
Elliptical Geometry
25
3.5
Ascending, descending nodes and line of nodes
27
3.6
Yearly Variation of Angular Inclination of Earth with the Sun
28
3.7
Vernal Equinox (γ)
28
3.8
Inclination Tilt
29
3.9
Right Ascension of the Ascending Node (Ω)
30
3.10
Argument of Perigee (ω)
30
3.11
Equatorial Orbit
33
3.12
Polar orbit
33
3.13
Prograde and Retrograde Orbits
33
3.14
Elliptical and Circular Orbits
34
3.15
LEO, MEO and GEO
34
3.16
Molniya orbit
37
3.17
Sun-Synchronous Orbit
40
3.18
Satellite Ground Track
42
3.19
Earth’s Rotation Effects
43
4.1
Remote Sensing Process
45
4.2
Electromagnetic Spectrum (EMS)
46
4.3
Optical Remote Sensing System
47
4.4
Thermal Remote Sensing System
48
4.5
Active Microwave Remote Sensing System
49
4.6
Various Types of Sensors Onboard Remote Sensing Satellites
50
4.7
Scanning Systems
51
5.1
Formulation of the Two-Body Problem
58
VIII
Fig. No.
Title
Page No.
5.2
Orbital Plane Angles
63
5.3
Geometry of the Celestial Sphere
66
5.4
Geometry of the Vernal Equinox
66
5.5
Heliocentric Coordinate System XYZ
67
5.6
Geocentric Equatorial Coordinate System, IJK
68
5.7
Earth-Centered Earth-Fixed coordinate system (ECEF)
68
5.8
Topocentric Horizon Coordinate System (SEZ)
69
5.9
Perifocal Coordinate System, PQW
70
5.10
Satellite Coordinate System, NTW and RSW
71
5.11
Solar and sidereal day
74
5.12
Kepler’s Second Law
77
5.13
True and Eccentric Anomaly
78
5.14
Geometry for the perifocal coordinate system
80
5.15
Orbital Element Perturbation Changes
85
5.16
Zonal Harmonic up to Sixth Degree [45]
88
5.17
Sectorial Harmonics up to 5 by 5
88
5.18
Tesseral harmonics up to 4 by 3
89
5.19
Nodal Regression
90
5.20
Apsidal Rotation
90
5.21
Satellite Orbits in Inertial Frame for a Period of 10 Days (Matlab)
103
5.22
Normalized Variation of Acceleration with Spacecraft altitude
104
5.23
5.24
5.25
5.26
Variation of Semi-Major Axis with Time and Its Absolute Error Due to SPTP for a Period of one Day Variation of Eccentricity with Time and Its Absolute Error Due to SPTP for a Period of one Day Variation of Inclination with Time and Its Absolute Error Due to SPTP for a Period of One Day Variation of RAAN with Time and Its Absolute Error Due to SPTP for a Period of One Day
106
106
107
107
IX
Fig. No. 5.27
5.28 5.29
5.30
5.31
5.32
5.33
5.34
5.35
5.36
Title Variation of Argument of Perigee with Time and Its Absolute Error Due to SPTP for a Period of One Day Variation of True Anomaly with Time and Its Absolute Error Due to SPTP for a Period of One Day Variation of Argument of Latitude with Time and Its Absolute Error Due to SPTP for a Period of One Day Variation of Semi-Major Axis with Time and Its Absolute Error Due to GPTP for a Period of One Day Variation of Eccentricity with Time and Its Absolute Error Due to GPTP for a Period of One Day Variation of Inclination with Time and Its Absolute Error Due to GPTP for a Period of One Day Variation of RAAN with Time and Its Absolute Error Due to GPTP for a Period of One Day Variation of Argument of Perigee with Time and Its Absolute Error Due to GPTP for a Period of One Day Variation of True Anomaly with Time and Its Absolute Error Due to GPTP for a Period of One Day Variation of Argument of Latitude with Time and Its Absolute Error Due to GPTP for a Period of One Day
Page No. 108
108
109
114
114
115
115
116
116
117
6.1
Orbit Plane Motion
126
6.2
Altitude vs. Swath Width Chart, Revisit Time 53 Days
128
6.3
Altitude vs. Swath Width Chart, Revisit Time 50 Days
128
6.4
Earth geometry viewed from space
134
6.5
Shaded Area Representing (
135
6.6
Satellite Life Time (STK)
135
6.7
Program flowchart
136
6.8
) with Its Associated Angle
Slewing Maneuver Angle Required Getting Full Coverage Corresponding to Altitude
138
X
Fig. No. 6.9
6.10
6.11
Title Required Days to Satisfy Full Coverage Corresponding to Altitude with Certain Slewing Maneuver Angle Maximum (Worst) Ground Resolution Corresponding to Altitude for Every Revisit Time Maximum & Minimum Ground Resolution Corresponding to Altitude for Revisit Time 50 Days
Page No. 139
139
140
6.12
Satellite at Altitude 688 km Ground Tracks
142
6.13
SSO Repeated Ground Track Orbits
147
6.14
Flowchart of Altitude Selection for SSO
149
7.1
Work Flow for OCM Activities
153
7.2
7.3
7.4
Schematic Drawing of a LEO Spacecraft under Stationkeeping for Drag Effect Estimated times between SK maneuvers for a typical Sunsynchronous satellite with a ballistic coefficient of Estimated SK
for a typical sun-synchronous satellite with a
ballistic coefficient of
154
156
157
7.5
Hoffman transfer
159
7.6
Out of plane maneuver
161
XI
List of Tables Table No.
Title
Page No.
