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1
AAS-95-129
MANEUVER PLANNING AND RESULTS FOR CLEMENTINE
(THE DEEP SPACE PROGRAM SCIENCE EXPERIMENT)
*
J. Carrico
†
, D. Carrington
‡
, M. Hametz
§
, P. Jordan
**
,
D. Peters
††
, C. Schiff
‡‡
, K. Richon
§§
, and L. Newman
***
This paper presents the methodology and techniques the authors used to
plan maneuvers for the Clementine (the Deep Space Program Science
Experiment (DSPSE)) mission. The authors were part of a team at
Goddard Space Flight Center that was responsible for planning the
trajectory maneuvers to take the spacecraft out of low-Earth orbit and
transfer to a lunar mapping orbit. This paper describes the maneuver
planning activities before and after each maneuver, not only the general
procedures but also the unique aspects of each maneuver. The
maneuver goals, control parameters used to achieve them, and
constraints and requirements for each maneuver are also discussed. The
authors also address the purpose of each maneuver, the use of several
maneuvers together to achieve the mission goals, the postmaneuver
reconstruction process, calibration of the spacecraft thruster, and the use
of the calibration to plan subsequent maneuvers. These issues are
discussed using actual flight data. The authors compare the actual
maneuvers with those planned before launch. The paper also describes
several trajectory maneuver contingencies and explains how they were
resolved.
The paper also describes the software and numerical algorithms used in
maneuver planning and modeling and provides a description of the
software’s operational use. In particular, this paper contains a discussion
of the application of the PC-based software program Swingby, which was
used to model Clementine’s engines and to target maneuvers. The
targeting, trajectory propagation, and engine model algorithms are also
explained.
*
This work was supported by the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center
(GSFC), Greenbelt, Maryland, under Contract NAS 5-31500.
†
Senior Member of the Technical Staff, Computer Sciences Corporation (CSC), 10110 Aerospace Road, Lanham-
Seabrook, Maryland 20706. Phone: 301.794.1955; E-mail: jcarrico@csc.com
‡
Section Manager, CSC.
§
Senior Member of the Technical Staff, CSC.
**
Senior Member of the Technical Staff, CSC.
††
Member of the Technical Staff, CSC.
‡‡
Member of the Technical Staff, CSC.
§§
Flight Dynamics Engineer, Clementine Project, Flight Dynamics Division (FDD), NASA GSFC. Greenbelt Maryland,
20771. Phone: 301.286.8845
***
Flight Dynamics Engineer, Clementine Project, FDD, NASA GSFC.
2
INTRODUCTION
On January 25, 1994, the National Aeronautics and Space Administration (NASA) Goddard Space
Flight Center (GSFC) Flight Dynamics Division (FDD) began supporting operations for the Clementine
(Deep Space Program Science Experiment (DSPSE)) mission as it launched from Vandenburg Air Force
Base. Clementine was a fast-track mission sponsored by the Ballistic Missile Defense Organization
(BMDO) to test the BMDO sensors in a deep space environment. The BMDO worked with NASA to
establish scientific goals to map 100 percent of the lunar surface and to perform a close fly-by of the
asteroid 1620 Geographos. The BMDO selected the Naval Research Laboratory (NRL) as the lead
laboratory for Clementine. At the NRL, the Trajectory and Maneuver Planning (TAMP) group was given
responsibility for all aspects of planning the trajectories and performing the related flight operations. The
NRL contacted the FDD, and the FDD's Flight Dynamics Facility (FDF) became a part of the TAMP team.
The FDF support personnel for Clementine were divided into two teams: The maneuver team was
responsible for trajectory design and maneuver planning, and the orbit team was responsible for orbit
determination and acquisition data generation. This paper describes the activities of the maneuver team.
Since the start of the Clementine program in early 1992, FDF’s maneuver team performed prelaunch
mission analysis, error analysis studies, and launch window calculations. After launch, FDF planned and
supported 13 trajectory adjust maneuvers until March 31, 1994. The FDF maneuver team submitted
approximately 70 maneuver plans to the DSPSE Mission Operations Center (DMOC) during operations,
most of which were in response to contingencies. After March 31, 1994, the NRL’s DMOC took over
maneuver planning, as originally agreed. During the early phases of operations FDF spent time training
TAMP personnel at DMOC to plan maneuvers so that they could operate independently during the later
phases.
Clementine was indeed a fast-track development mission, going from concept to launch in less than
2 years under a tight budget. As a result, the BMDO stated at the preliminary design review that the level of
acceptable risk was much higher than that of comparable missions. The key to Clementine’s success was
doing only what was absolutely necessary, identifying the resulting risks, and diminishing the risks by
planning for possible contingencies. Several risk-mitigation strategies used by the FDF team for trajectory
design and maneuver planning are discussed later.
BACKGROUND
The NRL built the Clementine spacecraft,
which is shown in Figure 1. The octagonal body of
the spacecraft is about 1.2 meters high and about 1.1
meters in diameter. It had a dry mass of 231
kilograms (kg), plus fuel loads of 219 kg bipropellant
and 12 kg monopropellant, totaling an initial
spacecraft mass of 462 kg. In low-Earth orbit (LEO)
the spacecraft was attached to a Thiokol Star-37FM
solid kick motor (not pictured), which made the total
mass in LEO approximately 1662 kg. The Star-
37FM was used to propel the spacecraft out of LEO
and on to the Moon. During this large maneuver, the
spacecraft was spin stabilized. The spacecraft was
spun down and three-axis stabilized shortly after the maneuver, and the empty motor casing and adapter
were dropped about a day later. All subsequent maneuvers used a Kaiser Marquardt R-4D 490 Newton
bipropellant thruster, which was pressure regulated using a bang-bang control system. During these
maneuvers, the spacecraft was three-axis stabilized. Attitude control was performed using the
monopropellant system.
Figure 1 Clementine in Deployed Configuration
3
Clementine was launched by a Titan IIG into
LEO and remained there for 8.5 days. At the end of the
LEO phase, the spacecraft performed a large transfer
trajectory insertion (TTI) maneuver to enter two cislunar
phasing loops for the transfer to the Moon. This first
cislunar phase is shown in Figure 2. On February 19,
1994, Clementine performed a maneuver that inserted it
into orbit around the Moon, beginning the lunar orbit
phase. For the next 2 months, it remained in a 5-hour
period elliptical polar lunar mapping orbit. It performed
a large maneuver and left lunar orbit on May 4, 1994,
entering a 19-day period phasing loop, the second
cislunar phase. This was in preparation for a gravity
assist from the Moon, which was to propel the spacecraft
to encounter the asteroid Geographos during the last
phase, which was called the cruise phase. Clementine
never finished its mission, however, because after it left the Moon a software anomaly caused it to burn all
of its attitude fuel prematurely, rendering the spacecraft uncontrollable. Despite this misfortune, the
mission has been widely acclaimed as a success because of the performance of the sensors and the complete
multispectral imaging of the lunar surface.
FDF MANEUVER PRODUCTS DELIVERED TO DMOC
FDF performed a host of analyses during the 2 years before launch; these were documented and
delivered as reports to the NRL, and some of the work was presented as a professional paper1. One of these
products, the baseline trajectory design, was the foundation for operational maneuver planning. This
complete baseline trajectory was a predicted spacecraft ephemeris file and was delivered with a list of all
the maneuvers, their start times, magnitudes, and directions. Complete trajectory designs were created and
delivered several times before launch reflecting changes in mission requirements and in the spacecraft itself.
The final prelaunch trajectory and maneuver list were delivered to the NRL 8 days before launch.
During operations, FDF was required to deliver a preliminary (or coarse) maneuver plan to DMOC
24 hours before the maneuver time. Nominally, the final maneuver plans were due 4.5 hours before the
maneuvers; however, because of the stability of the orbit determination solutions, the final plans were more
often delivered about 12 hours before the maneuver, allowing DMOC more time to test the commands
before uploading to the spacecraft. Each maneuver plan included a detailed maneuver plan for the next
burn and brief maneuver plans for subsequent burns in that phase. The team transmitted the plan using a
modem via a dedicated phone line connecting FDF to DMOC and faxed the plan as a backup. To assist in
training the TAMP personnel at DMOC, the FDF team also transmitted the software configuration files
used to plan the maneuvers so that the TAMP could reconstruct the maneuver planning process.
