AAS 20-649

ARTEMIS I TRAJECTORY DESIGN AND OPTIMIZATION

Amelia L. Batcha⇤, Jacob Williams†, Timothy F. Dawn‡, Jeffrey P. Gutkowski§,

Maxon V. Widner¶, Sarah L. Smallwoodk, Brian J. Killeen⇤⇤, Elizabeth C.
Williams††
, and Robert E. Harpold‡‡

This paper presents the overall trajectory design and optimization process for
NASA’s Artemis I mission to send an uncrewed Orion vehicle to a lunar Distant
Retrograde Orbit (DRO). The on-orbit trajectory begins at the Space Launch Sys-
tem (SLS) core separation and ends at the Orion service module Earth Entry In-
terface (EI) point. The details of the trajectory optimization process are presented,
including design of nominal and extended mission options, launch windows, and
abort options. Novel design techniques are also discussed to account for contin-
gencies, such as using auxiliary thrusters to protect against main engine failure
and applying trajectory shaping to mitigate or reduce eclipse durations.

INTRODUCTION
Artemis I is the mission formerly known as Exploration Mission 1.1, 2 It will be the first integrated
test of NASA’s Orion spacecraft and the Space Launch System (SLS) rocket.3 The Artemis program
is the foundation for sustainable human lunar exploration and beyond. The key characteristic of the
Artemis mission design is to support extensible capabilities through an architecture utilizing the
SLS and Orion vehicles for an array of missions. SLS and Orion are used as the crew transport
for missions into cislunar space, including a rendezvous with a reusable habitation element (called
Gateway), and a Human Landing System (HLS) to return astronauts to the surface of the Moon.4
To achieve a successful lunar landing for Artemis III, Artemis I has key mission priorities that
demonstrate NASA’s capability to extend human presence on the Moon, including:
• demonstrate Orion’s heat shield at lunar return re-entry conditions,
• validate required system performance that is mandatory to support crewed missions,
• demonstrate SLS ascent and launch vehicle operations,
• operate systems in flight environment,
• demonstrate Orion deep space environmental performance, communications, propulsion, and
navigation systems,
• demonstrate Exploration Ground Systems (EGS) and day of launch operations,
⇤
EG/Aeroscience and Flight Mechanics, NASA Johnson Space Center, Houston, TX 77058
†
EG/Aeroscience and Flight Mechanics, NASA Johnson Space Center, Houston, TX 77058
‡
EG/Aeroscience and Flight Mechanics, NASA Johnson Space Center, Houston, TX 77058
§
EG/Aeroscience and Flight Mechanics, NASA Johnson Space Center, Houston, TX 77058
¶
Jacobs Technology, Houston, TX 77058
k
EG/Aeroscience and Flight Mechanics, NASA Johnson Space Center, Houston, TX 77058
⇤⇤
EG/Aeroscience and Flight Mechanics, NASA Johnson Space Center, Houston, TX 77058
††
a.i. solutions, Houston, TX 77058
‡‡
ERC Inc., Houston, TX 77058

1
 • demonstrate flight operations management and execution, and
• retrieve the Orion Crew Module (CM)
For Artemis I, an uncrewed Orion will fly a round-trip mission to a lunar Distant Retrograde Orbit
(DRO) on a trajectory that includes two lunar flyby maneuvers, providing an excellent opportunity
to test out Orion’s systems in the cislunar regime. This paper describes how the Artemis I reference
trajectories were designed and optimized while adhering to subsystem constraints, and integrating
ascent, orbit, and entry phases of flight.

GENERAL ASSUMPTIONS

Mission Design and Optimization

The Artemis I mission is optimized with NASA’s Copernicus spacecraft trajectory design and
optimization application5 using the SNOPT optimization method.6 Copernicus (shown in Figure
1) makes use of a multiple-shooting approach, and the mission is designed using numerous coast
and burn trajectory segments that are numerically integrated both backwards and forwards in time.
In addition, a number of customized Copernicus plugins are employed to model specific aspects of
the mission.7 Figure 2 displays a Directed Acyclic Graph (DAG) of all the mission components
(segments and plugins) as defined in Copernicus to optimize this mission. Segments 1–25 represent
the SLS/ICPS part of the mission, while segments 26–52 represent the nominal Orion mission, seg-
ments 53-54 represent the DRO, and segments 55–70 represent the Auxiliary Down Mode (XDM)
segments.

Vehicle Assumptions

The Orion spacecraft serves as the primary crew vehicle for NASA’s Exploration Systems De-
velopment (ESD) missions. It is capable of conducting in-space operations in conjunction with
payloads delivered by the SLS. It consists of four main elements: the CM providing a habitable
pressurized volume to support crew members and cargo, the Service Module (SM) consisting of the
European Service Module (ESM) and the Crew Module Adapter (CMA) responsible for propulsion,
heat rejection and power generation, the Spacecraft Adapter (SA) as a structural connection to the
launch vehicle, and the Launch Abort System (LAS) providing abort capability to transport the CM
away from the launch vehicle during ascent. For this trajectory design and optimization, only the
CM and SM of Orion are included.
Orion is attached to the Interim Cryogenic Propulsion Stage (ICPS), the upper stage of SLS.
The ICPS performs all propulsive maneuvers until the ICPS/Orion spring separation post-TLI, after
which the Orion SM provides propulsive support the rest of the mission. The Orion SM consists
of three engine types: the main engine Orbital Maneuvering System Engine (OMSe), secondary
Auxiliary (AUX) thrusters, and the Reaction Control System (RCS). Copernicus only models the
first two. The OMSe has a thrust of about 26,000 N, while the eight AUX thrusters combined have
a thrust of about 3,400 N (and a slightly lower Isp).

