Upload
alisha-murphy
View
216
Download
0
Embed Size (px)
Citation preview
Final Version
Steven CooleyRich Luquette
Greg MarrScott Starin
Flight Dynamics
May 13-17, 2002
Micro-Arcsecond X-ray Imaging Mission, Pathfinder (MAXIM-PF)
Flight DynamicsPage 2
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Requirements & Assumptions (1 of 2)
Phase 1
200 km +/- 5 m
5cm control
15 m Knowledge
Phase 2
5cm control
15 m Knowledge
Optics Hub S/C
Detector S/C
20,000 km +/- 5 m
FreeFlyer S/C 100-500 m separationControl to ~10 microns
Detector S/C
Optics Hub S/C
Flight DynamicsPage 3
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Mission Orbit L2 Lissajous Heliocentric “Drift-Away” Variations on Drift Away (e.g., DROs stay closer to Earth)
Orbit Control and Knowledge Requirements Orders of Magnitude above Current Operational Missions Not Addressed Here
V and Acceleration Magnitude Values Very Coarse Approximations
No Noise CRTBP or Free Space Model No Perturbations (Moon, Jupiter, etc.) No Navigation Errors
Further Analysis Required
Requirements & Assumptions (2 of 2)
Flight DynamicsPage 4
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Lissajous Orbit Option
Orbit Characteristics Quasi Orbit Period of ~6 months Can Choose small or Large Amplitude Lissajous No Earth Eclipses MAXIM Adds Requirement of No Lunar Shadows (MAP)
Advantages Spacecraft do not Drift too Far from Earth
Communications (High Data Rate Missions) Spacecraft can be More Easily Replaced/Repaired Important for Long Missions
Small Launch Vehicle C3 (-2.6 for Phasing Loops, -0.7 for Direct) Disadvantages
Unstable Complicated Dynamics Can Lose Spacecraft (e.g., Propulsion Failure) All s/c in formation require propulsion (Operational Complexity)
Formation Keeping Costs May be Greater (Further Analysis Needed)
May Have increased variation in Formation Keeping Control Acceleration Magnitude (Harder to size thrusters)
6 Month Transfer Time High Thrust Propulsion System Likely Needed (Need to Correct LV
Errors QUICKLY)
Flight DynamicsPage 5
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Heliocentric Orbit Option
Orbit Characteristics Drift Away Orbit (0.1 AU/year)
Advantages Stable Dynamics
Simpler Operations Potentially No Orbit Overhead Costs Optics Hub may Not need propulsion
Relatively Short Transfer Times May Require Less Formation Keeping Costs (?) May be Able to Eliminate Need for High Thrust
Propulsion System Disadvantages
Higher Launch Vehicle C3 (0.4) Drift Away Concerns
Flight DynamicsPage 6
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Lissajous Orbit Option Phase 1
Flight DynamicsPage 7
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Desired Characteristics
Two S/C in formation, 200 km apart
Maintain inertial orientation of SC-to-SC line for 1 week observation
Optics Hub follows a ‘Ballistic’ lissajous orbit during Observation (the “Leader”)
Detector SC (the “Follower”) follows a shifted trajectory
For Given Observation, Position differs by a constant baseline vector
Driving Requirements
Time allocated for reorienting the SC-to-SC line
SC-to-SC line remains inertially fixed during observation
Lissajous Orbit Description(Phase 1)
Flight DynamicsPage 8
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Formation Initialization
Direct Transfer (One LV with a C3 of -0.7 km2/s2)
Large ‘Halo’ Orbit No Lunar Shadows Max L2-Earth-Vehicle Angle 30 Orbit Does Not “Collapse”