After each maneuver, the team reconstructed and calibrated the burn and delivered the results
within a few hours after the orbit solution was determined. Originally, FDF was responsible for delivering a
detailed postmaneuver report to DMOC; however, this report became unnecessary because the briefer
information proved to be adequate and faster.
Moon’s Orbit
Spacecraft Trajectory
Earth
Figure 2: Cislunar Phasing Loops
4
PRELAUNCH PREPARATIONS
The FDF teams started specific preparations about 9 months before launch.. These preparations
included
Writing operational timelines
Writing operational procedures
Selecting team members
Selecting shift leaders
Team training
Operational simulations
Software configuration and verification
Preparation for launch slip
These preparations are addressed in the following subsections.
Operational Timelines and Procedures
One of the most useful yet most laborious tasks in preparing for operations was developing the
mission timelines, which were the written step-by-step activities of each FDF team. The timelines also
included detailed information on data products, including who generates them, for whom, and when. The
timeline was intended to be used in operations to ensure that no steps or deliveries would be missed.
Developing the timeline, however, had the added benefit of documenting the roles and responsibilities of
the teams, which, in turn, allowed the teams to assess whether or not they had the procedures and software
tools to perform each step. Developing the timelines was also the first opportunity to work out the details of
the interfaces, such as agreeing on the format, coordinate frames, and units of data products.
To develop the timelines, one or two representatives from each team met in round-table fashion
and walked through the activities needed to support each maneuver. Starting at about maneuver minus 36
hours, the group talked through and charted the activities for each half-hour increment until support for that
maneuver would end, usually 24 hours after the maneuver. Each team explained their activities, the
products they needed from other groups, and the schedule for product delivery. The FDF teams usually met
once a week for about an hour starting about 9 months before launch. Since many of the maneuvers
required similar support, each team developed their own baseline timeline and made only slight
modifications for each specific maneuver.
The FDF investigated recovery strategies for each maneuver and had designed the baseline
trajectory with placeholders for correction maneuvers. As a risk mitigation strategy, the timelines included
these corrections as definitive maneuvers so that staffing profiles, product delivery schedules, and
operational procedures would automatically account for contingencies.
In parallel with writing the timelines, each team developed their own set of procedures describing
how to perform each activity. The maneuver team procedures were step-by-step instructions on how to
plan, reconstruct, and calibrate each maneuver. The procedures included software configurations, quality
assurance criteria, and even data file naming conventions. Each maneuver procedure was about five pages
and included worksheets for recording intermediate results. The procedures were compiled in an
Operations Handbook along with the procedures of the other FDF groups. The procedures were quite
useful during FDF training, and were also given to the DMOC TAMP personnel to assist in their training.
As the training and then the operations progressed, the FDF maneuver team became very familiar with the
maneuver planning process, so they developed single page checklists describing critical details of common
activities. The checklists including how to use the modem, fill out the maneuver plan, and assure the quality
5
of the data. The Operations Handbook was then used as a reference when questions arose about a specific
maneuver.
Team Makeup and Training
The six-member maneuver team was divided into two shifts, and each shift had a designated shift
leader. As a risk mitigation strategy, all members of the maneuver team were required to be able to perform
all functions, and both shifts were expected to be able to handle any problems that arose. Four of the
maneuver team members had been involved extensively with prelaunch mission analysis, two of them from
the very beginning of FDF’s support. The other two members joined the team about 4 months before
launch; they were initially designated as backups, however the rapid frequency of critical maneuvers during
the first month of support led to two shifts of three analysts each during times of around-the-clock critical
support. A technical manager supervised the team’s prelaunch mission analysis and training and supported
the team technically during operations. Two flight dynamics engineers (FDEs) and two mission managers
supervised all the FDF activities during operations.
In addition to supervising FDF operations, the two FDEs functioned as the liaison between the
maneuver team and other groups. They ensured that data products required by the maneuver team from
other groups were available when needed. They also conveyed the changing requirements, changing
schedules, and contingency situations. They filtered the myriad requests for information regarding the
planning process by serving as the external contact point for the maneuver team. The FDEs interfaced with
DMOC, the FDF orbit determination team, the FDF’s internal management, other GSFC support elements,
the NRL, the BMDO, the Air Force, the Deep Space Network/Jet Propulsion Laboratory (JPL), and other
ground networks. In addition, the FDEs were responsible for approving the maneuver plans generated by
the team before transmission to DMOC.
The first operations training for the maneuver team members was attending FDF software classes
and working through self-instruction tutorials. Next, the team members were given specific analyses to
complete which allowed them to become familiar with the details of the mission. The team also participated
in a variety of operational simulations, sometimes with just the team, sometimes with other FDF elements,
and sometimes with DMOC. These simulations provided an opportunity to develop and become familiar
with the timeline and procedures. Initial simulations included only nominal maneuver support activities,
while later simulations involved various contingencies, accomplished using simulated data created by
personnel not on the team. To ensure ample cross-training, team members who were less experienced in
some key area were assigned to work with team members who were experts in the area. As part of the risk
mitigation strategy, the simulations were used to train all maneuver team personnel to do all required jobs
so that no one person was a single point of failure. This training strategy was beneficial since, during LEO
support, around-the-clock support lasted many days longer than anticipated, demanding that each 12-hour
shift be able to replan maneuvers completely and handle any contingencies.
Software Preparation
Before launch, FDF faced the extensive task of verifying the operational software, including
modifying existing software and in some cases developing new software for the lunar orbit operations. Of
particular concern was the numerical integration of the very sensitive trajectories that Clementine would fly.
The transfer trajectory to the Moon and the gravity assist preceding the asteroid encounter were especially
sensitive to small perturbations. FDF, therefore, tested the software extensively against other FDF software,
benchmarks from previous work, and specially designed test cases. The operational software configuration
and procedures were based on these tests.
6
Preparation for Launch Slip
The NRL allocated 10 meters/second (m/s) of V above the baseline V to account for launch
slips. The maneuver team calculated Clementine’s launch window using this extra V, and by adjusting the
periods of the cislunar phasing loops. The resultant launch window was at least an hour long each day for
two weeks. In calculating the launch window, the maneuver team had designed trajectories from launch
through lunar orbit insertion (LOI) for each day of the launch window. To mitigate the risks of a launch
slip, the team summarized the maneuvers for these trajectory designs in a table in the maneuver planning
procedures. As it turned out, Clementine launched on the first day of its launch window only 8 minutes
after the launch window opened.
OPERATIONAL MANEUVER PLANNING AND CALIBRATION
This section presents a summary of the maneuver planning support tools, methods, processes, and
activities that were common to all the maneuvers supported by FDF. Later sections will cover each
maneuver, in detail, and address issues specific to those maneuvers.
Tools: Spreadsheet
The fuel budget spreadsheet created by the maneuver team was used both before launch and during
operations. This spreadsheet was used during the trajectory design phase to calculate the fuel required.
Closer to launch, the team used the tool to monitor the fuel budget as constraints and requirements changed.
This spreadsheet was updated throughout operations, providing a running total of the fuel remaining and the
spacecraft mass as the maneuvers were performed and error correction fuel was used.
In estimating the fuel budget, several margins were included to minimize risk. Analysis showed
that because of the high thrust-to-mass ratio of the R-4D engine, there would be no significant difference
between the amount of fuel used in a finite burn versus the amount predicted by the rocket equation based
on the impulsive V. However, a 1 percent finite burn penalty was added to each maneuver as a margin of
safety. The team also performed error analysis for each of the maneuvers and budgeted fuel to
accommodate worst case execution errors. The 10 m/s of V for the launch window was distributed in the
spreadsheet to the maneuvers which would be used to correct a launch slip.
An example of the spreadsheet used while Clementine was in LEO is shown in Table 1. Because
the NRL used English units while FDF’s software required metric, the maneuver team used the spreadsheet
to keep conversions consistent throughout the mission. For example, toward the top of the spreadsheet are
cells where the team input the thrust, specific impulse (Isp), and mass values, in English units. Next to the
English units are cells containing the converted metric units. All subsequent calculations in the spreadsheet
were done with the metric values to match FDF’s software as closely as possible. The layout of the
spreadsheet was designed to keep the calculations consistent and traceable.