3.1
Eccentricity Values
26
3.2
Classical Orbital Elements
31
3.3
Specialized Orbits Characteristics and Their Applications
41
5.1
Summaries of Coordinate Systems
71
5.2
Relative Accelerations form Other Bodies to a LEO Satellite
86
5.3
Forces Taken into Account by Each Propagator
95
5.4
TLE for the ISS (ZARYA) Spacecraft
96
5.5
TLE format
97
5.6
Physical Parameters of Satellite
102
5.7
5.8
Initial Conditions, End Conditions and Absolute Error between SPTP and HPOP for a Period of One Day Initial, End Conditions and Absolute Error between GPTP and HPOP for a Period of One Day
105
112
5.9
Accuracy Comparison between SPTP and GPTP
113
6.1
Mission Requirements That Affect Earth Referenced Orbit Design
119
6.2
Altitude Trades
123
6.3
Results of Calculation
128
6.4
Physical Parameters of Satellite
135
6.5
Selected Altitudes Results
141
6.6
SSO Parameters with an Integer Number of Revolutions in One Day
146
XII
Nomenclature Abbreviations AOCS
Attitude and orbit control
DCM
Direction Cosine Matrix
EMS
Electromagnetic Spectrum
ECEF
Earth Centered Earth Fixed
ECI
Earth Centered Inertial
GPTP
General Perturbation Technique Propagator
GEO
Geostationary Earth Orbit
GMST
Greenwich Mean Sidereal Time
GNSS
Global Navigation Satellite System
GPS HPOP JD
Global Positioning System High Precision Orbit Propagator Julian Date
LEO
Low Earth Orbit
LV
Launch Vehicle
MEO
Medium Earth Orbit
MCR
Mission Concept Review
MJD
Modified Julian Date
RS RGTO
Remote Sensing Repeated Ground Track Orbit
STK
Satellite Tool Kit
SPTP
Special Perturbation Technique Propagator
SSO
Sun Synchronous Orbit
SW
Swath Width
SRR
System Requirements Review
TTC
Telemetry, Tracking & Control Station
TRMM
Tropical Rainfall Measuring Mission
XIII
Symbols Satellite Azimuth Angle Geocentric Longitude Satellite Orbital Period Geocentric Latitude Right ascension of Ascending Node Argument of Perigee True Anomaly Declination Angle Right Ascension Angle Conservation of Mechanical Energy Orbital Semi Major Axis Atmospheric Drag Acceleration Drag Coefficient Orbital Eccentricity Satellite Elevation Angle Eccentric Anomaly Universal Gravitational Constant Specific Angular Momentum Inclination Angle Mass of Earth Satellite Mass Satellite Mean Motion Earth Radius Earth Gravitational Potential Semi Latus Rectum
Chapter 1 Introduction One of the most important reasons of Remote Sensing from space is more and deep study of our Earth planet and its atmosphere. For this purpose, the specific operational orbit, as one of the basic component of space mission, plays a special role in satellite system design. So first we have to know why we are going to space, in other words what are the objectives of a space mission? Second how does the orbit affect mission design? And finally which orbit can meet the mission requirements? After answering the previous questions we can design the orbit for our mission specifically design of the remote sensing satellite orbit and this is the goal of this thesis.
1.1 Overview In space, remote sensing is sometimes conducted from the space shuttle or, more commonly, from satellites. Satellites are objects which revolve around another object - in this case, the Earth. For example, the Moon is a natural satellite, whereas man-made satellites include those platforms launched for remote sensing, communication, and telemetry (location and navigation) purposes. Because of their orbits, satellites permit repetitive coverage of the Earth's surface on a continuing basis. Cost is often a significant factor in choosing among the various platform options.
The remote sensing instruments can be mounted on a variety of platforms to view and image targets. Although ground-based and aircraft platforms may be used, satellites provide a great deal of the remote sensing imagery commonly used today. Satellites have several unique characteristics which make them particularly useful for remote sensing of the Earth's surface. The path followed by a satellite is referred to as its orbit. Satellite orbits are matched to the capability and objective of the sensor(s) they carry.
2
Orbit selection can vary in terms of altitude (their height above the Earth's surface) and their orientation and rotation relative to the Earth.
Satellites at very high altitudes, which view the same portion of the Earth's surface at all times have geostationary orbits. These geostationary satellites, at altitudes of approximately 36,000 kilometers, revolve at speeds which match the rotation of the Earth so they seem stationary, relative to the Earth's surface. This allows the satellites to observe and collect information continuously over specific areas. Weather and communications satellites commonly have these types of orbits. Due to their high altitude, some geostationary weather satellites can monitor weather and cloud patterns covering an entire hemisphere of the Earth [1].
Many remote sensing platforms are designed to follow an orbit (basically northsouth) which, in conjunction with the Earth's rotation (west-east), allows them to cover most of the Earth's surface over a certain period of time. These are near-polar orbits, so named for the inclination of the orbit relative to a line running between the North and South poles. Many of these satellite orbits are also Sun-synchronous such that they cover each area of the world at a constant local time of day called local Sun time. At any given latitude, the position of the Sun in the sky as the satellite passes overhead will be the same within the same season. This ensures consistent illumination conditions when acquiring images in a specific season over successive years, or over a particular area over a series of days.
This is an important factor for monitoring changes between images or for mosaicking adjacent images together, as they do not have to be corrected for different illumination conditions. Most of the remote sensing satellites are in near-polar orbits, which means that the satellite travels northwards on one side of the Earth and then toward the southern pole on the second half of its orbit. These are called ascending and descending passes, respectively.
3
If the orbit is Sun-synchronous, the ascending pass is most likely on the shadowed side of the Earth while the descending pass is on the sunlit side. Sensors recording reflected solar energy only image the surface on a descending pass, when solar illumination is available. Active sensors which provide their own illumination or passive sensors that record emitted (e.g. thermal) radiation can also image the surface on ascending passes.
As a satellite revolves around the Earth, the sensor "sees" a certain portion of the Earth's surface (Swath Width). The values of swaths for space borne sensors generally vary between tens and hundreds of kilometers wide. As the satellite orbits the Earth from pole to pole, its east-west position wouldn't change if the Earth didn't rotate. However, as seen from the Earth, it seems that the satellite is shifting westward because the Earth is rotating (from west to east) beneath it. This apparent movement allows the satellite swath to cover a new area with each consecutive pass. The satellite's orbit and the rotation of the Earth work together to allow complete coverage of the Earth's surface, after it has completed one complete cycle of orbits [2].