Detector SC is maneuvered to the shifted orbit 200 km away Consider Initialization V as 6 Formation Re-Orientations FreeFlyers Stay Attached to Optics Hub
Flight DynamicsPage 9
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Formation KeepingSolar Radiation Pressure (SRP)
Acceleration Magnitude (1 AU) 4.5 x 10-6 (1+r) A/M (m/s2)
A = Cross Sectional Area exposed to Sun (m2) M = Mass of Spacecraft (kg) r = Reflection Factor. (r [0,1]) Approximate Result for all Mission Orbits Considered SMAD (3rd Edition, not 2nd edition)
SRP Acceleration Magnitude Differential Between 2 Spacecraft
4.5 x 10-6 | (1+r1) (A1/m1) – (1+r2) (A2/m2)| Assumed Dominant Term for 200 km Baseline (CRTBP model)
Assume Control Acceleration Magnitude 10-6 m/s2 Needed
Flight DynamicsPage 10
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Formation Re-OrientationFree Space Analysis (1/4)
Preliminary “Drift-Away” Orbit Results For “small” reorientation times (< 1 week), solar gravity has
“small” effect on V costs. Free space analysis (ie, gravity free) is a reasonable
approximation for small reorientation times in a “Drift Away” Further Study Needed (Especially for Applicability to
Lissajous Orbits)
Optics Hub
200 km
200 km
10
DistanceDetector at Obs 1
Detector at Obs 2
Flight DynamicsPage 11
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Formation Re-OrientationFree Space Analysis (2/4)
Impulsive Burn Analysis
One burn after obs 1 initiates translation of detector to the obs 2 location Magnitude: VImpulse = distance / reorientation time
Equal but opposite burn stops translation when obs 2 location is reached Total V = 2* VImpulse
Continuous Thrust Analysis
Acceleration is constant toward obs2 location for first half of the time Acceleration is of the same magnitude, but reversed for the remaining
time Total V (m/s) = 4*Vimpulse Acceleration = 4*Vimpulse / reorientation time
= 4*distance / (reorientation time)2
Flight DynamicsPage 12
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Formation Re-OrientationFree Space Analysis (3/4)
V Costs (both Continuous and Impulsive)
Linear Relationship with Distance Inverse Linear Relationship with Re-Orientation Time
Control Acceleration Magnitude (Continuous)
Linear Relationship with Distance Inverse Square Relationship with Re-Orientation Time
Flight DynamicsPage 13
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Formation Re-OrientationFree Space Analysis (4/4)
1 dayImpulsi
ve
1 dayContinuo
us
1 WeekImpulsive
1 WeekContinuous
Total V (m/s)
0.8 1.61 0.12 0.23
Acceleration (m/s2)
N/A 1.9 e-5 N/A 3.81 e–7
Notes: (1) 200 km baseline, (2) 10 re-orientation of Detector SC
Flight DynamicsPage 14
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Continuous Low Thrust Summary
Detector - Phase 1
Formation Keeping1 day1
Formation Reorientati
on1 day2,3
Formation Reorientation
(Delta)7 days2,3
Total V (m/s)
0.0864 1.61 0.23
Acceleration (m/s2)
1e-6 1.9 e-5 3.81 e-7
Notes: (1) Formation Keeping Costs Highly Dependent on SRP and thus the relative A/M ratios for the spacecraft. (2) The Formation Re-Orientation Costs are based on Free Space Calculations. This number should be multiplied by a “CorrectionFactor” > 1 to account for the L2 orbit. Low Thrust Software Needed for Future Refinements. (3) The Formation Reorientation values are considered a “delta” above the baseline Formation Keeping costs. (4) All Numbers are Coarse approximations.