7
Table 1
MANEUVER PLANNING V SPREADSHEET
DSPSE V Spreadsheet as of 2/2/94
R-4D Engine
English
Metric
g (m/s^2) :
9.8054
Lbm/Kg =
2.204622622
Isp
311.0
sec
3049.48
Ns/Kg
Thrust
110.0
Lbf
489.30
N
Star-37 Motor
English
Metric
g (m/s^2) :
9.8054
Isp
289.764
sec
2841.25
Ns/Kg
Thrust
10625.000
Lbf
47262.36
N
Pre TTI Mass
Mass Loss
2367.940
Lbm
1074.08
Kg
1657.0183
kg
TTI Delta-V
Spacecraft Masses
English
Metric
2968.24
m/s
Dry S/C + 2 Lbm He + Outage
522.2600
Lbm
236.8932
Kg
Fuel: Star-37
2367.9400
Lbm
1074.0795
Kg
Fuel: R-4D (useable)
466.4000
Lbm
211.5555
Kg
Fuel: ACS
27.0000
Lbm
12.2470
Kg
Comparison of English & Metric TTI Duration Caclulations
Interstage
107.4000
Lbm
48.7158
Kg
TTI
English
Metric
Units
Star-37 Burn-out
172.4000
Lbm
78.1993
Kg
Duration
64.57824
64.57000
seconds
Initial Mass
3663.4000
Lbm
1661.6903
Kg
Duration
1.0763039
1.0761667
minutes
Event
R-4D Delta-V (m/s)
R-4D Fuel
Other
Mass
Duration
Remaining
Remaining
Final Mass
Baseline Imp.
Add'nal Imp.
Total Finite
Used (Kg)
Loss (Kg)
(sec)
R-4D Fuel
S/C + ACS
(Kg)
ACS Lbm
R-4D Lbm
Total Lbm
Initial Mass
211.5555
1450.1348
1661.6903
0.00
3663.4000
LEO Maneuver
0.0
0.0
0.0
0.00
0.0
211.5555
1450.1348
1661.6903
0.00
3663.4000
LEO ACS
4.67
211.5555
1445.4628
1657.0183
8.44
0.00
3653.1000
TTI ( 64.58 s)
1074.08
64.57000
211.5555
371.3833
582.9388
0.00
1285.1600
Spin Down
0.5216
211.5555
370.8617
582.4171
1.15
1284.0100
Drop Interstage
126.92
211.5555
243.9465
455.5020
0.00
1004.2100
A1 Calibration
5.0
0.0
5.1
0.75
0.02
4.7
210.8018
243.9284
454.7302
0.04
1.66
1002.5084
P1
143.6990
145.1
21.14
0.31
131.7
189.6664
243.6154
433.2818
0.69
46.60
955.2229
TTI Makeup
23.0
23.2
3.29
0.00
20.5
186.3784
243.6154
429.9938
7.25
947.9740
P1c
52.0
52.5
7.34
0.16
45.8
179.0362
243.4566
422.4928
0.35
16.19
931.4372
CRT1
35.0
35.4
4.87
0.08
30.3
174.1668
243.3750
417.5418
0.18
10.74
920.5222
CRT2
35.0
35.4
4.81
0.08
30.0
169.3546
243.2933
412.6479
0.18
10.61
909.7330
P2
6.0
6.1
0.82
0.01
5.1
168.5354
243.2797
411.8151
0.03
1.81
907.8969
Mid-Course
1.0
1.0
0.14
0.00
0.8
168.3990
243.2752
411.6742
0.01
0.30
907.5863
Launch Window Margin
10.0
10.1
1.36
0.02
8.5
167.0378
243.2525
410.2903
0.05
3.00
904.5353
Cislunar ACS
0.06
167.0378
243.1936
410.2313
0.13
0.00
904.4053
LOI 1
453.1850
457.7
57.18
0.86
356.3
109.8617
242.3363
352.1979
1.89
126.05
776.4635
LOI 2
106.5
107.6
12.21
0.21
76.1
97.6551
242.1276
339.7827
0.46
26.91
749.0926
LOI 1 Correction
2.0
2.0
0.23
0.01
1.4
97.4301
242.1185
339.5486
0.02
0.50
748.5765
LOI 2 Trim
5.0
5.1
0.56
0.02
3.5
96.8682
242.1004
338.9686
0.04
1.24
747.2979
1st Month Lunar Orbit Control
19.1
19.3
2.14
0.05
13.3
94.7307
242.0505
336.7812
0.11
4.71
742.4754
1st Month Margin
5.0
5.1
0.56
0.02
3.5
94.1734
242.0324
336.2058
0.04
1.23
741.2069
LRT1
102.4
103.4
11.21
0.25
69.9
82.9621
241.7783
324.7404
0.56
24.72
715.9301
LRT2
103.8
104.8
10.97
0.25
68.4
71.9876
241.5243
313.5119
0.56
24.19
691.1755
Rotation Trim
5.0
5.1
0.52
0.02
3.2
71.4688
241.5062
312.9750
0.04
1.14
689.9918
2nd Month Lunar Orbit Control
20.8
21.0
2.15
0.05
13.4
69.3201
241.4518
310.7719
0.12
4.74
685.1348
2nd Month Margin
5.0
5.1
0.51
0.02
3.2
68.8059
241.4336
310.2395
0.04
1.13
683.9611
Node Rotation
9.6
0.0
9.7
0.98
0.00
6.1
67.8211
241.4336
309.2547
2.17
681.7899
Other Lunar Orbit Margin
15.0
15.2
1.54
0.05
9.6
66.2836
241.3837
307.6673
0.11
3.39
678.2903
Lunar Orbit ACS
0.10
66.2836
241.2839
307.5675
0.22
0.00
678.0703
LOD
511.0
516.1
47.89
0.73
298.4
18.3959
240.5582
258.9541
1.60
105.57
570.8960
LOD Correction
21.0
21.2
1.79
0.08
11.2
16.6010
240.4765
257.0776
0.18
3.96
566.7590
PP1
12.5
12.6
1.06
0.05
6.6
15.5389
240.4221
255.9610
0.12
2.34
564.2975
PP1 Correction
18.0
18.2
1.52
0.08
9.5
14.0175
240.3405
254.3580
0.18
3.35
560.7633
PA1
1.2
1.2
0.10
0.00
0.6
13.9164
240.3359
254.2523
0.01
0.22
560.5305
PA1 Correction
1.0
1.0
0.08
0.00
0.5
13.8322
240.3314
254.1636
0.01
0.19
560.3349
PP2
8.3
8.4
0.70
0.03
4.3
13.1345
240.3042
253.4387
0.06
1.54
558.7366
Post-Swingby PP2 Correction
10.0
10.1
0.84
0.04
5.2
12.2965
240.2679
252.5644
0.08
1.85
556.8091
Geographos Arrival Burn
10.0
10.1
0.84
0.04
5.2
11.4614
240.2316
251.6930
0.08
1.84
554.8880
Arrival Margin
10.0
10.1
0.83
0.04
5.2
10.6291
240.1953
250.8244
0.08
1.83
552.9732
Post LOD ACS
0.11
10.6291
240.0819
250.7110
0.25
0.00
552.7232
Sub-Totals
1497.1
269.0
1783.7
200.93
1210.05
1316.8
18.11
442.97
If LEO=15 & P1=128
2.50
0.00
15.6
8.1291
240.0819
248.2110
0.00
5.51
547.2117
Thrust & Isp Margin
2.00
0.00
12.5
6.1291
240.0819
246.2110
0.00
4.41
542.8024
Totals
1497.1
269.0
1783.7
205.43
1210.05
1344.8
18.11
452.89
0.0000
Total Delta-V:
1783.7
m/s
Goddard Space Flight Center
Total Fuel:
205.4
Kg
Flight Dynamics Division
Total Fuel:
452.9
Lbm
Computer Sciences Corporation
Excess Fuel:
13.5
Lbm
8
The main section of the spreadsheet shown in Table 1 was used for quality checks, fuel budget
prediction, and long-range planning with DMOC. The columns are
1. The names of the maneuvers and V margins
2. The baseline impulsive maneuvers needed to complete the mission
3. The additional V needed for error correction
4. The sum of 2 and 3, plus a 1 percent finite burn penalty
5. The total finite burn V (column 4) converted to fuel mass
6. Other mass loss, such as expected attitude control system (ACS) fuel usage or dropping the solid motor
casing
7. The expected duration of the bipropellant maneuver based on the mass loss
8. The remaining bipropellant fuel (fuel and oxidizer treated together)
9. The remaining ACS fuel plus the dry spacecraft mass
10. Total mass of the spacecraft after the trajectory maneuver
11. ACS Lbm: input for attitude fuel in pounds-mass (Lbm), as received from the NRL
12. R-4D Lbm: the bipropellant fuel used in Lbm to compare with the NRL’s calculations
13. Total Lbm: total mass of the spacecraft after the maneuver in Lbm to compare with the NRL’s
calculations
Tools: Swingby
The FDF Mission Analysis and Design Software Swingby2,3 proved to be the most important tool
used by the team. Although Swingby did require extensive modifications, it was chosen as the maneuver
planning and support software for the Clementine mission because it had a graphical user interface,
provided a variety of targeting schemes, met the numerical requirements, and was designed to support
analysis for multigravitational body trajectories. Swingby was used to design the trajectory and to
operationally plan, reconstruct, and calibrate the maneuvers throughout the mission. It had the capability to
fully model all gravitational sources and perturbations and could plan maneuvers around the Earth, Sun,
Moon, or an asteroid. It also could precisely model finite burn maneuvers and was used to plan both the
Star-37FM solid motor firing and the R-4D bipropellant maneuvers.
