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- I. Introduction
- II. Concept of Indirect Planetary Capture
- III. Orbit Selection for Periodic Orbit
- IV. Simulation and Comparisons
- V. Conclusion
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS - - PowerPoint PPT Presentation
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS - - PowerPoint PPT Presentation
6 th International Conference on Astrodynamics Tools and Technique (ICATT) INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS LI Xiangyu, Qiao Dong, Cui Pingyuan Beijing Institute of Technology Institute of Deep Space
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- I. Introduction
Planetary Capture A key process in planet exploration mission Plays an important role in the trajectory design
Interplanetary Trajectory Mission Orbits
Planetary Capture
Capture Trajectory Design Fuel Consumption Flight System Design Interplanetary Trajectory Design Midcourse Correction INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
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Current Capture Strategy Direct Capture Aerocapture Ballistic Capture
Easy to design INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
- I. Introduction
Exploits the gravitational force of planets to capture a spacecraft Take advantage of the aerodynamic force to reduce the velocity
From Belbruno and Miller 1993
Single impulsive maneuver at periapsis
v
p
r v
Fuel Saving Protection for high heat rate and overload Precise guidance and control Low energy Capture Long transfer time Multi capture
- pportunities
Fall when is high
v
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Circular Restricted Three body Problem (CRTBP) Libration(Lagrange) Points Periodic orbits Stable/Unstable Manifolds
Space observation Capture to periodic orbit Low energy transfer
3 3 3 3 3 3
(1 )( ) ( 1 ) 2 (1 ) 2 (1 )
s m s m s m
x x x y x r r y y y x y r r z z z r r
Communication relay
- I. Introduction
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS Planetary Capture
Nakamiya and Scheeres (2008,2010) Wang (2014)
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Concept Use periodic orbit as a park orbit Connect with interplanetary trajectory by stable manifolds Connect with mission orbit by unstable manifolds
Periapsis maneuver Stable manifold Periapsis maneuver Periodic orbit about libration points Interplanetary Trajectory Unstable manifold Mission orbit Small perturbation
- II. Concept of Indirect Planetary Capture
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
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- II. Concept of Indirect Planetary Capture
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
Process Three impulsive maneuver First periapsis maneuver Perturbation to generate unstable manifolds Second Periapsis maneuver
1
v v
2
v
3
, v a e Initial guess and correction
Process Three impulsive maneuver First periapsis maneuver Perturbation to generate unstable manifolds Second Periapsis maneuver
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- II. Concept of Indirect Planetary Capture
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
Maneuver Three impulsive maneuver First periapsis maneuver Perturbation to generate unstable manifolds Second Periapsis maneuver
1
v v
2
v
3
, v a e Initial guess and correction
Design Construct the periodic parking orbit Generate proper unstable manifolds same periapsis distance as mission orbit Generate proper stable manifolds for interplanetary design and midcourse correction
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- III. Orbit Selection for Periodic Orbit
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
Orbit Selection Two criteria
- Energy constrain
First maneuver as low as possible
- State constrain
The periapsis distance of natural unstable manifolds should close to that of mission orbits
1
v
2 1
2 2
ex ps ex es ps ps
v v v v v v r r
2
es ps
v r
2 1 2 3 3 2 2
2 2 1 2 2 2 2
p p ps p p p p p
v r r v r r r r v v r r
0,
ps
v v r
Periapsis of stable manifolds should close to the surface of Mars
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INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
- III. Orbit Selection for Periodic Orbit
Sun-Mars System Planar Orbits Planar Lyapunov orbit
- L1 orbit from to
- L2 orbit from to
Periapsis distance of stable manifolds
4
7.3 10
y
A km
5
7.5 10
y
A km
5
1.0 10
y
A km
6
1.5 10
y
A km
5
5.5 10
yc
A km
5
5.7 10
yc
A km
Critical amplitude
yc
A
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- III. Orbit Selection for Periodic Orbit
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
Planar Orbits Periapsis distance of unstable manifolds from to
5
5.5 10
y
A km
Candidate parking orbits
L1 orbit from L2 orbit from
5
5.7 10
y
A km
3589km 300000km
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Planar Orbits Periapsis State Periapsis phase angle
- III. Orbit Selection for Periodic Orbit
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
10 20 ~ 50
L1:
190 140 ~ 260
L2:
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INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