Flight DynamicsPage 15
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Lissajous Orbit Option
Phase 2
Flight DynamicsPage 16
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Possible Configuration Optics Hub has Minimal or no Propulsion Detector SC moves to a distance of 20,000 km from Optics Hub FreeFlyer SC Separates from Optics hub to a maximum separation of 500 m New Baseline May Require New Class of Continuous Thrusters for Detector SC
Formation Initialization (Phase 2, 20000 km Baseline)
Detector S/C(Phase 2)
Optics Hub S/C 20,000 km
FreeFlyer S/C
500 m
200 km
Detector S/C (Phase 1)
Flight DynamicsPage 17
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Formation Keeping(Phase 2)
Same 10-6 m/s2 from SRP Differential Assumed Larger Baseline Dynamics Plays a Greater Role
Control Acceleration Magnitude Depends on Position of SC in its Orbit Choice of Target
Sample Mission Orbit (Calculation Purposes Only)
Optics Hub at L2 Detector SC moves in a Circle about L2
20,000 km Radius In Ecliptic Plane Clockwise Motion (360/yr) Circular Restricted Three Body Problem No Other Forces modeled
Control Acceleration 10-5 m/s2
Combined Accel Mag 1.1 x 10-5
m/s2
Flight DynamicsPage 18
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Formation Re-Orientation
Free Space Analysis (Detector, Phase 2)
1 dayImpulsi
ve
1 dayContinuo
us
1 WeekImpulsive
1 WeekContinuous
Total V (m/s)
0.8 e2 1.61 e2 1.2 e1 2.31 e1
Acceleration (m/s2)
N/A 1.9 e-3 N/A 3.81 e-5
Notes: (1) 20000 km baseline, (2) 10 re-orientation
Flight DynamicsPage 19
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Continuous Low Thrust Summary
Detector - Phase 2
Formation Keeping1 day1
Formation Reorientatio
n1 day2,3
Formation Reorientation
(Delta)7 days2,3
Total V (m/s)
0.95 1.61 e2 2.31 e1
Acceleration (m/s2)
1.1 e-5 1.9 e-3 3.8 e-5
Notes: (1) Formation Keeping Costs Highly Dependent on SRP and thus the relative A/M ratios for the spacecraft. (2) The Formation Re-Orientation Costs are based on Free Space Calculations. This number should be multiplied by a “Correction Factor” > 1 to account for the L2 orbit. Low Thrust Software Needed for Future Refinements. (3) The Formation Reorientation values are considered a “delta” above the baseline Formation Keeping costs. (4) All Numbers are Coarse approximations.
Flight DynamicsPage 20
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Continuous Low Thrust Summary
FreeFlyer - Phase 2
Formation Keeping1 day1
Formation Reorientatio
n 1 day2,3
Formation Reorientation
(Delta)7 days2,3
Total V (m/s)
0.0864 4.1 e-3 6 e-4
Acceleration (m/s2)
1e-6 4.7 e-8 1 e-9
Notes: (1) Formation Keeping Costs Highly Dependent on SRP and thus the relative A/M ratios for the spacecraft. (2) The Formation Re-Orientation Costs are based on Free Space Calculations. This number should be multiplied by a “CorrectionFactor” > 1 to account for the L2 orbit. Low Thrust Software Needed for Future Refinements. (3) The Formation Reorientation values are considered a “delta” above the baseline Formation Keeping costs. (4) 500 m baseline (5) All Numbers are Coarse approximations.