Although other missions have used Swingby for prelaunch mission analysis, Clementine was the
first mission to use Swingby operationally, and it performed above expectations. The graphical user
interface was especially useful; without it, responding to the rapidly changing requirements and
contingencies would have been far more difficult. A more thorough discussion of Swingby’s use in
operations will be presented in a later paper4.
Numerical Methods: Trajectory Integration and Force Models
Because of the very sensitive trajectories that Clementine was going to fly, the maneuver planning
software, Swingby, needed to use highly accurate numerical models to propagate the spacecraft’s position
and velocity. The spacecraft’s motion was affected by a variety of influences, such as the gravitational
effects of the Sun, Moon, and planets; atmospheric drag; solar radiation pressure; and sometimes engine
thrust. Another software challenge was that at different times and during different phases of the mission,
different forces would be dominant. The maneuver team, therefore, chose specific force models for each
different phase of the mission. Each force model was tailored to include enough detail to give better
accuracy than the expected orbit determination accuracy yet simple enough not to impact computer
performance. Table 2 summarizes the force models used for each phase of the mission.
Table 2
9
FORCES MODELED DURING GIVEN MISSION PHASE
Mission
Phase
Earth’s
Gravity
Moon’s
Gravity
Sun’s
Gravity
Other
Major
Planets
Solar
Radiation
Pressure
Drag
LEO
GEM-T3
(21x21)
point mass
point mass
no
yes
yes
Cislunar
GEM-T3
(21x21)
point mass
point mass
no
yes
no
Lunar Mapping
point mass
LUN75A
(21x21)
point mass
no
yes
no
Cruise
point mass
point mass
point mass
yes
yes
no
Swingby was configured to use standard drag and gravity models. It used the Jacchia-Roberts
atmospheric density model to calculate the effects of drag. FDF updated the solar flux and exospheric data
needed by the drag model daily by downloading them from the National Oceanic and Atmospheric
Administration (NOAA). Solar radiation pressure was approximated by assuming a constant uniform
energy output from the Sun. The maneuver team configured Swingby to use the 50x50 Goddard Earth
Model T3 (GEM-T3), truncated to 21x21 terms. The gravity model used for the Moon was the 75x75
LUN75A model developed by JPL, truncated to 21x21 terms. The Sun and the other planets were modeled
as point masses. The positions and velocities of the Sun, Moon, and planets were read from JPL’s DE200
ephemeris. For modeling the cruise phase, Swingby was set up to include the additional point mass
gravitational forces from Venus, Mars, Jupiter, Saturn, and Uranus.
For each phase of the mission, the numerical coordinate system origin of integration was set to
match the dominant gravitational source of that phase. Accordingly, the Earth was the central body of
integration for the LEO and cislunar phases, the Moon the central body for the lunar mapping phase, and
the Sun the central body for the cruise phase. Based on premission error analysis, the team modeled the
trajectory approaching the Moon as Earth-centered, with the Moon as a point mass whenever planning
maneuvers in the cislunar phasing loops and used the Moon as the central body with its 21x21 gravitational
field when planning the lunar capture maneuver.
The maneuver team used three of Swingby’s numerical integration schemes to propagate
Clementine’s trajectory. All three of these schemes used the Cowell method to model the forces. For each
phase of the mission, the maneuver team chose the scheme that gave the best balance between accuracy and
computer performance. For the LEO phase, the team used Swingby’s Adam-Bashforth-Moulton 12th-order
predictor-corrector with a constant 60-second step size. They chose this because it was the fastest method
to integrate an LEO, and it had been extensively tested and configured to match the orbit determination
software for modeling atmospheric drag. For the free-flight portions of the mission beyond the Earth’s
atmosphere, the team used Swingby’s Runge-Kutta-Nystrom 6(8) dual-order integration scheme. This
integrator was configured to use a variable time step, with the step size automatically calculated to keep the
local relative error below 1 x 10-9. For modeling the trajectory during finite burn maneuvers, Swingby used
its Runge-Kutta-Verner 8(9) dual order integration scheme, which could also handle the velocity-dependent
atmospheric drag forces when needed. This integrator employed a variable time step method and the local
relative error was kept below 1 x 10-9. During finite burn maneuvers, the maximum step size allowed was
originally set at 1 second, but this constraint was eventually relaxed to about 30 seconds to speed up
computer processing time after analysis proved that the accuracy was not impacted.
As mentioned before, the spacecraft’s bipropulsion system was pressure regulated. This allowed
the team to numerically model the thrust and the specific impulse (Isp) as constants for a given maneuver.
Swingby used the thrust and Isp to calculate the mass depletion and the incremental change to the
10
spacecraft’s velocity over each integration time step. The prelaunch thrust and Isp values were used as a
starting point, but after each maneuver, the maneuver team calibrated the engine based on postmaneuver
orbit determination and calculated a thrust scale factor (TSF), which characterized the inefficiencies in the
engine. Swingby applied the TSF to the thrust when calculating the acceleration imparted to the spacecraft
by the engine. Swingby did not apply the TSF to the mass loss calculations, which may or may not reflect
the actual dynamics; this would depend on whether or not the cause of the thrust change also had an effect
on Isp, which would be hard to determine. Prelaunch analysis showed, however, that for Clementine’s
maneuvers any potential mass loss error would have a negligible effect for the expected TSFs of 2 to 5
percent. The calibrated TSF for each maneuver was used for any similar subsequent maneuvers.
Numerical Methods: Maneuver Targeting
Swingby was not only used to propagate Clementine’s trajectories but also to target the maneuvers,
that is, calculating the maneuver start times, durations, and pointing. Swingby’s targeter uses a differential
corrector shooting method to vary the initial conditions of a maneuver or maneuvers to achieve mission
goals sometime after the maneuver. Within Swingby this problem is formulated as an
initial-value/boundary-value problem and is solved using a Newton method with numerical partial
derivatives.
More specifically, Swingby’s targeting algorithm propagates an initial trajectory state through a
designated series of free-flight arcs and maneuvers until some end condition is met. The targeter evaluates
mission goals selected by the user, such as inclination or semimajor axis, and compares them to the desired
values. If the values are within a user-specified tolerance, the targeting is done. If not, the targeter
successively varies user-selected initial conditions, or “variables”, each by a user-selected perturbation.
The targeter uses these runs to create the sensitivity matrix, which contains the numerical partial derivatives
that indicate how the goals change with respect to the variables, at least to a linear approximation. The
targeter inverts the sensitivity matrix and multiplies by the deviations from the desired goals to estimate
corrections to the variables. This process is iterated until the goals are within tolerance.
In some cases, the targeting on the actual mission goals was not as well-behaved as targeting on a
related set of parameters. Specifically, the desired lunar orbit insertion conditions of an altitude at
periselene and a lunar inclination were achieved most easily by targeting on B-plane parameters. The B-
plane parameters are a linear set of targets that describe the geometry of the incoming hyperbolic
asymptote5. Swingby’s targeter uses a floating end-point algorithm3 that calculates the B-plane parameters
(each time the trajectory is propagated) that correspond to the desired altitude and inclination.