Environment Simulation

In Copernicus, all mission phases are integrated explicitly using the DDEABM integration method
(a variable-step size variable-order Adams-Bashforth-Moulton implementation) with a 10 12 error
tolerance.8 The JPL DE 421 ephemeris9 was used for the celestial body ephemeris of the Earth,

2
 Figure 1: Screenshot of Copernicus. Copernicus is used to design the Artemis I trajectory,
run the performance scans, and will also be used during the mission to provide real-time
optimization support.

S61
S60

S67 S68

S59
S64

S63
S6 S7

S11 S66
S74
S12 S65
S10 P6
S9
S13
S8 P12
S75 S48 S49

S14

S15 S50
S45 S46 S47
S58

S4 S5 S56
S3

S57
S16
S17
S18 S19 S20 S21 S22 S23
S34 S55
S35
S33 P4 P10

S36 S37
P11

S62 S38

S69

S44 S70 P8
S73
S1 S51

P14 S41 S42 S43

P1 P7

S53 S54 S40

S2 P5 S52
S39
P13
S29
S28 S30
S71 S25

S24 S72 S31

P2 P3

S32

S26
S27

P9

Figure 2: Copernicus Dependency Diagram. This shows the dependency information of the
segments and plugins in the mission. Circles are segments (red circles include finite burn ma-
neuvers) and squares are plugins. Arrows represent dependencies and dashed lines represent
constraints.

3
Moon, and Sun. The Earth departure phases use an 8⇥8 Gravity Recovery And Climate Experi-
ment (GRACE) GGM02C Earth gravity model.10 The Moon-centered phases use the Gravity Re-
covery and Interior Laboratory (GRAIL) GRGM660PRIM gravity model.11 A 50⇥50 model is
used for the close lunar flybys, a 4⇥4 model is used in the DRO, and an 8⇥8 model is used in other
cases. Third bodies are treated as point masses. The high-fidelity body fixed frames for the Earth
and Moon are used (i.e., IAU 76 80 from SOFA12 and MOON PA from SPICE, respectively) for
gravity models and the computation of geodetic parameters.

Destination Orbit
The destination orbit for Artemis I is a Moon-centered DRO. The details of this orbit were
described in an earlier paper,2 and an example is shown in Figure 3. The DRO is computed along
with the nominal mission as part of the same optimization problem. The initial state of the DRO is
propagated backwards in time to serve as the target for the DRO Insertion (DRI) burn. Note that the
nominal DRO is planar (i.e., in the Earth-Moon plane), but during the eclipse mitigation process, it
may be inclined (see subsequent eclipse section for details on this process).

Initial Epoch: 6 Sep 2018 17:16:25.075 TDB

Final State Constraint:

Moon
To Earth

Initial State:

Figure 3: Representative DRO Example (Earth-Moon Rotating-Pulsating Frame).2 When

targeting a DRO, a simple forward-shooting method is used to target a state two revolutions
after a perpendicular X-axis crossing. The only two control variables are the coast duration
t and the initial y-velocity (vy ) in the rotating-pulsating frame.

NOMINAL MISSION OVERVIEW

Figure 4 shows a visualization of a nominal Artemis I trajectory in Copernicus. The general
round-trip DRO trajectory design is largely based on earlier studies conducted for the Asteroid

4
 OTC-1
Earth OTC-2

TLI
Outbound
EI

OTC-5
DRI

RPF
Return
OPF Moon
DPC
DRD
RTC-4

DRO
Figure 4: Example Artemis-I Mission (Earth-Moon Two-Body Rotating Pulsating Frame).
This shows an example nominal mission case for a November 6, 2020 launch.

Redirect Crewed Mission (ARCM).13 The trajectory can be broken into three phases of flight:
Ascent, In-Space, and Entry. The Copernicus trajectory optimization software specializes in on-
orbit trajectory design, and therefore Copernicus plugins are used to simulate the ascent and entry
phases of flight which are discussed in the subsequent sections.
The trajectory begins at SLS Core Separation which places the ICPS/Orion stack into a 16 ⇥
975 nmi orbit (30 x 1806 km). The ICPS performs a Perigee Raise Maneuver (PRM) to raise the
perigee to 100 nmi (185 km). Then ICPS performs a Trans Lunar Injection (TLI) burn to target
the Outbound Powered Flyby (OPF) burn, which Orion performs as it flies by the Moon. About 10
minutes after TLI, an impulsive spring separation plugin models the separation between the ICPS
and Orion vehicles. The ICPS targets the Orion Target Interface Point (TIP) 40 seconds after the
spring separation. After another 41 seconds, Orion executes the Upper Stage Separation (USS)
burn to increase the separation distance with the ICPS. At 6 hours after TLI, Orion performs a
30 second Outbound Trajectory Correction (OTC)-1 burn to test the OMSe engine prior to its first
major burn behind the Moon with no communication to ground support – this is also called the
OMSe Checkout (OCO) burn component. Since ICPS performs a heliocentric disposal via lunar
flyby, the OTC-1 burn also reduces the ICPS and secondary payload recontact risk which is needed
since they are also headed towards the Moon. An optional OTC-2 burn can be used to provide the
optimizer with additional control to target OPF throughout a launch window. At the lunar flyby,
Orion performs its first major burn, OPF, followed by its second major burn, DRI, which inserts
Orion into the DRO. While in the DRO, an optional DRO Plane Change (DPC) burn may be used
to incline the DRO in order to avoid vehicle eclipse duration violations. After DRO operations, the
Orion performs the DRO Departure (DRD) burn to target the lunar Return Powered Flyby (RPF)

5
burn onto the Earth return trajectory. The return trajectory targets a high speed atmospheric entry
on the order of 36,000 ft/s (11 km/s), suitable for demonstrating the performance and effectiveness
of the Orion Thermal Protection System (TPS) heat shield, as well as relevant environments prior
to the first crewed launch of the system.