Flight DynamicsPage 21
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
DeltaV Analysis (All Phases)
Flight DynamicsPage 22
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
DeltaV Summary (1 of 3)
L2 Propulsion Insertion Module Carries All SC in Formation
Launch Vehicle Correction
Contingency
Mid-Course Correction (MCC)
Lissajous Orbit Insertion (LOI)
200 m/s – High Thrust
Flight DynamicsPage 23
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
DeltaV Summary (2 of 3)
Detector SC 125 m/s High Thrust for Lissajous Stabilization and Contingencies
25 m/s * 5 years
32 m/s Continuous Low Thrust for Formation Keeping in Phase 1 1e-6 m/s2 * 1 yr
117 m/s Continuous Low Thrust for Re-Orientation (1 day) in Phase 1 (45 targets) * (1e-6 + 1.9 e-5) m/s2 * (1 day to reorient) * (Correction Factor
of 1.5)
1389 m/s Continuous Low Thrust for Formation Keeping in Phase 2 1.1 e-5 m/s2 * 4 yr
2042 m/s Continuous Low Thrust for Re-Orientation (7 day) in Phase 2 (45 targets) * (1.1 e-5 + 3.8 e-5) m/s2 * (7 day to reorient) * (Correction
Factor of 1.5)
Flight DynamicsPage 24
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
DeltaV Summary ( 3 of 3)
Optics Hub 125 m/s High Thrust for Lissajous Stabilization and Contingencies
25 m/s * 5 years
FreeFlyer SC (per SC) 100 m/s High Thrust for Lissajous Stabilization and Contingencies
25 m/s * 4 years
380 m/s Continuous Low Thrust for Formation Keeping (Phase 2) 1e-6 m/s2 * 4 yr * (Correction Factor of 3)
13 m/s Continuous Low Thrust for Re-Orientation in 1 day (Phase 2) (45 targets) * (1 e-6 + 4.7 e-8) m/s2 * (1 day to reorient) * (Correction Factor of
3)
Notes: (1) In Phase 2, the Detector SC re-orients in 1 week while the FreeFlyers re-orient in 1 day. (2) All V values for all SC do not include engineering penalties, ACS Penalties, and cant angles. (3) Formation Re-Orientation (10) values include the necessary Formation Keeping contribution. (4) Double Counting of Formation Keeping costs during a Re-Orientation used to account for formation Acquisition Costs. (5) Formation Initialization Costs not explicitly listed here
Flight DynamicsPage 25
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Flight DynamicsTechnologies Required
Control Law algorithm development Improved Control Performance Collision Avoidance Re-Acquisition of Formation after Re-Orientation
Simulation Continuous Thrust model High Fidelity Force model
Relative Navigation needed Current Ground based Orbit Determination : 5 km position
knowledge
Flight DynamicsPage 26
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Flight DynamicsAdditional Trades to Consider
Continuous Low Thrust Transfer to L2 Feasibility of Using Low Thrust for Lissajous
Stabilization Consider Surface Coatings on SC or Other Methods to minimize
SRP Differentials Formation Keeping Costs are a function of Both Position
in Orbit and Choice of Target. By judicious choice of target sequence, Some V Optimization can be Realized.
Detailed Trajectory Design Study to Include Lissajous vs. Heliocentric Trade
Heliocentric Orbits with Better Communication Some can be Achieved Via Only Launch Vehicle
Considerations Distant Retrograde Orbits (~200 m/s)
Flight DynamicsPage 27
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Flight DynamicsIssues and Concerns
Continuous Thrusting will make OD more Difficult Very Difficult to Choose Class (acceleration magnitudes)
of Propulsion Systems Needed Very Coarse Estimates of Control Acceleration Magnitudes Different Phases of Mission New Technology: Thrusters with Greater Range of Thrust
Modulation? Relative Orbit Position Control & Knowledge
Requirements Orders of Magnitude above Current Operational Capability
Collision Avoidance Further extensive analysis required
High fidelity simulation w/ all force perturbations and sensor/actuator noise and error