The Maneuver Planning Process
As mentioned previously, the maneuver team used the prelaunch trajectory design as a baseline for
maneuver planning. Analysis before launch showed that the first maneuver, which was to be performed by
the Star solid kick motor, could not be modeled accurately as an impulsive maneuver, so in the baseline
trajectory it was modeled as a finite burn. The analysis also showed that the bipropellant R-4D engine’s
thrust-to-mass ratio was so large that there was a no inaccuracy in modeling its finite burns as impulsive, so
in the baseline trajectory all maneuvers after the first were modeled as impulsive. During operations the
maneuver team updated future maneuvers in the baseline trajectory after each maneuver was performed.
Because it was often necessary to plan multiple maneuvers concurrently to achieve mission goals, only the
first maneuver in the sequence would be modeled as a finite burn. Using impulsive burn modeling
whenever possible simplified the planning process; it was more consistent to compare an impulsive V
magnitude and direction to previous values than to compare burn durations, which is a function of the
changing spacecraft mass.
11
The maneuver team received the spacecraft’s state vector (position and velocity) from the FDF
orbit determination team and received the spacecraft’s current mass, which accounted for the loss of attitude
control fuel, from DMOC. The maneuver team propagated the state vector to the time or place of the next
maneuver, based on the most recent baseline trajectory plan. The maneuver team targeted most maneuvers
by varying ignition time, duration, and spacecraft pointing direction. The ignition time was generally
determined by orbital mechanics for minimal V, such as maneuvers at periapsis to lower apoapsis, or a
maneuver off the apsis to rotate the line of apsides. Other maneuvers that would not suffer a significant V
penalty were assigned ignition times based on convenience. For example, one trim maneuver (P2c) was
planned at 13:00 coordinated universal time (UTC) so that it occurred at the beginning of a standard work
day (08:00 Eastern Standard Time) and started on an even hour.
After the maneuver was targeted, the start time was truncated to the nearest tenth of a second, the
duration truncated to a hundredth of a second, and pointing angles to a ten-thousandth of a degree. The
pointing angles described the thrust vector in the spacecraft’s local Velocity-Normal-Binormal (VNB)
coordinate frame, and DMOC converted them to an actual attitude quaternion. The pointing angles were
given with enough significant figures to assure sufficient precision of the resultant attitude quaternion.
The maneuver team tested the truncated maneuver planning information by running a computer
simulation of the maneuver. If the trajectory goals were not be met with the truncated values, it was a clear
indication that the trajectory was still sensitive to small perturbations and that another maneuver would
probably be needed to trim the trajectory. (This same technique had been used before launch to identify
placeholders for correction maneuvers.)
Deliverables
Once maneuver targeting was complete, the FDF maneuver team prepared a maneuver plan for the
NRL and the other FDF groups. The plan consisted of the critical finite maneuver parameters followed by
other summary information of the finite maneuver and any subsequent impulsive maneuvers in the current
mission phase. The critical maneuver parameters were the burn start time, stop time, duration, and the
inertial direction of the thrust vector in the VNB coordinate frame. The additional summary information
included propulsion system characteristics such as the values for thrust, Isp, TSF, the total amount of fuel
used, the maneuver goals, and any comments describing unique features of the maneuver.
One maneuver team member prepared the plan, then another team member quality assured it. This
quality assurance involved double checking the critical numerical information on the plan, checking the data
values in the software configuration used to model the maneuver, many times rerunning the software or re-
creating the maneuver with a separate software configuration, and verifying that the maneuver would indeed
achieve the desired goals. Because this was the first collaboration between FDF and DMOC, it was
especially important to check such details as units and coordinate frames. When the reviewer was finished,
he or she would sign the hardcopy maneuver plan. The plan originator would then present the final plan to
the FDE and the mission manager who would check pertinent details of the plan and make sure they
understood how the maneuver was achieving the intended goals. Upon the FDE’s approval, the maneuver
team would then send the plan to DMOC.
The maneuver team sent an electronic copy of the plan to DMOC via modem, and faxed a
hardcopy as a backup. The maneuver team then followed up with a telephone call to the TAMP personnel
at DMOC, explained the details of the maneuver plan, and answered any questions. Hardcopies of the plan
were also distributed to the other FDF elements, and the predicted postmaneuver state was uploaded to the
FDF’s mainframe for use in orbit determination. In addition, the maneuver team gave a file containing the
expected accelerations from the propulsion system to the FDF orbit determination team so that they could
fit tracking data through the maneuver and determine a first quick look at the thrust scale factor.
12
Confirmation
As a consistency check, DMOC sent the FDF maneuver team a portion of the spacecraft command
file before it was uplinked. The maneuver team ran a computer simulation using this information, verifying
that DMOC had received the correct start and stop times of the maneuver, and that the attitude quaternion
that DMOC had calculated from the maneuver plan would indeed point the spacecraft properly. The
maneuver team relayed the results of this verification to DMOC through the FDE.
Contingency Preparation
Each time the maneuver team planned a maneuver, they also planned alternative strategies in case
the maneuver was aborted or missed. The alternate strategies were calculated ahead of time to determine
how quickly a correction would be needed in case the maneuver failed. Many of Clementine’s maneuvers
were considered critical because if the maneuver was missed, it would be impossible to recover the mission
with a later maneuver. A prime example was the first lunar orbit insertion maneuver (LOI-1). Had this
maneuver been missed, the spacecraft would not have been captured into lunar orbit and would have been
catapulted into orbit around the Sun. For such cases when the mission could not be recovered by a
correction maneuver, the maneuver team investigated alternative trajectories that would recover some of the
mission goals.
Reconstruction and Calibration
After the maneuver was performed, DMOC sent the commanded start and stop times along with
the telemetered attitude quaternion observed at the start of the maneuver to the FDF maneuver team. The
maneuver team also received the best estimated trajectory (BET) state vector from the FDF orbit
determination team. The BET vector was determined using all available tracking data up until the time of
the maneuver, and was usually delivered within 30 minutes after the maneuver ended. The epoch of the
BET vector was usually 15 to 30 minutes before the maneuver start time. Figure 3 shows the BET and its
relationship to the maneuver along the spacecraft’s trajectory.
Upon receipt of the observed information from DMOC, the maneuver team performed the analytic
reconstruction. This involved propagating the BET vector until the observed start time and applying a
maneuver of the observed duration using the observed attitude quaternion. This reconstruction was the first
indication of the maneuver’s performance. The results of this reconstruction were given to the FDE who
relayed the information to DMOC.
The next maneuver reconstruction that had been planned, the accelerometer reconstruction,
became one of the casualties of the Clementine fast-track approach. The software interface with DMOC
that would have enabled FDF to receive and process the attitude and accelerometer telemetry became a low
priority as launch approached, and the file formats and software were never tested before launch. After
each maneuver, FDF was to reconstruct the maneuver by using the accelerometer data instead of an engine
model, and using the actual attitude history during the maneuver instead of the attitude at ignition. The
results of this reconstruction were to be sent to DMOC within an hour after burnout, and would have been
the first indication of the maneuver performance based completely on observed data. The FDF did
eventually receive some accelerometer data in text form and used the start and stop times as a coarse check
on the maneuver. The FDF team also reconstructed some of the burns using the text data, but only as a
proof of concept. Although the reconstructed information from the accelerometer would have been “nice”
to have after each maneuver, there never was a situation where it was critical for support.
The next form of reconstruction was combined with maneuver calibration, and was called the
Keplerian calibration. This was performed when enough postmaneuver tracking data was collected to
ensure a reliable solution, usually by 6 to 10 hours after the maneuver, depending on the orbit geometry and
13
available ground stations. The FDF orbit determination team delivered an observed postmaneuver solution
to the maneuver team with an epoch about ten minutes after the maneuver burnout. (Refer to Figure 3
which shows these orbit states.) The maneuver team first propagated the BET state to the observed ignition
time, and then modeled a maneuver for the observed duration at the observed attitude, which was the
observed attitude quaternion at ignition converted back to pointing angles in the spacecraft’s local VNB
coordinate frame. The postmaneuver trajectory was then propagated 10 minutes to the epoch of the
observed postmaneuver orbit determination vector. Using the observed postmaneuver state represented in
Keplerian elements as goals, the team used Swingby’s targeter to vary the TSF until there was agreement
with all six of the Keplerian elements. If the Keplerian elements could not be matched to two decimal
places, the maneuver team included the spacecraft’s pointing angles as variables, effectively solving for a
pointing bias. The TSF determined would then be used to plan subsequent similar maneuvers. Had there
been any significant pointing bias, it would have been used as well, but there never was much of a bias.