ASCENT TO SEPARATION

The first part of the mission (see Figure 5a) consists of the period from the SLS launch to the
separation of the Orion vehicle from the ICPS. This phase is initially included in the optimized
trajectory in Copernicus, using a plugin that queries a database of SLS launch trajectories14 gen-
erated at MSFC by the Program to Optimize Simulated Trajectories (POST) tool.15 This provides
Copernicus a close approximation of the ascent phase that can be used during optimization.16 The
SLS database consists of a set of data grids of core separation state vectors computed at monoton-
ically increasing launch azimuth values. Each point in the grid represents a single POST run over
an incremented launch azimuth sweep. There is one grid per month which uses the mean monthly
trajectory in order to account for seasonal wind variation. When setting up the mission for optimiza-
tion, the Copernicus plugin reads the launch epoch from the trajectory, and based on the calendar
month, will use the corresponding grid. During optimization, the CoreSep state is interpolated from
the grid using the launch azimuth as the independent variable.

All launch azimuths target a 16 ⇥ 975 nmi insertion orbit at Core Separation. Approximately 45
minutes after CoreSep, the vehicle stack has coasted near apogee where ICPS performs the PRM to
raise the Low Earth Orbit (LEO) perigee altitude to achieve a stable orbit condition. The TLI burn
begins prior to the next perigee passage and occurs at a true anomaly between 40 and 95 in
order to intercept the Moon throughout the launch period each month. The objective function to
be minimized for this problem is the combined ICPS and Orion total v. It should also be noted
that these targets are generated for a nominal short-class mission without the OTC-1 and OTC-2
maneuvers, or any Orion trajectory mitigations.

This entire mission phase, as seen in Figure 5a is considered an estimate since the ICPS phase
of flight is not officially modeled in Copernicus. After the initial optimization of the entire mission
(see Figure 6), feasible missions from this phase⇤ are reprocessed by the launch vehicle provider
to create a high fidelity simulation. The Orion trajectory team incorporates the high fidelity TLI
targets back into Copernicus through the use of a TLI targets plugin. Therefore, the Pre-ICPS/Orion
Spring Separation (see “Orion Sep” in Figure 5a) is then used as the starting point for the on-orbit
mission optimization. After these high fidelity targets are implemented, everything from launch to
this point is no longer directly modeled. The one optimization variable for this part of the mission
then becomes the launch epoch, which uniquely determines the corresponding Orion Sep state by
interpolation of the database. Note that, while the TLI targets plugin does support interpolation,
for production runs, interpolation is not necessary since all points in the database lie on the integer
UTC minute. These correspond to the points computed in the launch window scan (see subsequent
sections).

⇤
Points that exceed the available vehicle performance (e.g., if the azimuth and inclination bounds exceed SLS range
safety limits) are excluded.

6
 Core Sep
Ascent PRM TLI

Earth-Centered Orion Sep

(a) Launch to Orion Spring Separation. Ascent is performed by the SLS and the
Perigee Raise Maneuver (PRM) and Trans Lunar Injection (TLI) are performed
by the ICPS.
constr
Earth-Centered
Moon-Centered

OPF (XDM)

USS OTC-1 OTC-2 constr

DRI DRO

OPF OTC-5 DRI (XDM)

Orion Sep Orion TIP (XDM)
constr

(b) Orion Spring Separation to DRO Insertion. The outbound part of the mission includes two major
burns: OPF and DRI. The Auxiliary Down Mode (XDM) branch is constrained to arrive at the post-
DRI epoch at the same time, state and mass as the nominal OMSe branch.
(Nominal)

Nominal DRD
DPC 1 DRO rev
Nominal EI
~~
~

Short Class +1 day

~~

+2 days
~

+1 rev - 2 days
~
~~

+1 rev - 1 day
~~

Long Class +1 rev EI

~~

+1 rev + 1 day
~~

+1 rev + 2 days
~

(c) DRO Stay Time and Mission Duration for Different Mission Classes. Extended missions can be
used to achieve desired landing lighting conditions not otherwise possible with the nominal mission of
approximately 26 days.
Moon-Centered
Earth-Centered

RPF (XDM)

constr constr
DRO DRD EI

RPF
RTC-4 (XDM)
(d) DRO Departure to Earth EI. The return part of the mission includes two major burns: DRD and
RPF. The Auxiliary Down Mode (XDM) branch is constrained to arrive back on the nominal trajectory
at the conclusion of RTC-4.
constr
Figure 5: Mission Timelines. In these charts, indicates continuity constraints in
the multiple shooting transcription. States are propagated forward and backward from the
epochs (the direction of propagation is indicated by the arrows). The red lines are burns and
the black lines are coasts.