Swath Width
Fig. (1. 1) Area Seen from the Satellite on the Earth Surface If we start with any randomly selected pass in a satellite's orbit, an orbit cycle will be completed when the satellite retraces its path, passing over the same point on the Earth's surface directly below the satellite (called the nadir point) for the next time.
4
The exact length of time of the orbital cycle depends on mission requirement. The interval of time required for the satellite to complete its orbit cycle is not the same as the "revisit period". Using steerable sensors, a satellite-borne instrument can view an area (off-nadir) before and after the orbit passes over a target, thus making the 'revisit' time less than the orbit cycle time. The revisit period is an important consideration for a number of monitoring applications, especially when frequent imaging is required (for example, to monitor the spread of an oil spill, or the extent of flooding). In near-polar orbits, areas at high latitudes will be imaged more frequently than the equatorial zone due to the increasing overlap in adjacent swaths as the orbit paths come closer together near the poles [2].
1.2 Problem Statement It can be emphasized that the quality of a space mission is proportionally depends on its orbital selection. Orbital selection (determination of its parameters), in its turn should meet the requirements specified for the mission.
In a remote sensing mission, the satellite orbits the Earth to scan certain target area on the Earth surface. The communication system is responsible for transferring these images to the ground station. To perform the mission appropriately, two points should be considered: 1. The orbit of the satellite should be designed to achieve the mission requirements. In other words, the orbit should be selected so that the satellite can image the specified area with the required frequency. 2. The satellite should be kept in its orbit without deviation along the mission life time. In this thesis, we analyze the possible methods for one set of orbital parameters selection in Earth Remote Sensing System (ERSS) to fulfill the above-mentioned requirements. Mathematical tools are developed to calculate the orbit that satisfies the mission requirements. From the mission requirements for a remote sensing satellite are:
5
1. The size of the images obtained from the spacecraft (depends on orbital parameters and payload characteristics). 2. The number of days in which a complete set of images is obtained for the whole target area. 3. The rate by which the images are obtained. Starting from the above requirements, the developed tools that calculate the most suitable orbits for the mission are given. The output of these tools is the orbital parameters (altitude, inclination, period …).
1.3 Work description The scientific goal of this thesis is to design the orbit that achieves the mission requirements for a remote sensing satellite. The description of the task will be as follows: 1. Literature review on the previous work, in the field of satellite orbits and flight dynamics. 2. Analysis of satellite orbits, design and determination satellite orbits for Earth observation missions and criteria for selecting orbits for remote sensing satellites. 3. Study of space, inertial coordinate systems, time systems and space perturbations. 4. Development of satellite dynamics engineering model and trade-off study regarding the onboard payload. 5. Design of an algorism for remote sensing satellite orbit selection. 6. Simulation analysis of the results. 7. Conclusion and future work.
6
1.4 Thesis Organization This thesis contains 8 chapters: Chapter 1 presents an overview, problem statement and thesis organization. Chapter 2 introduces the background of satellite orbit selection and design process. Also introduces a review on orbit design methods. Chapter 3 gives the insight into Space missions and the associated spacecraft's orbits. This includes the definition of various space missions (remote sensing, communication, navigation…) and the associated orbits that achieve each mission type. Chapter 4 presents the satellite payload characteristics and requirements for the remote sensing mission. Based upon these characteristics and mission requirements the selection of the suitable orbital parameters is done. Chapter 5 introduces a survey of the orbital dynamics. This includes a description of the two body problem, Kepler’s laws and equation of motion, reference coordinate systems, reference time systems, orbital perturbation and finally designs and implements an algorithm for a satellite orbit propagator based on two different techniques. Chapter 6 introduces the bases of orbital selection and three different methods for selecting the remote sensing satellite orbit based on the mission requirements. Chapter 7 gives a brief description of orbit maintenance. This includes the role of the thrust force to compensate the external disturbance forces that acting on the satellite causes the satellite to decay or deviate. Chapter 8 concludes the design of the remote sensing satellite orbit and identifies the major tradeoffs for selecting the satellite orbit parameters for the remote sensing mission.
7
Chapter 2 Background and Literature Review Selection of orbital parameters for Earth observation satellites is the most reflective factor upon fulfillment of the space mission requirements. Practically, straight forward approach for selection of these parameters does not exist. Therefore, it is necessary to follow a complex process that requires tradeoffs among the different parameters and the corresponding orbit-related requirements. Multiple mission requirements often drive the orbit to different or even opposite trends. For Earth observation satellites, the most important orbit-related requirements are the Earth coverage, payload performance characteristics, ground communication, environment and survivability, orbit life time, availability of launch vehicle and legal and political constraints. In this chapter we will present a background on the design process of orbital parameters and also introduce some ideas and methods used for orbital selection of the remote sensing mission.
2.1 Orbital Selection and Design Process Effective orbit design requires clearly identifying the reasons for orbit selection, reviewing these reasons regularly as mission requirements change or mission definition improves, and continuing to remain open to alternatives. Orbit design has no absolute rules; several different designs may be credible. For example, communications may work effectively through a single large satellite in geosynchronous orbit or a constellation of small satellites in low Earth orbit. The design process includes the following steps [3]: Step 1: Establish Orbit Types This step involves examining the four types of orbits. These types are: 1. Earth referenced orbits are used to cover the Earth for example: The Global Positioning System GPS. 2. Space referenced orbits are used to cover space for example: The Hubble Space Telescope.
8
3. Transfer orbits are used to transition a satellite from one orbit to another for example: Hohmann Transfer. 4. Parking orbits are used as a transition orbit between the initial and final orbit. For our mission, we have only one segment with an orbit type Earth referenced orbit. Step 2: Determine Orbit related Mission Requirements We define orbit related requirements for each mission segment. For our single segment mission, we have to decide the following requirements: 1. Maximum altitude for observations: as altitude increases, coverage will be better but resolution will be worse. It is decided that our orbit altitude will range from 500Km to 800Km. However, we can consider this as a limit for good resolution until we get from the payload designers a condition on the altitude for good resolution. 2. Earth coverage: Earth locations of interest will affect orbit selection. 3. Field of view (or swath width) is a function of altitude. This is determined to be around 10 Km. 4. Continuity: it is required to observe continuous area of certain location on Earth. In our design we want a global coverage of Earth. 5. Radiation and survivability: If we put our orbit altitude less than 1000 Km, so we can neglect environmental effects. 6. Launch capability: this must be examined to augment orbit selection process. This is out of the scope of this work. 7. Ground communication: This is out of the scope of this work. 8. Orbit life time depends on the altitude and the orbit shape. This will be taken into consideration in the selection of the orbit altitude.
