INVESTIGATION OF ALTERNATIVE RETURN STRATEGIESFOR 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. HowellPurdue University

Michael W. Weeks

NASA Johnson Space Center

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

Precision Earth Entryfrom Polar LLO

Ephemeris (EPHEM) Model:Sun Perturbed Earth-Moon System

( ) ( ) ( )( )( )

( ) ( )( ) ( )

( )( )

1 1111 1 31 2

1 1 11

3

3 3 32

, , ,j js

s

js j js

P P P PP PPP P P PP P

PP P P P P PP Pj

r t r t r tf t x t x t x t

r t r t r t r t

µµ

=

− = − − + −

∑

( ) ( )1 31 2 , From JPL DE405 EphemeridesP PP Pr t r t ⇒

Moon (P2)

Earth (P1)

Sun (P3) Spacecraft (PS)

1 sP Pr1 2P Pr

1 3P Pr

( )2000ˆ

ECI JX γ

11

1

ss

s

P PP P

P PECI

rx

r

=

( ) ( ) ( )( )1

1 1 1 31 2

1, , ,

ss s

s

P PECIP P P P P PP PECI

P PECI

rx f t x t x t x t

r

= =

The Synodic Rotating Frame (SRF)

x

y

Lunar Orbit(Based on Planetary Ephemerides)

Moon (M)

Earth (E)

EMr

ECI = Earth Centered Inertial Frame (EME J2000)SRF = Synodic Rotating Frame

Ephemeris Model vs.The Circular Restricted 3-Body Problem

CR3BPEPHEM

x

y

( )a t

Spacecraft (PS)

1 sP Pr x

y

a

Spacecraft (PS)

1 sP Pr

The Hill Sphere in the Earth-Moon CR3BP

33

Moons

Earth

r a µµ

=

x

y

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

Assessing Entry Constraint Couplingand it’s Impact on Startup Arc Selection

• For each Earth Entry Interface (EEI-k, for k=1,…,6) State1. 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 CR3BP6. Identify Ωk’ H

( ) ( ) ( ) ( ) ( )( )1 1 1 1 31 2, , ,s s s

EEI

tP P P P P P P PP P

EEIt

x t x t f x x x dτ τ τ τ τ= + ∫

EEI-1 Dispersion Manifolds:Intersections w/ Hill Sphere (SRF View)

L5

L2

L4

Lat/Lon of Intersections Along Hill Sphere

Intersections with Hill Sphere

EEI-2 Dispersion Manifolds:Intersections w/ Hill Sphere (SRF View)

L3

L4 L1

L5

L3 L5

L4L1

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 CanBe Deduced From Hill Sphere Projections

Impact of Entry Longitude Errors30

Iter

atio

ns14

Iter

atio

ns

+135

-135

Targets: Altitude = 121.912 km, FPA = -5.86 deg, ∆V = 1.5 kpsInitial Longitude: 76.01 deg

Impact of Entry Latitude Errors

21 It

erat

ions

10 It

erat

ions

4 Ite

ratio

ns+1.5

+0.5

-0.5

Targets: Altitude = 121.912 km, FPA = -5.86 deg, ∆V = 1.5 kpsInitial Latitude: -1.29 deg

Impact of Entry Azimuth Errors24

Iter

atio

ns8

Itera

tions

-24

+24

Targets: Altitude = 121.912 km, FPA = -5.86 deg, ∆V = 1.5 kpsInitial Azimuth = 8.41 deg

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.