7
 Figure 6: ICPS and Orion Vehicle Performance for Launch Targets Generation Scan. For the
initial scan, the entire mission is optimized from ascent to EI which is used to generate the
launch targets. This plot shows three example launch periods at the beginning of 2021.

ORION ON-ORBIT TRAJECTORY

The Orion in-space portion of the trajectory begins at the ICPS/Orion Spring Separation (“Orion
Sep” in Figure 5a). For optimized trajectories incorporating the TLI targets plugin, this state and
time are entirely functions of the launch epoch. Figures 5b-5d show the detailed timelines of the
on-orbit portion of the Artemis I mission, from Orion Spring Separation to Entry Interface (EI).
In these diagrams, the arrows indicate the direction of propagation of the mission phases in the
Copernicus multiple-shooting transcription. Segments numerically integrated forward from one
time (e.g., tOP F ) and backwards from a later time (e.g., tDRI ) have intermediate state, time, and
mass constraints imposed to achieve a continuous mission when converged. Once the ascent to
Orion separation mission phase is eliminated using the TLI database, the objective function is the
total Orion v required, which is to be minimized.
The thrust directions for all burns are modeled by the spherical angles ↵ (right ascension) and
(declination), as functions of time:17

↵(t) = ↵0 + ↵˙0 (t t0 ) (1)

(t) = 0 + ˙0 (t t0 ) (2)

Where t0 is the burn start time, and the direction of the thrust vector û at time t is given by:

û(t) = [cos ↵(t) cos (t)]ê1 + [sin ↵(t) cos (t)]ê2 + [sin (t)]ê3 (3)

Where the basis vectors [ê1 , ê2 , ê3 ] can be:

• the IJK frame (ê1 = i, ê2 = j, ê3 = k)
• the Copernicus VUW controls frame (ê1 = v/kvk, ê3 = h/khk, ê2 = ê3 ⇥ ê1 ).
• the Copernicus VNC controls frame (ê1 = v/kvk, ê2 = h/khk, ê3 = ê1 ⇥ ê2 )
Note that these frames can be defined in either an inertial or rotating reference frame. In some cases
(e.g. OPF and RPF), burns are parameterized in a “VUW” Earth-Moon rotating-of-date frame⇤ so
⇤
An “of-date” frame in Copernicus is an inertial frame where the rotating frame is fixed at an epoch

8
that when stepping through epochs in the scan, the previous case seeds a better initial guess for the
next case. The significant burns in the mission are:
• Upper Stage Separation (USS) : Used to reduce near-field recontact risk. A fixed v =
5.5 ft/s (1.6764 m/s) burn along the velocity vector.
• Outbound Trajectory Correction (OTC)-1 : Includes the OCO burn component, a 30 sec burn,
optimized ↵ and , parameterized as J2000-VNC.
• Outbound Trajectory Correction (OTC)-2 : A small AUX burn (used nominally during the
launch window as an extra control in order to allow the OPF epoch and DRO state to be
fixed), optimized ↵ and , parameterized as J2000-IJK.
• Outbound Powered Flyby (OPF) : A major burn with optimized t, optimized ↵ and ,
parameterized in an Earth-Moon Two-body rotating “of date” VUW frame. This burn is mostly
in the anti-velocity direction.
• DRO Insertion (DRI) : A major burn with optimized t, optimized ↵ and , parameterized
in an Earth-Moon Two-body rotating “of date” IJK frame.
• DRO Plane Change (DPC) : An optional burn used to incline the DRO, with optimized t,
optimized ↵ and , parameterized in an Earth-Moon Two-body rotating “of date” IJK frame.
• DRO Departure (DRD) : A major burn with optimized t, optimized ↵ and , parameterized
in an Earth-Moon Two-body rotating “of date” IJK frame.
• Return Powered Flyby (RPF) : A major burn with optimized t, optimized ↵ and , parame-
terized in an Earth-Moon Two-body rotating “of date” VUW frame. This burn is mostly in the
velocity direction.
In general, the major optimization variables are:
• The finite burn control law parameters ↵0 , 0 , (and optionally ↵˙0 , and ˙0 ) for each of the
optimized maneuvers.
• The burn time t for each of the optimized maneuvers.
• The various intermediate flight times.
• The launch epoch.
• The OPF and RPF flyby epochs.
• The OPF and RPF flyby state parameters (periapsis radius, eccentricity, inclination, ascending
node, argument of periapsis, and true anomaly). At the start of the burn, the flyby periapsis
radius is bounded to be no less than 100 km above the lunar surface. The true anomaly is
bounded to be within ±90 .
• The EI epoch.
• The EI longitude, latitude, velocity, azimuth, and flight path angle. The EI state is numerically
integrated backwards and constrained to provide state and time continuity with the forward-
integrated return trajectory (this allows for specifying the EI altitude directly rather than being
imposed as a nonlinear constraint). The geodetic altitude is specified to be 121.92 km.
The main problem constraints are:
• The various time and state continuity conditions along the trajectory (see Figure 9).
• There is a minimum 5.15 day outbound (launch to OPF) flight time constraint in order to
maximize flight time and ensure consistency for the secondary payloads on board ICPS.
• The EI longitude, azimuth, and flight path angle are constrained to be on the EI target line
(see Figure 7). The nominal and XDM return phases are specified to have the same EI state
and time.

9
 • Auxiliary Down Mode (XDM) constraints as explained in the next section.