Epoch of Postmaneuver Solution
10 Minutes Postmaneuver Arc
Maneuver Arc
Maneuver Start
Maneuver Burnout
Premaneuver
Spacecraft
Trajectory
Postmaneuver
Spacecraft
Trajectory
Epoch of BET
Figure 3 Events Along the Spacecraft Trajectory Near a Maneuver
Before launch, another type of reconstruction and calibration was considered, called V
calibration, which would have been based entirely on the pre- and postmaneuver tracking data. The V
calibration procedure was similar to the Keplerian calibration, except that rather than targeting on the
observed postmaneuver Keplerian elements, the goals were the observed V vector. This observed V
vector was calculated by propagating the BET to the observed burnout time without any thrust and
subtracting the velocity vector from the velocity vector of the observed postburn state back-propagated to
the same epoch. This was an approximation, but for high-thrust maneuvers, the benefits may outweigh the
slight inaccuracy.
Although V calibration was never used in operations, some preliminary analysis of Clementine’s
maneuvers showed that it could be a viable means of reconstructing a maneuver if the Keplerian elements
are not well behaved. The maneuver team had originally considered using this method to reconstruct the
lunar orbit departure (LOD) maneuver because the trajectory would be hyperbolic with respect to the Moon
and would initially have wildly varying Keplerian elements with respect to the Earth.
MANEUVER DESCRIPTIONS
14
The team’s general procedures and considerations for supporting maneuvers have been outlined
above, while the following sections describe some specific details for each major phase of the mission that
FDF supported operationally: LEO, the first cislunar phasing loop phase, and the lunar orbit phase. The
lunar orbit phase is divided into a discussion of the lunar orbit insertion and lunar mapping orbit control.
Table 3 summarizes all the maneuvers and shows the prelaunch and actual V magnitude, the parameters
that were varied to target the maneuver, and the maneuver goals. The execution error column is based on
maneuver calibration, and is explained in a later section.
Low-Earth Orbit
Before launch, the maneuver planning activities were expected to be minimal during the LEO
phase; a coarse TTI maneuver plan was due to DMOC the day after launch, an updated coarse plan 24
hours before TTI, and then the final plan 6 hours before ignition. The TTI maneuver and the maneuvers in
the cislunar phasing loops were targeted to achieve specified periselene radius, inclination, and right
ascension of the ascending node at the Moon. Because TTI consisted of a solid motor firing, its duration
was fixed, and only the thrust direction and ignition time could be varied. In addition, TTI had to be
performed within sight of a transportable groundstation in Hartebeesthoek, South Africa.
After launch, however, the “minimal” maneuver support for LEO turned out to be 24-hour support
for almost a week. The spacecraft’s battery became discharged during the first 2 days of the mission, and
the solar arrays could not be deployed until Clementine had left LEO. Many times this situation caused
DMOC to consider performing TTI early to move Clementine out of LEO. There was one “ideal” time
each day that Clementine could perform TTI for little if any fuel cost above baseline, so the team calculated
and delivered these maneuver plans to DMOC. FDF also calculated and delivered plans to reach the Moon
if DMOC had to wait an orbit or two after the ideal opportunity on each day. These combinations of
analysis scenarios meant that during the 8.5 days that the spacecraft was in LEO, FDF delivered more than
55 TTI maneuver plans to DMOC. In some of these situations, FDF was asked to plan to leave LEO within
12 hours.
All these requests for TTI maneuver plans meant that whichever shift was on duty had to replan the
entire cislunar phase several times. To complicate matters, the area where FDF is located, Washington, DC,
was experiencing one of the iciest winters in recent history. The shift on duty was never sure if the next
shift would be able to reach GSFC, so the value of fully training both shifts in all functions was
emphatically demonstrated during this period.
As it turned out, DMOC was able to recharge the battery completely during LEO, and an early
departure was not necessary. An uplink problem prevented TTI from occurring on the nominal date, so
Clementine left LEO 1 day after the prelaunch plan. This delay proved the worth of the phasing loop
approach to the cislunar trajectory design, since by simply adjusting the period to compensate for the extra
day in LEO the mission goals could still be met without a fuel penalty.
15
Table 3
SUMMARY OF CLEMENTINE MANEUVERS
V (m/s)
Maneuver
Variables
Goals
Date &
Time
(UTC)
Duration
(sec)
Fuel
Used
(Kg)
Prelaunch
Commanded
Execution
Error
LEO
-
-
-
15.0
0.0
-
TTI
Ignition; Pitch;
P1; P2; P3
Radius at Periselene;
Lunar Inc; TOD Ecliptic RAAN
2/3/94
06:29:04
64.6
1074.1
2966.1
2968.2
-0.2%
ISA-
Separation
-
-
2/4
07:12:39
-
-
-
-
-
A1
-
-
-
-
-
5.0
0.0
-
P1
Ignition; Duration;
P2 magnitude
Radius at Periselene;
Lunar Inc; TOD Ecliptic RAAN
2/5/94
10:00:53
196.0
31.5
154.2+
23.0
217.9
-2.0%
P1c
Duration; Pitch;
Yaw; P2
Radius at Periselene;
Lunar Inc;TOD Ecliptic RAAN
2/6/94
10:00:00
28.2
4.5
50.0
32.6
-2.4%
ROT-1
-
-
-
-
-
50.0
0.0
-
ROT-2
-
-
-
-
-
50.0
0.0
-
P2
Duration; Pitch
Radius at Periselene;
Lunar Inclination
2/15/94
12:52:32
6.3
1.0
6.0
7.2
+3.0%
P2c
Duration; Pitch
Radius at Periselene;
Lunar Inclination
2/16/94
13:00:00
1.2
0.2
1.0
1.4
-6.5%
Lau.Window
-
-
-
10.0
-
-
LOI-1
Ignition; Duration
Argument of Periselene; Period;
Radius of Periselene after LOI2
2/19/94
12:51:32
370.1
59.4
448.44
457.8
+0.5%
LOI-2 Miss
-
-
2/20/94
12:42:24
?
0.2
-
-
N/A
LOI-2
Ignition; Duration;
Pitch
Argument of Periselene; Period;
Radius of Periselene
2/21/94
12:16:17
75.9
12.2
106.52+2.0
103.9
-0.4%
LOI-Trim
Ignition; Duration;
Pitch
Period; Radius of Periselene;
Argument of Periselene
2/22/94
12:17:10
3.7
0.6
5.0
5.2
+3.3%
MNT-1
Ignition; Duration;
Pitch
Radius of Periselene; Period;
Argument of Periselene
3/11/94
14:37:31
13.9
2.2
19.05
19.3
-1.5%
1st Month
(Margin)
-
-
-
-
5.0
-
-
LROT-1
Ignition; Duration;
Pitch; Yaw
Post LROT2: Period; Radius of
Periselene; Arg of Periselene;
Long. of Asc. Node (LAN)
3/26/94
02:21:07
74.3
11.9
102.39
105.8
+0.2%
LROT-2
Ignition; Duration;
Pitch; Yaw
Period; Radius of Periselene;
Argument of Periselene; LAN
3/26/94
12:41:06
72.5
11.6
103.8
107.0
-0.7%
LROT-
Trim
Ignition; Duration;
Pitch; Yaw
Period; Radius of Periselene;
Longitude of Ascending Node
3/27/94
18:30:00
2.6
0.4
5.0
3.9
-3.3%
MNT-2
Duration; Pitch
Period; Radius of Periselene;
Argument of Periselene
4/12
17:16:48
20.79
7.8
-
2nd Month
(Margin)
5.0
-
-
Node
Rotation
(Removed by
LROT burns)
9.57
0.0
-
Margin
15.0
-
-
LOD
509.2+21.0
-
-
PP1
2.14+18.0
-
-
PA1
1.59+1.0
-
-
PP2
23.32+10.0
-
-
Trim
10.0
-
-
GeographosA
rrival
10.0
-
-
Italic V numbers indicate that this was extra V considered as margin before launch.