- III. Orbit Selection for Periodic Orbit
Sun-Mars System Spatial Orbits Vertical Lyapunov orbit Large periapsis distance Infeasible Halo orbit
- L1 orbit from to
- L2 orbit from to
Periapsis distance of stable manifolds
5
2.9 10
zc
A km
Critical amplitude
4
2.7 10
z
A km
4
6.6 10
z
A km
4
3.7 10
z
A km
5
6.5 10
z
A km
5
2.9 10
zc
A km
zc
A
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- III. Orbit Selection for Periodic Orbit
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
Halo Orbits Periapsis distance of unstable manifolds from to Candidate parking orbits
L1 orbit from to L2 orbit from to
3589km 300000km
5
2.9 10
z
A km
5
2.9 10
z
A km
5
6.6 10
z
A km
5
6.5 10
z
A km
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Halo Orbits Periapsis State Orbital Inclination Periapsis phase angle Periapsis Spatial angle
- III. Orbit Selection for Periodic Orbit
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
20 i
L1: L2:
i 140 i 20 i 130 i
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Halo Orbits Periapsis State Orbital Inclination Periapsis phase angle Periapsis Spatial angle
- III. Orbit Selection for Periodic Orbit
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
10
L1: L2:
i 5 ~ 20 190 182 ~ 202
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Halo Orbits Periapsis State Orbital Inclination Periapsis phase angle Periapsis Spatial angle
- III. Orbit Selection for Periodic Orbit
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
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L1: L2:
i 41 17 40
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INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
- IV. Simulation and Comparisons
Direct capture Indirect capture First impulsive maneuver Perturbation velocity Third impulsive maneuver
2
2 (1 )
d p p
e v v r r
(1 )
p
r a e
2 1
2
ps ps
v v v r
3
(1 )
pu p
e v v r
2
1 / v m s
1 2 3
v v v v 3589
ps
r km
s p u
T T T T
Capture Time
s
T
Stable manifold transfer time
p
T
Parking time
u
T
Unstable manifold transfer time
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INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
- IV. Simulation and Comparisons
Mission Orbit I 200km circular orbit Parking orbit L2 planar Lyapunov orbit
5
5.7 10
y
A km (km/s) Direct Capture (km/s) Indirect capture (km/s) (km/s) (day) 1.88 1.780 1.779 775.37 0.001 2.09 1.859 1.858 0.001 3.39 2.492 2.487 0.005
v
d
v v
T
d
v v
Low orbit capture:
- Cost the same velocity as direct capture
Long transfer time Provides a chance to explore the space environment in the vicinity of Mars and Lagrange points without extra velocity increment
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INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
- IV. Simulation and Comparisons
Mission Orbit I 200km circular orbit Parking orbit L2 planar Lyapunov orbit
5
5.7 10
y
A km
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INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
- IV. Simulation and Comparisons
Mission Orbit II 800km*60000km elliptic orbit Parking orbit L2 Halo orbit (km/s) Direct Capture (km/s) Indirect capture (km/s) (km/s) (day) 1.88 0.518 0.493 696.85 0.025 2.09 0.602 0.572 0.030 3.39 1.272 1.205 0.067
v
d
v v
T
d
v v
5
4.6 10
z
A km
Middle orbit capture:
- As the periapsis of mission orbit increases, the indirect capture
requires less velocity than direct capture
- Save more fuel for higher excess velocity v
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Mission Orbit II 800km*60000km elliptic orbit Parking orbit L2 Halo orbit
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
- IV. Simulation and Comparisons
5
4.6 10
z
A km
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INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
- IV. Simulation and Comparisons
Mission Orbit III 20000km circular orbit Parking orbit L1 Halo orbit (km/s) Direct Capture (km/s) Indirect capture (km/s) (km/s) (day) 1.88 1.329 0.897 691.03 0.432 2.09 1.481 0.976 0.505 3.39 2.540 1.609 0.931
v
d
v v
T
d
v v
5
3.4 10
z
A km
High orbit capture:
- Save more than 30% velocity
- Keep the same efficiency in high v
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INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
- IV. Simulation and Comparisons
Mission Orbit III 20000km circular orbit Parking orbit L1 Halo orbit
5
3.4 10
z
A km
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- IV. Simulation and Comparisons
INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
Mission Orbit IV Elliptic orbit with different periapsis distances Parking orbit L1 Lyapunov orbit
0.9 e
- Cost is approximately constant regardless of the periapsis distance
2.5 / v km s
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INDIRECT PLANETARY CAPTURE VIA PERIODIC ORBIT ABOUT LIBRATION POINTS
- V. Conclusion
Indirect capture could save velocity increment than direct capture at the cost of long transfer time Shows better efficiency for high altitude and high
- rbit
insertion Extra scientific returns Increases transfer flexibility Reduce gravity loss
v
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