It is important to note that the EI state is parameterized in an Earth-fixed reference frame, which
will produce locally-optimal solutions roughly every day for the EI epoch. The problem setup (i.e.,
propagating backwards in time from EI) makes it straightforward to vary the EI epoch in the scan
by one day increments and quickly re-converge the solution.

AUXILIARY DOWN MODE

While the nominal Artemis I mission utilizes the OMSe throughout, the OPF and RPF phases
each include a parallel trajectory option in which Orion performs an Auxiliary Down Mode (XDM),
and continues the duration of the region using these secondary thrusters, deviating from the nominal
OMSe trajectory. These parallel trajectories are a part of the optimization problem in order to protect
against a main engine failure. During the Shuttle program, trajectory flight controllers assessed
thruster downmode contingencies in the event of an OMSe failure, in an attempt to minimize the
penalty that resulted from changing the number of thrusters from two nominally planned OMSe, to
one.18 Similarly, the Artemis I trajectory uses this strategy if a contingency requires switching from
the main OMSe to the secondary auxiliary thrusters. These engine configurations have a tremendous
impact on performance due to different thrust and Isp capabilities if the Time of Ignition (TIG) of
the auxiliary thrusters occurs at the OMSe optimal time. This results in a performance penalty
that is beyond what is available in Orion’s propellant margin. Therefore, an optimization strategy
assuming both the OMSe and AUX produces a balanced ignition time for the outbound and return
flyby burns, thus reducing the downmode penalty in the event of a main engine failure. This comes
at a cost compared to an OMSe-optimal TIG, however, pre-planning a potential downmode protects
Orion’s propellant budget.

Figure 5b and Figure 5d represent the XDM timelines for OPF and RPF, respectively. For the
OPF XDM, the OPF AUX burn starts 10 seconds after the OPF OMSe TIG (assuming a failed
OMSe startup). The burn time, the burn ↵ and angles, and the burn ↵˙ angular rate are optimized
for the AUX engines and target the position vector on the nominal trajectory at 18 hours after the
OPF OMSe TIG. The 18 hour waypoint was chosen to allow Orion to be in a Tail-to-Sun attitude for
15 hours for thermal considerations, followed by a 2 hour optical navigation observation of either
the Earth or Moon. At this outbound waypoint, OTC-5 is an AUX burn with an optimal burn time
and burn ↵ and angles that targets the DRI, which is backwards propagated from the nominal
DRO. DRI uses the recovered OMSe and uses an optimized burn time, and burn ↵ and angles
to target the nominal DRO insertion epoch, state, and mass. The total propellant mass used by the
XDM OPF through DRI segments is constrained to be equal to the propellant mass used by the
nominal OPF through DRI segment burns.

The RPF XDM sequence is initially similar to the OPF XDM sequence. The RPF AUX burn starts
10 seconds after a failed RPF OMSe startup. Burn time, burn ↵ and angles, and burn ↵˙ angular
rate are optimized to target the nominal position vector 18 hours after the RPF OMSe TIG. At this
return waypoint, RTC-4 uses an optimal burn time and burn ↵ and angles to target the nominal
EI epoch, mass, and state, which is backwards propagated to an area close to the lunar sphere of
influence. The total propellant used by the XDM RPF through RTC-4 segments is constrained to be
equal to the propellant mass used by the nominal RPF segment burn.

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EXTENDED MISSION CLASSES
To increase launch availability throughout the year and still maintain desirable launch and land-
ing lighting conditions, the optimal nominal mission can be adjusted to produce a set of extended
mission options.2 These missions vary according to the total mission duration, as shown in Fig-
ure 5c. Short class missions consist of the nominal mission, nominal +1 and +2 days of extra total
mission duration. Long class missions add an additional DRO stay time period, and ±1 and ±2
days of extra mission duration. The initial guess for these classes are generated by incrementing
the EI epoch from the nominal case by the appropriate time offset (both the DRD and EI epochs are
allowed to vary). In addition, the long class extended missions can ideally have up to two generally
local optimal solutions, and therefore, both of these are checked and the mission with the lowest
total Orion v is selected. This methodology of using DRO stay time to gain back landing light-
ing was originally seen as an option, if desired, by the Artemis Program. However, in the years
of Artemis I design iterations, these extended missions are now considered a part of the nominal
trajectory. Within a given launch period, the mission class will only be allowed to switch once to
limit operational complexity.

EARTH ENTRY INTERFACE

The terminal mission constraint for the optimization problem is the EI target line, an analytical
curve that approximates the allowable landing zone for a skip entry off the coast of San Diego.19, 20
The target line has both horizontal and vertical components, and defines constraints on longitude,
azimuth, and flight path angle as functions of geodetic latitude and velocity. The horizontal target
line is shown in Figure 7. The EI target line constraints are implemented as a Copernicus plugin.

Unallowed

Figure 7: EI Target Line with Allowable Zone. The blue target line approximates the green
region in the optimization problem. The unallowed part of the curve is excluded due to the
SM disposal requirements near the Hawaiian islands.

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ADDITIONAL CONSTRAINTS AND MITIGATIONS
Some desired constraints are not included in the nominal mission optimization because they are
discontinuous, or otherwise make convergence difficult. For these constraints, the strategy is to
exclude them from the nominal mission scan (see Figures 9a-9c) but then to check them after the
fact. If none of the constraints are violated, then the mission is accepted. If any are violated, a
mitigation process is introduced. The constraints of this type are:
• Maximum and minimum bounds for distance traveled between EI and splashdown site
• Sunrise and sunset time constraints for landing
• Maximum eclipse durations throughout the trajectory
• Non-viable latitude locations for EI
Specific criteria are established to define the bounds for violations in each mission. The follow-
ing subsections provide the current limits for these bounds and a brief description of how these
mitigation strategies are implemented.