Control Law Evaluation Continuous Low Thrust Simulations Continuous Low Thrust Trajectory Optimization Software Needed
Flight DynamicsPage 28
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
SupplementaryMaterial
Flight DynamicsPage 29
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Miscellany
Satellite Operators Should employ strategies to balance the fuel usage amongst all the SC in the Formation
Flight DynamicsPage 30
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
SupplementaryMaterial – Lissajous Orbit
Flight DynamicsPage 31
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Sample Impulsive Re-Orientation (1 of 2)
(20,000 km baseline, 10 in 7 days)
Force model Full Ephemeris Sun/Earth/Moon/Jupiter Point Mass SRP Both SC Have same A/M Ratio (Cr A/M = 0.013)
Initial Optics Hub State (ECI MJ2000) UTC Gregorian Date: 23 Jan 2003 05:02:45.56 UTC Julian Date: 2452662.71024955 X: -993733.7803065266900000 km Vx: -0.3149752411661734 km/sec Y: 913746.5347422765300000 km Vy: -0.2540742769815505 km/sec Z: 396534.8804631549300000 km Vz: -0.0421253073023613 km/sec
Initial Detector State Offset Position by b1 = 20000*(1, 0, 0) Identical Velocity
Final Optics Hub State UTC Gregorian Date: 30 Jan 2003 05:02:45.56 X: -1.1621310681357966e+006 km Vx: -0.2462221518003097 km/sec Y: 757799.1103539797500000 km Vy: -0.2561905904275567 km/sec Z: 369320.0722157274700000 km Vz: -0.0457073285913774 km/sec
Final Detector State Offset Position by b2 = 20000*(cos(10),sin(10), 0) Identical Velocity
Flight DynamicsPage 32
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Sample Impulsive Re-Orientation (2 of 2)
Astrogator Simulation First Maneuver Magnitude of 7.3 m/s Second Maneuver Magnitude of 4.4 m/s Total Maneuver Magnitude of 11.7 m/s
Free Space Approximations (Impulsive) Two Equal Impulsive Maneuvers of 6 m/s Total V of 12 m/s
Comparison of Astrogator vs. Free Space Fairly Good Agreement for this Sample Case Small Re-Orientation Times Astrogator’s Unequal Maneuver Size Need for Previously Discussed
“Correction Factor”
Flight DynamicsPage 33
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Sample Lissajous Orbit Delta-V Budgets
Direct TransferC3 = -0.677 km2/kg2
Lissajous 800(y-amplitude ~ 800K
km)
Direct TransferC3 = -0.677 km2/kg2
Lissajous 400(y-amplitude ~ 400K
km)
Transfer with Phasing Loops
andLunar FlybyC3 = -2.6 km2/kg2
Lissajous 200(y-amplitude ~ 200K
km)
Correct Delta Inaccuracy
50 m/s 50 m/s 20 m/s
Phasing Loops n/a n/a 50 m/s
Final Perigee Correction
n/a n/a 15 m/s
Midcourse Corrections 5 m/s 5 m/s 5 m/s
Lissajous Insertion 2 m/s 108 m/s 5 m/s
Lunar Shadow Avoidance
N/A 10 m/s per yr 10 m/s per yr
Trajectory Maintenance
4 m/s per yr 4 m/s per yr 4 m/s per yr
Total, 5 years 77 m/s 233 m/s 165 m/s
Notes: (1) Total does not include engineering penalties,ACS Penalties, finite burn losses, cant angle, contingencies. Low Thrust not Considered here. (2) No Corresponding Chart for Heliocentric Orbit Option
Flight DynamicsPage 34
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Direct vs. Phasing Loop Transfer
(Lissajous Orbit Option)
Phasing Loops with Lunar Swingby More Robust Operationally Complex 10 Launch Days per Month
(MAP 3 & 5 loop option) Reduced C3 Costs (Not
really a factor here)
Direct Transfer Higher Risk (Little Time to
React to Unforeseen Contingencies)
Simpler Operationally 22 Launch Days per Month
Constellation-X Example. Courtesy Lauri Newman
Flight DynamicsPage 35
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Libration Point Trajectory Manifolds
L1 L2L3
L5
L4
Y
zeclipticnorthpole
xview from the
ecliptic north pole
~1.5 x106 km
Earth/Moon
Flight DynamicsPage 36
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Selected Lissajous Orbit Option Issues
Define Lissajous Orbit Parameters Phasing Loop vs. Direct Transfer Define Maximum L2-Earth-Spacecraft Angle for