16
After the TTI maneuver was (finally) performed and tracking data became available, the maneuver
team reconstructed the maneuver and solved for the actual thrust vector and thrust scale factor (TSF). The
TTI had an effective pitch bias of 5.3 degrees, a yaw bias of 2.3 degrees, and a TSF of 0.998. The biases
were due to the spacecraft coning during the maneuver (as mentioned, Clementine was spin stabilized for
TTI while all other maneuvers were three-axis stabilized.) The 0.998 TSF is an indication that the effective
V for the TTI was about 2962 m/s. Before the maneuver, TTI was expected to be 2968
15 m/s, and the
expected pointing error was less than 5 degrees. Premission error analysis had led to budgeting extra
bipropellant fuel to correct for errors in TTI. The premission analysis was used for reference during the
reconstruction to determine the best error-correction strategy. The three proposed strategies were a two-
burn rotation of the line of apsides in the large phasing loop, applying a binormal component of V at the
first perigee maneuver (P1) by pitching the spacecraft, or performing the maneuver off-perigee. The key
criterion for determining a strategy was V cost. Performing P1 slightly after the first perigee and adding a
small maneuver at the second perigee corrected the trajectory for the minimum V.
Cislunar Phasing Loops
The transfer trajectory from LEO to the Moon was designed as two phasing loops, with maneuvers
at both perigees. P1 increased the semimajor axis so that apogee was approximately at the lunar orbit
distance. The second perigee maneuver, P2, was targeted simultaneously with P1 to control the phasing of
the spacecraft so that the spacecraft would encounter the Moon as the trajectory intersected the lunar orbit.
Usually, simultaneously targeting the P1 and P2 maneuvers simply transferred V between the two
maneuvers such that the sum of the Vs was nearly constant.
In addition to raising apogee, P1 was performed 18 minutes after perigee so that it would rotate the
line of apsides, correcting for the pointing error during TTI. This was accomplished by allowing the start
time of P1 to be varied. P2 was fixed to start right at the second perigee. Swingby’s targeter was, therefore,
set up to vary the ignition time and duration of P1 maneuver, with the maneuver along the velocity vector,
and the magnitude of the impulsive P2 maneuver. The goals were specified as floating end-point radius at
periselene, lunar inclination, and ecliptic right ascension of the ascending node (RAAN) at the time of LOI.
Because P1 was the first firing of the bipropellant engine, it was uncalibrated. Maneuver
reconstruction revealed that the bipropellant engine ran about 2 percent cold (e.g., a TSF of 98 percent).
This slight error required that a trim, or correction, maneuver (P1c) be performed. The team first tried
avoiding P1c by planning the correction as part of P2, but the V cost was prohibitive. The P1c was
planned similarly to P1, simultaneously planning P2 as well. P1c was planned to occur about 24 hours after
P1, which gave ample time for orbit determination and other preparations. Furthermore, premission error
analysis showed that small V savings to be gained by performing the maneuver earlier than 24 hours was
not worth the risk of using poor tracking data solutions or rushing the maneuver support.
In planning P1c, the team evaluated whether to target only the two in-plane components of V,
which would control periselene radius and inclination at LOI or to also target the ascending node by using
the out-of-plane component of V. Both cases were planned, and the V cost of using all three components
was not significantly higher than just using two, so all three were used.
After discussion with DMOC, the maneuver team planned P1c with a TSF of 1.0 because it was
thought that the 2-percent TSF on P1 may have been due to an anomaly. The P1c burned about 2.4 percent
cold, so P2 was planned with a 98 percent TSF. However, P2 burned about 1 percent hot yielding a 3-
percent execution error. The hot burn at P2 resulted from a combination of several factors. Foremost was
that P2 was a very short burn
it lasted only 6 seconds (P1 lasted 196 seconds and P1c lasted 28 seconds).
In addition, because of spacecraft heating, the pressure in the tanks before P2 was unusually high, well
above the upper pressure limit of the onboard pressure regulation system. During the 6-second maneuver,
17
the system was simply blowing down, never triggering the pressure regulation and never reaching steady
state. The abnormally high tank pressure caused a higher inlet pressure, which increased the thrust.
The next maneuver was then a correction to P2 (P2c), which had a duration of 1.2 seconds. After
discussions with the NRL spacecraft engineers, it was determined that P2c should be planned with a TSF of
1.0, since very short maneuvers would not really be pressure regulated. At one point, FDF wondered
whether P2c should even be performed because the spacecraft engineers thought such a short maneuver
might show as much as 20 percent error. The FDF team reasoned that since this was a small correction
burn, even an 80 percent correction of the 3 percent P2 error would be advantageous, and the residual error
could be corrected during lunar orbit insertion. FDF and DMOC concurred, and P2c was performed. The
maneuver was calibrated at 0.975.
Lunar Orbit Insertion
The LOI maneuvers were planned before launch as two simple retrograde maneuvers performed at
periselene to reduce Clementine’s energy, capture it into lunar orbit, and establish the proper mapping orbit.
The first maneuver (LOI-1) was designed to use about 80 percent of the V needed to establish the proper
lunar mapping orbit, and the second maneuver (LOI-2) would be executed three revolutions later (24 hours)
following orbit determination. This second maneuver would lower aposelene and create the desired 5-hour
period mapping orbit. However, in response to changing requirements and errors from previous maneuvers,
LOI became more complex than planned.
The LOI maneuvers depended on the incoming transfer to establish the correct altitude of
periselene and inclination. Although the inclination was correct, small errors not fully corrected by P2c
caused the periselene altitude to be higher than desired. If uncorrected, the higher altitude would eventually
require an extra maneuver during the first mapping month, possibly resulting in some science data loss.
Consequently, the team investigated alternative insertion schemes that could correct the altitude while
capturing the spacecraft and establishing the mapping orbit.
The maneuver team determined that LOI-2 could be performed slightly off apsis, thereby achieving
the desired post maneuver altitude. However, this had the unfortunate side-effect of rotating the argument
of periselene away from its target value of 331.5 degrees. To compensate for this, LOI-1 could also be
performed off apsis, however, this affected the periselene altitude before and after LOI-2. By manually
adjusting these maneuvers iteratively, it was finally determined that performing LOI-1 1.5 minutes before its
periselene and performing LOI-2 4.5 minutes after its periselene would have the combined effect of
restoring the proper altitude while preserving the argument of periselene. Furthermore, the combined V
required for LOI-1 and LOI-2 for this new plan was the same as the baseline. A quick error analysis
confirmed that even with a 5 percent burn error at LOI-1, Clementine would be captured into lunar orbit
and that corrections could be made by adjusting LOI-2.
After discussion with DMOC, the new technique was implemented because (1) there was no fuel
penalty; (2) the slight changes to the maneuver times did not require schedule changes; (3) the new plan
posed no risk to the maneuver planning process; and (4) the new technique would eliminate an extra
correction maneuver during mapping.
LOI-2 was planned to occur three orbits after LOI-1 but was aborted immediately after ignition
due to a telemetry flag that showed that the sensor door was open. Although DMOC thought that the door
was probably closed, LOI-2 was not a critical maneuver and could be aborted without jeopardizing the
mission. Maneuver reconstruction based on orbit determination revealed that approximately 1.2 m/s of
thrusting had occurred before the maneuver was aborted. The team replanned a new LOI-2 for the
following day.
18
The new LOI-2 was successful in establishing the desired mapping orbit; however, FDF received
word that the start of mapping would be delayed a few days until after a pass over the Apollo-16 landing
site. Because of perturbations, the mapping orbit’s altitude at periselene increased each day during the first
month. This meant that the delay in the start of mapping would cause the altitude to grow beyond its upper
limit of 450 km unless an extra maintenance maneuver was added. Consequently, a joint decision with
DMOC was made to perform a trim/maintenance burn, LOI-2c, the day after LOI-2, to lower the altitude at
periselene. After it was performed, the resulting mapping orbit met all the prelaunch requirements.