EI Downrange
The EI downrange limit, or entry range, is defined as the distance traveled by the Orion spacecraft
during descent from EI to the landing site. The entry downrange constraint21 is defined to be:

~ targ |✓range  4000 nmi

2498 nmi  |R (4)

where |R ~ targ | is the landing site position vector magnitude, and ✓range is the range angle between
EI and the landing site in radians. Note that this constraint is always activated when a mission is
examined for mitigation. This safeguard prevents any other mitigation algorithm from causing this
relatively simple constraint to be violated.

Landing Lighting
Landing lighting pertains to the time to and from sunset and sunrise of splashdown, respectively.
The duration of Orion’s descent from EI to the landing site is estimated to be 20 minutes. With
this duration, the EI epoch, the latitude/longitude of the landing site, and the time from sunrise and
time to sunset can be calculated using a Copernicus lighting plugin. The default buffers required
for these times are 1.0 hour after sunrise and 0.5 hour prior to sunset. Depending on whether
the violation is closer to sunrise or sunset, either constraint will be activated. This restriction is
necessary to allow enough sunlight to perform recovery operations of the vehicle post-splashdown.
The landing lighting constraint would reduce mission availability by almost 50% if the long class
mission durations were not employed.

Eclipse Mitigation Algorithm

The Orion spacecraft is limited to eclipse durations of no longer than 90 minutes.22, 23 This re-
striction was originally put in place due to the susceptibility of the solar cells to debond from Orion’s
solar arrays when in the extremely cold environment of an eclipse. This restriction is currently in
place also due to power and battery capacity concerns. The eclipse constraint, on its own, reduces
mission availability by a minimum of 18%.23, 24 To attempt resolving these issues and bring these
missions back into the fold, a mitigation algorithm was developed to reshape the trajectory and bring
violating eclipses under the duration threshold.

12
 For the eclipse mitigation analysis, the trajectory is divided into six regions. These regions will
often identify what type of trajectory shaping strategy is necessary or indicate whether mitigation is
even required. The regions are color coded in Figure 4 and also described in Table 1.

Table 1: Eclipse Mitigation Regions

Region Number Label Boundary
1 Pre-OTC-1 Core Sep ! OTC-1
2 Pre-OPF OTC-1 ! OPF
3 Post-OPF (outbound) OPF ! DRI
4 DRO DRI ! DRD
5 Pre-RPF DRD ! RPF
6 Post-RPF (return) RPF ! EI

The algorithm must also account for the XDM mission phases, where Regions 3 (outbound) and 6
(return) include the parallel trajectories that deviate from the nominal trajectory. Consequently, each
path requires an individual eclipse analysis. Using the trajectory from each region, if an eclipse is
found, the data provided to the eclipse mitigation algorithm includes the eclipse start time, duration,
and eclipse type (Earth, Moon, or multi-body). Using this information, along with a Copernicus plu-
gin that dynamically calculates the percentage of sunlight experienced by Orion, any violations of
the eclipse constraint throughout the mission are located, and the proper eclipse mitigation method
to apply is determined. There are five possible trajectory shaping methods that can be utilized:
1. Inclining the DRO
(a) Optimizes vz of DRO state and leverages v from OTC-1 and OPF burns to incline the
entire DRO
(b) Most common method of eclipse mitigation
2. Activating the DRO Plane Change (DPC)
(a) Activates DPC burn three days after DRI to incline from the Earth-Moon plane (see
Figure 5c)
3. Combining Inclination Methods
(a) Employs methods 1 and 2 to apply two layers of inclination to the DRO
4. Switching OTC-1 Burn Direction
(a) Reverses the burn direction of OTC-1 from inward to outward (toward or away from the
Earth-Moon line respectively) by modifying the ↵ and burn direction angle values
5. Utilizing DRD and RPF Burns
(a) Optimizes DRD and RPF burn durations
The eclipse mitigation algorithm will choose the appropriate strategy from this list and apply the
necessary mitigation to the trajectory. The trajectory is then reoptimized to obtain a minimum v
solution where the mitigated eclipse duration is equal to the allowable limit. When the solution
has converged, the trajectory will then be checked to see if another eclipse violation exists in the
mission. If so, a separate mitigation will be performed for each eclipse violation, one at a time, in
mission chronological order using this process until all violations are mitigated.

EI Latitude Mitigation
It can be seen in Figure 7 that there is a section of the EI target line between 14 and 21.9
latitude, in which the manifold does not have an acceptable solution. This is due to the SM disposal

13
requirements near the Hawaiian islands. Thus there is a discontinuity in the EI constraint. This
is accounted for by splitting the latitude violation boundary into thirds. If the EI state is on the
boundary of one of these regions, a latitude constraint is activated to constrain it to the upper or lower
regions of the target line. If the EI state is in the unallowable region, two separate optimizations are
performed (one with the EI latitude constrained to the upper target line region and the other being
constrained to the lower target line region). The converged solution with the lowest v is then
selected.