Communication Purposes (MAP was 10.5 degrees) Define how sensitive Spacecraft is to Shadow in Phasing
Loops Review Lessons Learned from Other Libration Point Missions
such as MAP & Triana Insure that Thrusters are sized large enough to produce
Desired DeltaV in a Reasonable time (For Transfer Trajectory)
Flight DynamicsPage 37
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Large Lissajous / Direct Transfer
projection onto ecliptic plane(ie, top view)
projection onto xz plane(ie, side view)
projection onto yz plane(ie, view from earth)
Flight DynamicsPage 38
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Small Lissajous / Direct Transfer
projection onto yz plane(ie, view from earth)
projection onto ecliptic plane(ie, top view)
projection onto xz plane(ie, side view)
Flight DynamicsPage 39
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Small Lissajous / Lunar Gravity Assist
•Y-Amp ~ 200k
•Z-Amp ~ 300k
projection onto yz plane(ie, view from earth)
projection onto ecliptic plane(ie, top view)
projection onto xz plane(ie, side view)
Flight DynamicsPage 40
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Triana (L1 Lissajous Orbit) DSN/USN Support Requirements
(Example from Triana Peer Review)
Mission Phase Tracking RequirementsTTI => TTI + 6 hrs All DSN 26-m stations with view of Triana will be scheduled
for continuous support;USN station may be prime for first contact, depending on
TTI longitude
TTI + 6 hrs => TTI + 72 hrs DSN prime, continuous support from 26-m and 34-m sites;USN as backup
TTI + 72 hrs => TTI + 144 hrs At least 4 hrs per day of range and range ratedata from USN sites in alternating hemispheres;At least 2 hrs per day of range and range rate
data from DSN sites in alternating hemispheres
TTI + 144 hrs => LOI + 6 weeks At least 4 to 6 hrs per day of range and range ratedata from USN sites in alternating hemispheres;
DSN as backup
After LOI + 6 weeks 16 hrs of range rate and 20 minutes of range data per dayfrom USN sites, alternating between hemispheres
Note: Since USN had planned Dedicated Triana Support, Some of these Requirements may be Overkill. Data Courtesy Greg Marr.
Flight DynamicsPage 41
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
MAP Lunar Shadows (L2 Lissajous Mission Orbit)
Sample Worst Cases MAP is a small amplitude Lissajous
Moon Farther from L2 8 Hour Shadow with Maximum Depth of 4.5%
Moon Closer to L2 6 Hour Shadow with Maximum Depth of 13%
Note: Data courtesy Mike Mesarch
Flight DynamicsPage 42
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
SupplementaryMaterial – Heliocentric Orbit
Flight DynamicsPage 43
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
MAXIM-PF Range From Earth(Heliocentric Orbit Option)
Reference: August 99 MAXIM IMDC Study
Flight DynamicsPage 44
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
MAXIM-PF Trajectory in Solar Rotating Coordinates(Heliocentric Orbit Option)
Reference: August 99 MAXIM IMDC Study
Flight DynamicsPage 45
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Heliocentric Orbit Option
Phase 1
Flight DynamicsPage 46
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Formation Initialization
One LV with a C3 of 0.4 km2/s2
Needed to put the trajectories beyond Earth’s sphere of influence (SOI is ~106 km) Relatively Quickly
One SC is maneuvered to the shifted orbit 200 km away from the other’s origin
Flight DynamicsPage 47
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Desired Characteristics
Two S/C in formation, 200 km apart
Maintain inertial orientation of SC-to-SC line for 1 week observation
One SC follows a circular, heliocentric orbit
Other SC follows a shifted, circular, heliocentric trajectory with orbit plane parallel to the plane of the first SC
Center of shifted trajectory lies on the Sun-target line 200 km from Sun