Step 3: Assess Applicability of Specialized Orbits It involves examining whether the unique characteristics of a specialized orbit offers an advantage over traditional Low Earth Orbit (LEO), Medium Earth Orbit (MEO)
9
and Geosynchronous Earth Orbit (GEO). The characteristics of each orbit type will be introduced later on at chapter 3. For an Earth referenced orbit, specialized orbits are: Geosynchronous, Sun synchronous, Molniya, Frozen orbit (orbit parameters do not change), and Repeating ground track orbits. We must determine if a specialized orbit applies. For our mission, a repeating ground track and Sun synchronous orbit will be required.
Step 4: Evaluate Whether a Single Satellite or a Constellation is needed This step involves determining whether a single satellite is sufficient or an entire constellation is required. As a rule, single satellites are less expensive and therefore desired if they can accomplish the mission. However, single satellites are often complex and provide no redundancy (if you lose the satellite you cannot accomplish the mission). A constellation of small inexpensive satellites may be a better solution. But in our study we will design for a single satellite case and the constellation case will be implemented in the future work. Step 5: Perform Mission Orbit Design Trades It involves choosing an orbit based on the mission the satellite will be asked to perform. Some considerations when selecting orbits are; coverage, sensitivity or performance,
environment
and
survivability,
launch
capability,
ground
communications, orbit lifetime, and legal or political constraints. Select the mission orbit by evaluating how orbit parameters affect each of the mission requirements from the previous considerations. This process establishes a range of potential altitudes and inclinations, from which we can select one or more alternatives. Step 6: Determine Launch Options and Cost This step involves calculating how much it will cost to get the satellites on orbit. It is not our interest in this thesis.
10
2.2 Review on Orbit Design This section summarizes the recent knowledge on the various methods for designing the remote sensing satellite orbit.
Wiley J. Larson and James R. Wertz [3] explained nearly all of the topics regarding the design of satellite orbits in their book named “Space Mission Analysis and Design”. They gave information about the orbit design process, tradeoffs for selecting the satellite orbital parameters corresponding to the mission requirements and orbit maintenance. Mission analysis of different satellite applications can also be found in their book.
David A. Vallado [4] gave a good reference in this study. He explained many problems in astrodynamics in his book named “Fundamentals of astrodynamics and applications. He gave deeply information about equation of motion, two body and n body problem, Kepler’s problem and Kepler’s equation. Also he explained the special and general perturbation techniques used to simulate and design the orbital propagators in this thesis. This book is rapidly becoming the standard astrodynamics reference for those involved in the business of spaceflight
A simple method was written in the thesis written by Dr. Ossama Abdelkhalik [5]. He first calculated the required altitude for the given swath width and revisit time. He used this altitude to check the condition of Earth Sun synchronous orbits and get the nearest altitude to the calculated one that satisfies this condition. After he had fixed the altitude, he calculated from it the actual swath width that can be achieved using an Earth Sun synchronous orbit.
Asghar Ebrahimi [6] worked on the remote sensing satellite orbit design. He presented that Earth observing systems are evaluated by performance parameters including area coverage and observation repetitivity. The type of mission is in fact determined by the area to be covered (global or regional) and by whether the
11
repetitivity requirement calls for continuous or intermittent observation. He presented studies on single satellite mission analysis for intermittent coverage, concentrating on manipulation of the ground track patterns of satellite. He described an orbit design analysis oriented to obtain efficient revisit coverage and repeat cycles by instruments embarked on satellite deployed on orbit. Results are depicted, by considering an orbit analysis for observation of the Middle East area. The orbit to be used in any particular remote sensing mission has always been determined through a trade–off between coverage objectives and the capabilities of the sequential trace pattern development, taking also into account the desired ground resolution.
Moshe Bar-Lev [7] discussed the EROS (Earth Resources Observation System) program that intended to operate a constellation of 8 commercial imaging satellites in LEO (Low Earth Orbit). His article presented the requirements and considerations regarding the choice of the orbits for a single and multi-satellites. Two kinds of orbits were compared: Sun synchronous orbits and inclined orbits. The altitude choice and technique for the Sun synchronous orbits, providing required ground track repeatability of EROS orbits and constellation are described. The advantages of using the constellation instead of a single satellite are to increase the amount of imagery received, allows daily revisit for any point with minimal imagery angle and achieve imagery opportunities for areas with high cloudiness. M.A. Zayan and F. Eltohamy [8] presented a general approach to the evaluation of the node periods of rotation and of orbital radius that meet the mission requirements. The orbital configuration of a remote sensing satellite was designed to determine if baseline orbital parameters are appropriately specified to meet the mission goal.
Muhammad Adnan [9],[10] discussed the study of perturbation of a satellite orbit due to the presence of other gravitational bodies such as Moon and Sun from the conservative perturbing forces and from the non-conservative perturbing forces
12
such as the nonhomogeneity and oblateness of the Earth, atmospheric drag and thrust. To solve this perturbed problem of Keplerian orbit, Cowell’s method was used, followed by Runge-Kutta method to simplify the equations involved. The study helped to simulate what is meant by orbital propagator. Also he discussed the establishment and relevant accomplishments of a simple facility used for students learning aids based on the Keplerian Orbit parameters.
Li Qiao [11] presented a preliminary analysis of the orbit design for the Garada project. The Garada mission is an Earth observation Synthetic Aperture Radar (SAR) satellite mission. It should be a 560km circular Sun-synchronous orbit. The proposed orbit is assessed in terms of the lifetime, solar illumination time, revisit time and GPS signal coverage. Since the user requirements in terms of maximum revisit time is one day for forest and one hour for floods of the interest area, a constellation design was required to satisfy this requirement.