LAUNCH WINDOW
To generate launch window trajectories, the “optimal point” is found first, which is the optimal
launch azimuth point per day that corresponds to the minimum ICPS plus Orion total v. An
appropriate mission class and length is selected based on Orion constraints and any additional con-
straints are added in order to mitigate violations. The final optimized trajectory is used as the seed
to compute the launch window. The optimization problem is then altered in the following ways:
• The launch epoch is fixed.
• The secondary payload outbound transit time with a minimum bound of 5.15 day from launch
to OPF is removed.
• The OPF epoch tOP F is fixed to ensure a variable launch azimuth mission design approach is
achieved. This helps to ensure more consistent outbound transit times.
• OTC-2 is enabled as an optimized burn
• The DRO insertion state and time (tDRI ) is locked down. Operationally this helps the mission
planning for the FOD team to ensure the same DRO is achieved during the entire window.
Each day consists of a 1-minute launch window sweep of up to ± 4 hours before and after the
optimal point (see Figure 9c). Note that, since the launch window scan is done using the TLI
database (beginning at the Orion Sep point), only the Orion v is being minimized in the objective
function. Since the epochs that are infeasible for SLS/ICPS have already been excluded from the
database, only Orion needs to be considered. The launch scan continues (forward and backwards)
until any of the following conditions are violated:
• The problem does not converge (i.e., the mission is infeasible)
• Orion exhausts its available propellant for major burns
• The launch to OPF duration is < 4 days
An example launch window in shown in Figure 8.

SCAN METHODOLOGY
A continuation method is used to perform epoch scans of the basic mission, mission classes, and
computation of the launch window. This method is implemented in the JSC tool DAMOCLES,2
which is a wrapper to Copernicus for performing large scans in parallel in an HPC environment.
There are three kinds of scans: an epoch scan (see Figure 9a), a mission class scan (see Figure 9b),
and a launch window scan (see Figure 9c).
During the scan, the lunar geometry is used in various ways to update the initial guess to provide
robust convergence. It was mentioned above how parameterizing states and burns in the Earth-
Moon rotating frame helps with this. Additionally, for epoch steps (see Figure 9a), rather than using
integer days, a better time step is computed for each epoch using a simple lunar ephemeris25 so that
the Earth-Moon geometry is similar. The average size of this step is about 24.84 hours. Another

14
 Figure 8: Example Launch Window Scan. The launch window scan proceeds in one minute
steps backwards and forwards from the optimal mission to the start and end of the window.

strategy is to update the initial guess for the DRO at each epoch using the following empirically-
determined approximation:

2Tp = 26.426 days (5)

6
vy = 1.17228407314 ⇥ 10 r 0.952752324405 km/s (6)

where 2Tp is the period of two revolutions in the DRO, vy is the v velocity of the DRO initial state
in the rotating frame (see Figure 3), and r is the Earth-Moon distance at the selected epoch.

OFF NOMINAL MISSIONS

For every nominal mission trajectory, the Artemis I mission design team will create a set of off-
nominal missions (each of which requires the solution of a new optimization problem spawned off
from the nominal mission). These off-nominal missions provide pre-built solutions to conceivable
single-point failures. They are designed such that the mission accomplishes objectives in order of
priority. The off-nominal trajectories can be broken into three categories depending on the goal of
the off-nominal trajectory: alternate missions, returns to nominal trajectory, and aborts:
• An alternate mission is a response to a failure that occurs prior to the Orion-ICPS separation.
In this scenario, the baseline mission is infeasible and is replaced with a scenario within ve-
hicle constraints. For example, a partial TLI burn may force Orion to target a highly elliptical
Earth orbit instead of a lunar flyby into the DRO. This alternate mission will maximize the
Orion re-entry speed, but may not meet other objectives, such as testing optical-navigation
capability.
• A return to the nominal trajectory is a response to a relatively small failure, such as a missed
or partial Orion burn. In this scenario, a burn did not perform as expected due to a failure
or operational constraint. A recovery burn is used to return Orion to the baseline Artemis I
trajectory and ensures all intended mission objectives are met. For example, if the DRD burn
is missed, a recovery burn will be performed later to target the RPF burn.
• An abort trajectory is a response to a significant failure. It is used in the event the vehicle
cannot complete the nominal mission and must abort to ensure vehicle recovery. For example,

15
 One lunar cycle step
Initial Epoch ...

... ... ... ... ...

One day step

(a) Nominal Mission Scan Logic. An epoch sweep is completed from an initial epoch to a final epoch
by stepping (in parallel) by about one day time increments (due to the Earth-Moon geometry) and by
one lunar cycle time increments, until the full epoch range is completed from beginning to end.

One DRO Rev

Nominal Mission

One day step

Short Class Long Class
(b) Short and Long Class Missions. For each day, starting with the nominal short class mission, the
others are then generated by adding time to the total mission duration. Eight possible missions are
generated per day.

1 min step
... ...

Selected Mission
(c) Launch Window Scan. For the selected mission class on a given day, the launch window is then
generated in one minute steps (truncated to the nearest integer UTC minute). The scan proceeds
forwards and backwards in time until the entire window is generated.

Figure 9: Scan Methodology. A continuation method is used for all scans. The arrows indicate
that one case is used as the initial guess for the next case. Parallelization is an important
component of the scan methodology that ensures results can be generated in a reasonable
amount of time. The final results from the scan are the launch window solutions (as well as
any off nominal missions spawned from them).