Driving Requirements
Time allocated for reorienting the SC-to-SC line
SC-to-SC line remains inertially fixed during observation
Heliocentric Orbit Description(Phase 1)
Flight DynamicsPage 48
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Formation Keeping (1/2)(Heliocentric Orbit, Phase 1, 200 km
Baseline)
Apply control accelerations continuously to maintain the inertial orientation of the SC-to-SC line
~0.01 m/s per week Only Solar Gravity modeled Circular Earth Orbit about
Sun SRP Differential
Acceleration not considered here (Very Important Term)
Maximum control accelerations
are needed when the trajectories are coplanar (it’s counter-intuitive)
0.8 x 10-8 to 1.6 x 10-8 m/s2
8 to 16 micro-newton thrust for a 1000 kg SC
Control acceleration magnitude-vs-
time since station-keeping starts
Flight DynamicsPage 49
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Formation Keeping (2/2)(Heliocentric Orbit, Phase 1, 200 km
Baseline)
Control Acceleration Magnitude Depends on
Position of SC in its Orbit Choice of Target
Control Acceleration Magnitude Varies (Approximately) Linearly with Baseline Assuming:
For Our Range of Baselines Ecliptic Target with RA=DEC=0 Only Solar Gravity modeled Circular Orbit
Flight DynamicsPage 50
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
SupplementaryMaterial – General
Flight DynamicsPage 51
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
Formation Re-OrientationFree Space Analysis Revisited
Impulsive Analysis One Burn at Observation 1 (Magnitude V1) & One Burn (Same Magnitude,
Opposite Direction) at Observation 2 V1 (m/s) = Distance (m) / t0 (s) Total V (m/s) = 2 V1 = 2 * Distance (m) / t0(s) (t0 is time to re-orient)
Continuous Thrust Analysis Acceleration is a positive constant (magnitude A) from t = 0 to t = t0/2 Acceleration is a negative constant (same magnitude) from time t0 /2 to
time, t0 At time, t=0 & t = t0, Velocity is 0 At time, t= t0/2, Velocity reaches a maximum of V2 = 2 V1 = 2 * Distance
/t0 Total V (m/s) is Twice that of Impulsive Case: 4 * Distance / t0 A = Distance / (t0/2)2 = 2 V2 / t0 = 4 V1 / t0
Flight DynamicsPage 52
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
References (1 of 3)
Marr, Cooley, Franz, Roberts, Triana Trajectory Design Peer Review, 2001.
Cuevas, Newman, Mesarch, Woodard, An Overview of Trajectory Design Operations for the MAP Mission, AIAA 2002-4425, AIAA Astrodynamics Specialist Conference, August 2002.
Mesarch, Andrews, The Maneuver Planning Process for the MAP Mission, AIAA 2002-4427, AIAA Astrodynamics Specialist Conference, August 2002.
Mesarch, Contingency Planning for the MAP Mission, AIAA 2002-4426, AIAA Astrodynamics Specialist Conference, August 2002.
L. Newman, Constellation-X Reference Mission Description Document, Govind Gadwal, ed., 2002.
Mesarch, Vaughn, Concha, Flight Dynamics IMDC Study for the MAXIM Mission, August 1999.
Flight DynamicsPage 53
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
References (2 of 3)
Cooley, Marr, Starin, Petruzzo, Flight Dynamics IMDC Study for the Fresnel Lens Gamma Ray Telescope, January 2002.
Cooley, Marr, Starin, Petruzzo, Flight Dynamics IMDC Study for the Fresnel Lens Gamma Ray PathFinderTelescope, January 2002.
Concha, Cooley, Folta, Hamilton, Flight Dynamics IMDC Study for the Stellar Imager, July 2001.
Markley, Maxim Mission White Paper, January 31, 2002. Grady, MAXIM Pathfinder Mission Concept Design
Powerpoint Presentation, MPF Mission Definition Team Meeting, September 18, 2000.
Wertz, ed., Spacecraft Mission Analysis and Design, 3rd Edition, Microcosm, 1999.
Flight DynamicsPage 54
Final Version
MAXIM-PF, May 13-17, 2002Goddard Space Flight Center
References (3 of 3)
Luquette, Sanner, A nonlinear approach to spacecraft formation control in the vicinity of a collinear libration point, AAS001-330, 2001.