Ronald J. Boain [12] developed the background and information necessary to explain what a Sun synchronous orbit is and how it works. He provided the equations to enable the mission analyst and system engineer to do quick and simple calculations for the orbit parameters selection and to compute mission parameters important to satellite design without having to resort to sophisticated computer programs.
Zhang Jinxiu and Cao Xibin [13] discussed an integrated, workstation-based software system in order to adapt the trend to digital and integrated design of small satellite and Nano-satellite and formation flying small satellite or Nano-satellite satellites. The system integrated Satellite Tools Kit (STK) with great demonstration and verification and satellite orbit design software. After combined satellite orbit design software and STK, an integrated system for satellite orbit design and mission
13
analysis was built. The system was used to analyze, optimize and verify the project of satellite orbit design during the phase of conceptual design and study.
Mehran Mirshams [14] presented and analyzed the constraints and the criteria of orbital selection for Earth Remote Sensing Satellite Systems (ERSS) also he presented the formulas for determination of orbital parameter.
Fabio Ceccanti [15] illustrated a possible validation mission for such the following concept: “Small Earth Observation satellites can obtain higher resolution with smaller payloads when operating at very low altitude. The life limiting effect of residual atmospheric drag can be reduced flying elliptical, low-altitude perigee orbits, with perigee right above the mission target; however, such orbits are severely affected by Earth gravitational field an isotropy and drag it. The use of on-board electric propulsion enables this class of missions, making it possible to control and maintain orbital parameters without adding too much to the overall vehicle mass and size”.
T. Ravindra Babuovided [16] scene computation procedure adapted in various Indian Remote Sensing missions, a comprehensive view, description on orbit selection procedure, the concept of image referencing scheme, different reference frames and transformations among them and definitions of basic terms were discussed with diagrams.
Salem A. [17] developed an Object Oriented Satellite Tool (OOST) to study and simulate the problems of satellite orbit design. This tool performed all the orbital calculations needed and simulated the geocentric orbit to perform the required mission.
S.Chouraqui [18] presented the simulation of the satellite orbit analysis based on data collected from NASA/NORAD two line elements. This analysis included orbit
14
determination and prediction of the satellite position, satellite velocity, orbit eclipse and ground trace.
Prasenjit Sengupta [19] presented semi-analytical techniques for satellite orbit design that are useful for the responsive space problem. In particular, the coverage by a satellite over a designated area on the Earth's surface was studied as a function of orbital elements. The semi-analytical nature of the methods developed enabled the evaluation of several performance metrics associated with the responsive space problem without the need for numerical integration of the orbit's parameters over the satellite's lifetime. He also discussed the analytical formulae for velocity increments required for orbit maintenance. These formulae are useful for estimating a fuel budget associated with the satellite mission. Also he presented semi-analytical techniques for the study of the coverage by satellites in Earth’s orbits [20]. In particular, the coverage by a satellite over a designated area on the Earth’s surface was studied as a function of orbital elements. The semi-analytical natures of the methods developed enabled the evaluation of several performance metrics associated with the coverage problem without the need for numerical integration of the orbit’s parameters over the satellite’s lifetime. He presented analytical formulas for velocity increments required for orbit maintenance.
N. Pie [21] discussed the requirements and the concepts for repeating ground track orbits and applications to the ICEsat mission. This mission was to study the short and long term changes in the ice mass in the Greenland and Antarctica regions The satellite of this mission was therefore placed into a frozen near-polar near-circular repeat ground track to ensure an adequate coverage of the polar regions while keeping the ground track periodic and reducing the variations in the orbital elements, and more specifically the semi-major axis of the ICESat orbit.
15
Hasan Murtaza [22] introduced a design method of a small satellite for remote sensing missions including the calculations for the budget of power, mass and dimensions for all the subsystems used for this mission.
P. Kenpankho [23] introduced the e-Learning on satellite orbit design. It was divided into three parts which were the concept design, orbit calculation, and simulation. He gave a scope on the various types of satellite orbits that used for remote sensing missions, their calculations and simulation.
Davide Di Domizio [24] described a model for satellite systems preliminary design based on European Space Agency (ESA) concurrent design approach. He illustrated space systems preliminary design aspects based on a concurrent engineering methodology. A general description of a typical space system and its subsystems was provided and sizing criteria were provided for each subsystem. He included a description of the implementation of the model and some conclusive remarks.
Giulio Bau [25] with the help of The Group of Space Dynamics of UPM (GSDUPM) had developed a new regularization scheme, called DROMO, which was characterized by only 8 ODE’s and exhibited a higher accuracy when compared with other propagation schemes. It could be used as a general-purpose propagator, but it turned to be useful when height fidelity propagation is mandatory. DROMO allowed a new approach to the dynamics of Near Earth Objects (NEO’s) in the long term, especially appropriated to consider the influence of the anisotropic thermal emission on the dynamics.
Eshagh and Najafi Alamdari [26] evaluated the perturbations in orbital elements of a low Earth orbiting satellite. They put the outcome of a numerical orbit integration process is the position and velocity vectors of satellite in an inertial coordinate system. The velocity and position vectors were converted into the corresponding orbital elements. Perturbations in a satellite motion affect the orbital elements in the
16
sense of Keplerian motion. They investigated the perturbing accelerations acting on a low Earth orbiting satellite using the second-order vector differential equations of motion of a satellite. Mitra Farahmand [27] described the models of four common orbital propagators and outlined the process of integrating them into the Horizon Simulation Framework (HSF). The results of the Two-Body, J2, and J4 propagators from the HSF were compared against the outcomes of these propagators in MATLAB and Satellite Toolkit (STK). The MATLAB algorithms verified the functionality of the propagators and determined the accuracy of the HSF implementation. The compassion against STK validated the formulation of the HSF propagators. Kenneth R. Pollock [28] examined the performance of three different orbital propagators to determine which provide the best performance for use in Low Earth Orbit Rendezvous. The performance evaluation was based upon the propagator's accuracy and the amount of time required producing a solution. A Cowell highfidelity propagator was used as a base line for comparison with an Encke and Clohessy-Wiltshire propagator. All comparisons were performed in a Local Vertical, Local Horizontal Reference Frame with the target spacecraft at the coordinate center.