16
 in the event of a propellant leak, an abort may be performed to take advantage of the current
propellant reserves by placing the vehicle on a trajectory to a viable EI.
Each of these off-nominal cases can be further divided into sub-cases with specific parameters.
For example, an abort can be a direct return abort or include a lunar flyby. The abort TIG can occur
at a variety of times, with different engine types, and with a variable number of subsequent abort
burns. Due to the large amount of cases, sub-cases and parameters, a Mission Design Matrix (MDM)
was formulated to track the different trajectories that need to be created, verified, and delivered. An
estimated 10,000 off-nominal trajectories will be generated for each nominal launch day.

INTERACTION WITH FLIGHT OPERATIONS

The design for the Artemis I trajectory is an iterative process with the JSC Flight Operations
Directorate (FOD), specifically with the Flight Dynamics Officers (FDOs). For the success of the
operational trajectory, the FDOs and Orion engineering trajectory design team work closely to alter
the design in order to meet operational requirements. In addition, various trajectory products, in-
cluding optimized Copernicus mission files and plugins, ephemeris files, and summary report data
are transferred to the FDOs to support flight rule development and pre-flight and real-time opera-
tional needs. Successful convergence of the Copernicus trajectory is critical, since FDO tools rely
on Copernicus mission files to create an initial trajectory guess that is used for vehicle burn plan
generation and as an input to the FOD ground targeting software, which ultimately generates the
data loaded directly onto the vehicle.
In addition to the Copernicus trajectory, the data is also post-processed to generate summary
reports to provide the FOD with crucial information needed for real time operations. A report for
each launch time contains a timeline of mission events (e.g., burns, ground sight loss of signal, and
separations), a summary of eclipse times and durations, and Orion’s view of ground stations and
Tracking and Data Relay Satellite System (TDRSS). They also contain various plots of trajectory
parameters such as velocity and altitude, as well as relative motion plots of Orion and the ICPS
after separation to check for possible recontact. For each launch day in a scan, a summary report is
generated with the aggregate eclipse, vehicle performance, Deep Space Network (DSN) coverage,
and lighting with respect to important mission events. Another report summarizing the eclipses is
generated for an entire launch window. All reports are automatically generated at the end of the
scan process.

CONCLUSION

Trajectory design is a complicated merging of vehicle capabilities, programmatic constraints and

desirements, risk trades, mission objectives, and physics. The creation of a flight-ready reference
trajectory relied heavily on the integrated efforts of the SLS, Orion, EGS programs, ESD, and FOD.
The Artemis I mission design has evolved over the years, but even when the performance based
reference trajectory for the optimal launch per day was solidified, many permutations needed to be
analyzed and adjustments made to the trajectory. Maximizing mission availability, which is a key
asset to have when launching a system for the first time, drove these permutations. The alterations
are also necessary to create a large enough pre-flight product suite for operations to provide initial
guesses for vehicle targets and to account for off-nominal situations. This impelled the JSC team
to develop novel trajectory design techniques and the tools Copernicus and DAMOCLES to emu-
late what whole organizations did in past human spaceflight programs. Even though Artemis I is

17
uncrewed, the trajectory design process that has been created will be used as the groundwork for all
future human spaceflight missions.

ACKNOWLEDGEMENTS

The authors wish to thank the many people who have contributed to the Artemis I mission design
process, especially: Sam Pedrotty, David Lee, Randy Eckman, Scott Craig, Seth Thompson, Adam
Harden, Andrew Scott, Timothy Stuit, and Natasha Peake. We also thank Jeremy Rea for providing
Figure 7. A portion of this work was funded by NASA JSC under contract NNJ13HA01C.

NOTATION

ARCM Asteroid Redirect Crewed Mission

AUX Auxiliary
CM Crew Module
CMA Crew Module Adapter
DAG Directed Acyclic Graph
DPC DRO Plane Change
DRD DRO Departure
DRI DRO Insertion
DRO Distant Retrograde Orbit
DSN Deep Space Network
EGS Exploration Ground Systems
EI Entry Interface
ESD Exploration Systems Development
ESM European Service Module
FDO Flight Dynamics Officer
FOD Flight Operations Directorate
GRACE Gravity Recovery And Climate Experiment
GRAIL Gravity Recovery and Interior Laboratory
HLS Human Landing System
HPC High Performance Computing
ICPS Interim Cryogenic Propulsion Stage
JPL Jet Propulsion Laboratory
JSC Johnson Space Center
LAS Launch Abort System
LEO Low Earth Orbit
MDM Mission Design Matrix

18
MSFC Marshall Space Flight Center
NASA National Aeronautics and Space Administration
OCO OMSe Checkout
OMSe Orbital Maneuvering System Engine
OPF Outbound Powered Flyby
OTC Outbound Trajectory Correction
POST Program to Optimize Simulated Trajectories
PRM Perigee Raise Maneuver
RCS Reaction Control System
RPF Return Powered Flyby
RTC Return Trajectory Correction
SA Spacecraft Adapter
SLS Space Launch System
SM Service Module
SNOPT Sparse Nonlinear OPTimizer
SOFA Standards of Fundamental Astronomy
SPICE Spacecraft, Planet, Instruments, C-matrix and Events
TDRSS Tracking and Data Relay Satellite System
TIG Time of Ignition
TIP Target Interface Point
TLI Trans Lunar Injection
TPS Thermal Protection System
USS Upper Stage Separation
UTC Coordinated Universal Time
XDM Auxiliary Down Mode

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