Talk charts for 20th AAS/AIAA Space Flight Mechanics Meeting presentation, held in San Diego, CA on February 14-17, 2010

1. INVESTIGATION OF ALTERNATIVE RETURN STRATEGIES
FOR ORION TRANS-EARTH INJECTION DESIGN OPTIONS
Belinda G. Marchand and Sara K. Scarritt
The University of Texas at Austin
Thomas A. Pavlak and Kathleen C. Howell
Purdue University
Michael W. Weeks
NASA Johnson Space Center

2. Autonomous Targeting Goals
• LLO  EEI via 3 Deterministic ∆V’s
– EEI Targets: ALT, FPA & AZ, LAT & LON
– Controls: Up to 3 Deterministic ∆V’s
– Feasible Total ∆V < 1.5 km/sec
– Turn-key return capability required
• Targeting in Sun perturbed Earth-Moon 3BP
– N-body regimes (for N > 2)  Iterative Solution Process
– Feasible or Optimal Algorithms Require Startup Arc
– Quality of startup arc is crucial for onboard determination
• 2BP vs 3BP Startup Arcs

3. Precision Earth Entry
from Polar LLO

4. Ephemeris (EPHEM) Model:
Sun Perturbed Earth-Moon System
( ) ( ) ( )( )
( )
( ) ( )
( ) ( )
( )
( )
1 11
11 1 31 2
1 1 11
3
3 3 3
2
, , ,
j js
s
j
s j js
PP PPPP
PPP PPPP
P
PP PP PPPPj
r t r t r t
f t x t x t x t
r t r t r t r t
µ
µ
=
 
− =− − +
 
 −
 
∑
( ) ( )1 31 2
, From JPL DE405 EphemeridesPPPP
r t r t ⇒
Moon (P2)
Earth (P1)
Sun (P3) Spacecraft (PS)
1 sP P
r 1 2P P
r
1 3P P
r
( )2000
ˆ
ECI JX γ
1
1
1
s
s
s
PP
PP
PPECI
r
x
r
 
=  
 
( ) ( ) ( )( )
1
1 1 1 31 2
1
, , ,
s
s s
s
PPECI
PP PP PPPPECI
PPECI
r
x f t x t x t x t
r
 
= 
 




5. The Synodic Rotating Frame (SRF)
ˆx
ˆy
Lunar Orbit
(Based on Planetary Ephemerides)
Moon (M)
Earth (E)
EM
r
ECI = Earth Centered Inertial Frame (EME J2000)
SRF = Synodic Rotating Frame

6. Ephemeris Model vs.
The Circular Restricted 3-Body Problem
CR3BPEPHEM
ˆx
ˆy
( )a t
Spacecraft (PS)
1 sP P
r ˆx
ˆy
a
Spacecraft (PS)
1 sP P
r

7. The Hill Sphere
in the Earth-Moon CR3BP
3
3
Moon
s
Earth
r a
µ
µ
 
=   
 
ˆx
ˆy

8. Comparison of Moon-to-Earth Transfers:
CR3BP vs. EPHEM Models
Close-up View Near the Moon:
(SRF View)
Targets: Altitude = 121.912 km, FPA = -5.86 deg, ∆V = 1.0 kps

9. Assessing Entry Constraint Coupling
and it’s Impact on Startup Arc Selection
• For each Earth Entry Interface (EEI-k, for k=1,…,6) State
1. Uk = set of sample perturbed states relative to EEI-k
2. Wk = set of trajectories generated by
Wk forms the dispersion manifold for EEI-k.
3. Ωk = [SRFCECI] Wk
4. Ωk’= Ωk * a / a(t)
5. H = surface defined by Hill Sphere in the SRF of the CR3BP
6. Identify Ωk’ H
( ) ( ) ( ) ( ) ( )( )1 1 1 1 31 2
, , ,s s s
EEI
t
P P P P P P P PP P
EEI
t
x t x t f x x x dτ τ τ τ τ= + ∫

10. EEI-1 Dispersion Manifolds:
Intersections w/ Hill Sphere (SRF View)
L5
L2
L4
Lat/Lon of Intersections Along Hill Sphere
Intersections
with Hill Sphere

11. EEI-2 Dispersion Manifolds:
Intersections w/ Hill Sphere (SRF View)
L3
L4 L1
L5

12. L3 L5
L4
L1
EEI-3
L1
L4
L3
EEI-4
L5
L1
EEI-5
L5
L1
EEI-6
EEI-k (k=3,4,5,6) Dispersion Manifolds:
Intersections w/ Hill Sphere (SRF View)
EEI Constraint Coupling Can
Be Deduced From Hill Sphere Projections

13. Impact of Entry Longitude Errors30Iterations14Iterations
+135◦
-135◦
Targets: Altitude = 121.912 km, FPA = -5.86 deg, ∆V = 1.5 kps
Initial Longitude: 76.01 deg

14. Impact of Entry Latitude Errors
21Iterations10Iterations4Iterations +1.5◦
+0.5◦
-0.5◦
Targets: Altitude = 121.912 km, FPA = -5.86 deg, ∆V = 1.5 kps
Initial Latitude: -1.29 deg

15. Impact of Entry Azimuth Errors24Iterations8Iterations
-24◦
+24◦
Targets: Altitude = 121.912 km, FPA = -5.86 deg, ∆V = 1.5 kps
Initial Azimuth = 8.41 deg

16. Conclusions
• Without loss of generality, the precision entry problem can be
studied within the context of the CR3BP and the results are easily
transitioned and nearly identical to those in the EPHEM model.
• Intersections of EEI dispersion manifolds with Hill Sphere, in SRF,
yields useful information regarding entry constraint coupling. This
knowledge can be used in future studies to enhance startup arcs
and, subsequently, targeting performance.
• Validated constraint coupling conjectures, from Hill sphere
analysis, for FPA & LON, FPA & LAT, and FPA & AZ, by analyzing
targeter performance in the presence of EEI errors in LON, LAT, and
AZ, respectively.
• A multi-body analysis in the SRF of the Earth-Moon system offers a
more representative set of startup arcs than those obtained from
2BP approximations. The resulting improved startup arcs facilitate
an efficient onboard targeting process.