2.3 Thesis Objectives The main two objectives of this thesis are: 1. Design the remote sensing satellite orbit for a single satellite case by selecting its orbital parameters that meet the mission requirements. The constellation case will be implemented in the future work. 2. Design and simulate two different propagators based on two techniques. One based on the special perturbation technique and the other one based on the general perturbation technique. The orbital propagator is a computer simulation that computes the position and velocity of an Earth orbiting satellite. The orbit propagator begins with an initial position and velocity vector using orbital mechanics. The propagator then calculates new vectors with the passing of time.
17
Chapter 3 Space Missions and the Associated Spacecraft's Orbits Space missions are developed to discover the Earth. Satellite is a part of the space system. The satellite is put into the desired orbit and has a payload depending upon the intended application. The satellites may be categorized in a number of ways such as by orbit altitude, eccentricity or inclination as we will explain that later on. It is important to note that the specific mission for a satellite will have strong impact on the design of its orbit. The primary task of the satellite mission analysis team is to select the optimum orbit which best enables the satellite and payload to perform their missions. The task is performed by first analyzing the mission, payload and satellite design requirements to determine if the mission is feasible. Providing the mission is feasible, trade-offs are performed in order to find a suitable orbit that meets the mission goals. In this chapter, a survey of the space mission analysis processes, classifications and several important characteristics of the space mission orbits and their associated missions are introduced.
3.1 Space Missions and Space Systems All space missions begin with a need, simply, why we are going to space? In other words what are the objectives of space missions? Generally, these overall space mission objectives are to communicate, to navigate, to observe, or to investigate. According to the mission objectives we have main four types of space missions: Communication, Remote sensing, Navigation, and Scientific research [29]. The selection (defining) the space mission objectives and constraints will define the space system that will meet these objectives with lowest possible cost and risk. The overall space system consists of 4 elements, Fig. (3.1), that must interact together to realize the mission objectives, these elements are the satellite (space segment), the ground station (ground segment), the launching vehicle and the orbit[30].
18
Space System
Satellite (Space Segment)
Launcher
Ground Stations (Ground segment)
Telemetry, Tracking & Control Station (TT&C)
Orbit
Data Receiving Station
Fig. (3. 1) Space System Elements 4. The Satellite (Space Segment) A space system can include a single satellite or a collection of satellites (constellation). A satellite consists of two main parts: the payload and the bus. i.
Payload: It is the part (equipment) that actually performs the mission. It means that the type of payload a satellite has, depends directly on the type of mission it is performing.
ii.
Bus (Platform): It provides the resources required to functioning the payload. It provides electrical power, maintains the right temperature, processes data, communicates with Earth and other satellites, controls the payload orientation and satellite attitude in orbit, and holds everything together. The bus includes the following functional subsystems: a. Bus structure. b. Bus mechanisms. c. Attitude and orbit control (AOCS). d. Electrical power system. e. Thermal control system. f. Telemetry, command and data handling. g. Propulsion system.
19
5. Ground Stations (Ground Segments) The ground station consists of two main parts: i.
Telemetry, Tracking and Control station (TT&C): It consists of command subsystem and telemetry subsystem. It enables commands to be sent up to the satellite units, and status information to be returned to the ground.
ii.
Data receiving stations: They receive data generated by the satellite. The data can be received directly by the end users or can be delivered to the end users indirect. The detailed structure of both ground segments vary with the mission type.
6. The Launcher Normally the launcher (a rocket) cannot inject the satellite into its final orbit. When the rocket finishes its job and burns out, the satellite remains in a parking orbit. It is a temporary orbit where the satellite will stay until transforming to its final orbit (mission orbit). Transfer orbit is an intermediate orbit that takes the satellite from its parking orbit to the final mission orbit.
7. The Orbit It is the trajectory, on which the satellite travels around the Earth. Theoretically, we can put a satellite into a limitless number of orbits, but we must select (design) the orbit which best fulfills the mission. This means that the specific mission for a satellite will have a strong impact on the design of its orbit, hence we have to scope on the orbit characteristics to decide which orbit can meet the mission requirements.
As we said before that the primary task of the space mission analysis team is to select the optimum orbit which best enables the satellite and payload to perform their missions. Thus, the following section outlines the need for understanding the space mission development life cycle from its inception through launch and operations.
20
3.2 Mission Development Process There is no single avenue by which a mission is initiated. An original concept for a mission to obtain scientific data may come from members of the science community who are interested in particular aspects of an Earth science problem, or it may come from an individual or group, such as a scientific team working on a particular issue, who know of an opportunity to provide unique measurements. As a project matures, the effort typically goes through the phases shown in Fig. (3.2), from pre phase (A) formulation to operation phase. Formal reviews are typically used as control gates at critical points in the full system life cycle to determine whether the system development process should continue from one phase to the next, or what modifications may be required [31].
Pre phase A
Mission Concept Review (MCR)
Formulation
Conceptual Study
Phase A Concept & Technology Development
System Requirements Review (SRR) System Definition Review (SDR)
Phase B Preliminary Design & Technology
Preliminary Design Review (PDR) Non-Advocate Review (NAR)
Completion
Phase C
Implementation
Final Design & Fabrication
Phase D System Assembly, Test & Launch
Operation Phase (MO & DA)
Critical Design Review (CDR) System Integration Review (SIR)
Flight Readiness Review (FRR) Operational Readiness Review (ORR)
Post Launch Assessment Review (PLAR)
Mission Operations & Data Analysis
Fig. (3. 2) Space Mission Life Cycle
21
Life cycle phases are used to help plan and manage all major aerospace system developments. Everything that should be done to accomplish a project is divided into distinct phases, separated by control gates. For NASA, the phases are lettered: Pre-phase A, phase A, phase B, phase C, phase D and Operation phase. Phase boundaries are defined at natural points for project progress assessment and go or no go decisions. Decomposing the project into life cycle phases organizes the development process into smaller more manageable pieces. Since early decisions commit later activities and more mature systems are harder to change, systems engineering done in the early phases has the greatest impact on mission success. The project life cycle is divided mainly into two main parts; formulation and implementation. Phases of formulation and implementation are divided into incremental pieces. This allows the development team to access their progress, estimate system, project performance, plans the next phase, and allows decision makers to assess management and technical progress. First, the formulation is the first part of the management life cycle where system requirements are baselined, feasible concepts are determined, a system definition is baselined for the selected concept(s), and preparation is made for progressing to the Implementation part. The implementation phases are divided as follows [31]: i.
Pre-Phase A (Concept Studies): The purpose of this phase is to produce a broad spectrum of ideas and alternatives for missions from which new projects can be selected. The tasks of this phase will be: Define the mission needs, goals and objectives. Perform studies of a broad range of mission concepts that contribute to goals and objectives. Develop draft project level requirements, operations concept, and potential technology needs. Complete
Mission
Concept
Review
approaches as a baseline for phase A.
(MCR):
review
overall
22
ii.
Phase A (Concept & Technology Development): The purpose of this phase is to determine the feasibility of a suggested new system in preparation for seeking funding. The tasks of this phase will be: Define mission success and minimum mission. Perform trade studies to compare mission concept options. Develop a baseline mission concept, including best technical approach, project execution, cost and schedule. Complete the requirements to the subsystem level. Identify requirements flow between and across subsystems. Begin needed technology developments. Complete
System
Requirements
Review
(SRR):
Review
requirements as baseline for final concept. Establishes the System Requirements baseline. Complete System Definition Review (SDR): Review baseline for phase B. Establishes the Functional baseline. iii.
Phase B (Preliminary Design & Technology Completion): The purpose of this phase is to define the project in enough detail to establish an initial baseline capable of meeting mission needs. The tasks of this phase will be: Refine concept of operations. Allocate functions and resources (e.g., mass margins). Define the mission requirements. Establish design solution that meets mission needs. Demonstrate that technology development is complete. Preliminary Design Review (PDR): Review requirements, design and operations as baseline for detailed design. Non Advocate Review (NAR): Review the space mission and instruments designs that meet the mission requirements. Review management processes sufficiency to develop and operate the mission. Review mission cost estimation to be launch on time and within budget.
23
Second, the implementation is the part of the management life cycle where the detailed design of system products is completed and the products to be deployed are fabricated, assembled, integrated and tested; and the products are deployed to their customers or users for their assigned use or mission. The implementation phases are divided as follows: i.
Phase C (Final Design and Fabrication): The purpose of this phase is to design a system (and its associated subsystems, including its operations systems) so that it will be able to meet its requirements. The tasks of this phase will be: Demonstrate that the detailed system design meets requirements. Design the space mission orbit is the primary task of this phase. Demonstrate that the design drawings are complete. Begin fabrication of test and flight article components, assemblies, and subsystems. Critical Design Review (CDR): Review design drawings and test plans.
ii.
Phase D (System Assembly, Integration and Test, and Launch): The purpose of this phase is to build the subsystems (including operations systems) and integrate them to create the system, while developing confidence that it will be able to meet the systems requirements. The tasks of this phase will be: Perform system assembly, integration, and test. Verify system meets requirements. Prepare system for deployment. Launch system. Verify deployment and operations. Complete
Flight
Readiness
Review
(FRR):
Review
system
preparedness for launch. iii.
Phase E (Operations and Sustainment): the purpose of this phase is to ensure that the certified system is ready for operations. The tasks of this phase are: Implement the mission operations plan developed in earlier phases.
24
Collect and archive mission and science data. Complete Post Launch Assessment Review (PLAR): Review to assess readiness to proceed with full, routine operations. Choosing the most appropriate mission orbit which best enables the satellite and payload to perform their missions is an important part of the overall mission design. The task is performed by first analyzing the mission, payload and satellite design requirements to determine if the mission is feasible as we mentioned above. Providing the mission is feasible, trade-offs are performed in order to find a suitable orbit that meets the mission goals. The specific operational orbit as one of the basic component of space mission plays a special role in satellite system design. It can be emphasized that the quality of a space mission is proportionally depends on its orbital selection. Orbital selection (determination of its parameters), in its turn is a faction of requirements specified for the mission. To know which orbit is suitable for remote sensing satellites, we must understand the orbital geometry, orbital elements and the various types of space mission orbits.
3.3 Orbit Geometry The two-body equation of motion describes conic sections. The object depends on its velocity and the magnitude of the central force to follow the conic section. If an object lacks the velocity (insufficient kinetic energy) to overcome the gravitational attraction (potential energy) then it will follow a closed path (circle or ellipse). However, if the object has enough velocity to overcome the gravitational attraction then the object will follow an open path (parabola or hyperbola) and escape from the central force. For the particular case of Earth-orbiting satellites, the circular and elliptical orbits are used to meet that mission[32]. Fig. (3. 3) shows the basic geometry of various possible conic sections. The parameters describe the size and shapes of the conics are the semi-major axis (a) and the eccentricity (e) respectively. Fig. (3. 4) depicts a satellite orbit with additional parameters whose conic section is an ellipse. The parameters are shown in Fig. (3. 4) are defined as:
25
i.
Semi-major Axis (a). It is the half distance between perigee and apogee, a measure of the orbits size, also the average distance from the attracting body.
ii.
Linear Eccentricity (c). It is the half distance between the foci.
iii.
Eccentricity (e). It is the ratio between the linear eccentricity(c) and the size of the ellipse (a); describes the orbit’s shape.
iv.
Perigee. It is the closest point in an orbit to the attracting body.
v.
Apogee. It is the farthest point in an orbit to the attracting body.
Fig. (3. 3) Conic section geometry
Fig. (3. 4) Elliptical Geometry
26
These parameters apply to all trajectories. A circular orbit is a special case of the elliptical orbit where the foci coincide (c = 0). A parabolic path is a transition between an elliptical and a hyperbolic trajectory. The parabolic path represents the minimum energy escape trajectory. The hyperbolic is also an escape trajectory; and represents a trajectory with excess escape velocity. Table (3.1) shows the values for the eccentricity for the various types of orbits. Eccentricity is associated with the shape of the orbit. In the following section we will discuss the orbital parameters to define the orbit and understand it.
Table (3. 1) Eccentricity Values Conic Section
Eccentricity (e)
Circle Ellipse Parabola Hyperbola
e=0 0 1
3.4 Orbital Parameters It is usual to define an orbit and the position of the body describing that orbit by six quantities called the elements. Three of them define the orientation of the orbit with respect to a set of axes, two of them define the size and shape of the orbit, and the sixth (with the time) defines the position of the body within the orbit at that time. For the particular case of Earth-orbiting satellites, certain terms are used to describe the position of the orbit with respect to the Earth[30]. 1. Line of Apsides. It is the line joining the perigee and apogee through the center of the Earth. 2. Ascending and Descending Nodes. The satellite orbit cuts the equatorial plane at two points: the first, called the descending node (N1), where the satellite passes from the northern hemisphere to the southern hemisphere, and the second, called the ascending node (N2),where the satellite passes from the southern hemisphere to the northern hemisphere (Fig. 3.5). 3. Line of Nodes. It is the line joining the ascending and descending nodes through the center of the Earth.
27
Fig. (3. 5) Ascending, descending nodes and line of nodes 4. Equinoxes: The inclination of the equatorial plane of Earth with respect to the direction of the Sun defined by the angle formed by the line joining the center of the Earth and the Sun with the Earth's equatorial plane follows a sinusoidal variation and completes one cycle of sinusoidal variation over a period of one year (Fig. 3.6). The sinusoidal variation of the angle of inclination is defined by inclination angle = 23.4o sin (2π/t), where t is 365 days. This expression indicates that the inclination angle is zero for t = t/2 and t. This is observed to occur on 21 March, called the spring equinox, and 21 September, called the autumn equinox. The two equinoxes are understandably spaced 6 months apart.
During the equinoxes, it can be seen that the equatorial plane of Earth will be aligned with the direction of the Sun. Also, the line of intersection of the Earth's equatorial plane and the Earth's orbital plane that passes through the center of the Earth is known as the line of equinoxes. The direction of this line with respect to the direction of the Sun on 21 March determines a point at infinity called the Vernal Equinox (γ) (Fig. 3.7).
28
Fig. (3. 6) Yearly Variation of Angular Inclination of Earth with the Sun
Fig. (3. 7) Vernal Equinox (γ) In three dimensional spaces, it takes three parameters each to describe position and velocity. Therefore, any element set defining a satellite’s orbital motion requires at least six parameters to fully describe that motion. There are different types of element sets, depending on the use. The Keplerian, or classical, element set is useful for space operations and tells us four parameters about orbits, namely: Orbit size Orbit shape Orientation (orbit plane in space and orbit within plane) Location of the satellite
29
The classical set of six orbital elements is defined by the following parameters[33]: 1. Semi-Major Axis (a). It describes an orbit’s size and it is a half of the distance between apogee and perigee on the ellipse. This is a significant measurement since it also equals the average radius, and thus is a measure of the mechanical energy of the orbiting object. 2. Eccentricity (e). It measures the shape of an orbit. Recall from the orbit geometry section it can be defined as
.
Size and shape relate to orbit geometry, and tell what the orbit looks like. The other orbital elements deal with orientation of the orbit relative to a fixed point in space.
3. Inclination (i). It is the first angle used to orient the orbital plane. It is a measurement of the orbital plane’s tilt. This is an angular measurement from the equatorial plane to the orbital plane
, measured counter-
clockwise at the ascending node while looking toward Earth (Fig. 3.8). Inclination is utilized to define several general classes of orbits as shown in the following section.
Fig. (3. 8) Inclination Tilt
30
4. Right Ascension of the Ascending Node (Ω). It is a measurement of the orbital plane’s rotation around the Earth. It is an angular measurement within the equatorial plane from the Vernal Equinox eastward to the ascending node (Fig. 3.9).
0o= Vernal Equinox (γ)
Fig. (3. 9) Right Ascension of the Ascending Node (Ω) 5. Argument of Perigee (ω). Inclination and Right Ascension fix the orbital plane in inertial space. The orbit must now be fixed within the orbital plane. For elliptical orbits, the perigee is described with respect to inertial space. The Argument of Perigee, ω, orients the orbit within the orbital plane. It is an angular measurement within the orbital plane from the ascending node to perigee in the direction of satellite motion
Fig. (3. 10) Argument of Perigee (ω)
(see Fig. 3.10).
31
6. True Anomaly (ν). At this point all the orbital parameters needed to visualize the orbit in inertial space have been specified. The final step is to locate the satellite within its orbit. True Anomaly, ν, is an angular measurement that describes where the satellite is in its orbit at a specified time, or Epoch. It is measured within the orbital plane from perigee to the satellite’s position in the direction of motion
. True
Anomaly locates the satellite with respect to time. Table (3.2) summarizes the Keplerian orbital element set, and orbit geometry and its relationship to the Earth.
Table (3. 2) Classical Orbital Elements Element
a
Name
Description
Definition
Remarks
semi-major
orbit size
half of the major axis of the
orbital period and
ellipse
energy depend on orbit
axis
size eccentricity
orbit shape
e
ratio of half the foci separation (c) to the semi-major axis (a)
inclination
orbital
angle between the orbital plane
plane’s tilt
and equatorial plane, measured
i
counterclockwise at the ascending node
Ω
ω
right
orbital
angle, measured eastward, from
ascension
plane’s
the Vernal Equinox to the
of the
rotation
ascending node
ascending
about the
node
Earth
argument
orbit’s
angle, measured in the direction
of perigee
orientation
of satellite motion, from the
in the orbital
ascending node to perigee
closed orbits: 0 ≤ e