Lunar Mapping Orbit Control
Clementine’s lunar mapping orbit was an approximately 5-hour period polar orbit with an
eccentricity of 0.375. It was designed to take 2 months (two lunar rotations) to completely map the Moon,
with the second month’s lunar groundtrack interleaving between the first. Mapping was done near the
periselene, and the data were telemetered to Earth near aposelene. The argument of periselene was around
30 degrees below the lunar equator for the first month and around 30 degrees above for the second month,
which maximized coverage at both poles. A more complete description of the lunar orbit design will be
presented in another paper6.
Because of the very nonspherical lunar gravity potential and the strong gravitational effect of the
Earth and Sun, the lunar mapping orbit was not very stable. During the first month, the altitude of
periselene increased, and in the second month it decreased. In addition, the argument of periselene rotated.
Without any maintenance maneuvers, the lunar mapping requirements of a periselene altitude between 400
and 450 km and an argument of periselene between -27 degrees and -30 degrees would have been violated
after approximately 2 weeks. The requirements for the second month were the same for altitude, and from
+27 degrees to +30 degrees for argument of periselene. Therefore, the prelaunch baseline trajectory
included maintenance maneuvers planned in the middle of each month. To handle the osculation of the
lunar orbit elements for analysis and monitoring, the orbital elements were always calculated at periselene.
This provided consistency despite the large perturbations of the gravity field.
To maintain the interleaving of the 2 months’ groundtracks, the period had to be maintained, so the
maintenance maneuvers were targeted to adjust periselene altitude and argument of periselene, while
preserving the premaneuver period. This task was accomplished by varying the velocity magnitude and
pitch angle, and resulted in a nearly radial maneuver. The maneuver also had to be performed so that it did
not disrupt mapping, so it was performed after data collection and before aposelene.
The first maintenance maneuver was 19.3 m/s, which compared very well with the prelaunch value
of 19.05 m/s. When the maneuver was performed, it was 1.5 percent cold, but it had been targeted with
enough margin that requirements were met until the next scheduled maneuver.
Two rotation maneuvers, LROT-1 and LROT-2, were designed to rotate the argument of
periselene from -30 degrees to +30 degrees after the first month of mapping. These maneuvers used a
standard bielliptic transfer technique7,8. Clementine’s sequence included an extra revolution between the
maneuvers for orbit determination; if the first maneuver had a problem, the second maneuver could be
replanned, or even canceled if necessary, and no fuel would be wasted while a correction strategy was
developed. With the extra revolution, the maneuvers were planned 10 hours, 20 minutes apart.
The rotation maneuvers were first planned as impulses, and an analytic formulation based on two-
body in-plane orbit mechanics was used to generate a first guess at the maneuver start times, directions, and
magnitudes. The second maneuver was then retargeted with a plane change so that the longitude of the
ascending node of the orbit after the rotation maneuvers would fall properly between the orbits in the first
month, ensuring that the first and second month’s orbits interleaved. After this out-of-plane component was
targeted, half of it was subtracted from LROT-2 and added to LROT-1. The two in-plane maneuvers were
identical in magnitude because it was a symmetric problem, so dividing the out-of-plane component equally
19
minimized the total V. LROT-1 was then planned as a finite burn to achieve the postmaneuver orbital
elements from the impulsive targeting. After this, LROT-2 was modeled as a finite burn, targeting on the
desired orbital period, radius at periselene, and longitude of the ascending node.
Because the timespan between LROT-1 and LROT-2 was so short, the maneuver team was staffed
to handle replanning LROT-2 quickly if needed after LROT-1. The first shift planned both maneuvers
before LROT-1 and delivered them to DMOC. The second shift took over after LROT-1 and reconstructed
the maneuver based on the orbit determination solution. The second team then had to recommend whether
the original LROT-2 plan should be used or a new plan should be generated. Because LROT-1 executed
about 2 percent hotter than expected, LROT-2 was replanned and delivered to DMOC within the original
pre-LROT-1 schedule. LROT-2 was about 0.7 percent cold, which would have caused extra maintenance in
the second month of mapping. DMOC and FDF agreed to plan another small trim maneuver about 30 hours
later, which was similar to the first month’s maintenance maneuver. This was the last maneuver planned by
FDF because DMOC assumed maneuver planning responsibilities after March 31.
TRENDS ACROSS ALL MANEUVERS
This section describes the results of the maneuver planning process as a whole and compares the
actual maneuvers with the prelaunch predictions.
V Budget
During mission planning, error analysis showed the need to budget contingency V to recover
from potential errors. Figure 4 shows the baseline V planned for the Clementine mission, the baseline V
including error correction margins, and the actual V used. As expected before launch, the actual V lies
between the baseline values and the baseline with margin values, indicating that the V budgets were well
planned. Figure 4 shows a very close comparison between the planned V totals pre-flight and in-flight. By
the time of the lunar rotation burn, the V expended was only 36.4 m/s over the baseline plan, and 65.7 m/s
under the baseline plus margin amount.
Early in the mission, the V expended rose above both the baseline and baseline plus margin
values because of TTI pointing errors. This is due to the fact that the baseline error correction strategy for
an anomalous TTI was to use a pair of apsidal rotation maneuvers, CRT1 and CRT2. However, after the
actual TTI maneuver, an off-apsis P1 maneuver was planned instead to provide the necessary trajectory
corrections, using less fuel than the rotation maneuvers would have used. Figure 4 therefore shows the
actual V dropping below the baseline plus margin values by the time of CRT1.
Figure 4 shows that from CRT2 on, the total V for each maneuver was very close to the baseline
V (without any margin). The margins to correct bipropulsion maneuver errors were allocated before
launch based on expected worst case values: 3 percent magnitude error and 2 degrees yaw and pitch errors.
The actual magnitude errors were less than 2 percent for the large maneuvers, and there was no detectable
pointing errors. Therefore, once the TTI errors were corrected, the planned margin for the remainder of the
maneuvers was mostly unused.
Thrust Scale Factor
Figures 5, 6, and 7 show Clementine maneuver TSF results. Figure 5 shows the difference
between the TSF used by the maneuver team to plan the maneuver and the actual TSF determined after the
maneuver; this difference is the maneuver planning error. One reason for errors is that it takes several
maneuvers before the spacecraft engineers and the maneuver team become comfortable with a TSF value.
Selecting the proper TSF was also hampered by the greatly varying burn durations for the first several
20
maneuvers. Figure 6 shows the variation in actual TSF as a function of maneuver duration. As expected,
the smaller duration burns had scattered TSF values, while the longer maneuvers had TSFs all around 98
percent. LROT-2, which was fairly long, had a low thrust scale factor because it unexpectedly was
triggered into backup pressure regulation mode, which used different pressure sensors on different tanks for
pressure regulation.
DSPSE Delta-V --
Baseline, Baseline with Margin, and Actual
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
A1 Cal
P1
TTI makeup
P1C
CRT1
CRT2
P2
P2C
LWmargin
LOI1
LOI1c
LOI2
LOI2trim
1st month LOC
1st month margin
LRT1
LRT2
Rotation trim
Maneuver Name
Cumulative Delta-V After Each Maneuver (m/sec)
baseline
baseline w/margin
actual
Figure 4 Planned and Actual Vs
Figure 5 does show a general trend toward better prediction of TSF as the mission progressed but
only for the longer duration maneuvers. The correlation between maneuver planning error in Figure 5 and
burn duration is shown in Figure 7. The shorter maneuvers have the greatest errors, so regardless of when
in the mission the maneuver was executed, the shorter duration burns had unpredictable TSFs. This was
expected because the shorter maneuvers never achieved steady state pressure regulation.
21
DSPSE Maneuver Results
Planned and Actual Thrust Scale Factors
92.00
93.00
94.00
95.00
96.00
97.00
98.00
99.00
100.00
101.00
102.00
P1
P1C
P2
P2C
LOI1
LOI2
LOI2trim
1st month LOC
LRT1
LRT2
Rotation trim
Maneuver Name
Thrust Scale Factor (%)
planned TSF
actual TSF
Figure 5. Maneuver Results -- Planned and Actual Thrust Scale Factors
Maneuver Thrust Scale Factor vs. Burn Duration
93.00
94.00
95.00
96.00
97.00
98.00
99.00
100.00
101.00
102.00
050 100 150 200 250 300 350 400
Burn Duration (seconds)
Post Calibration Thrust Scale Factor (%)
P1C
P1
P2
P2C
LOI1
LOI2
LOI2trim
1st month LOC
LRT1
LRT2
Rotation Trim
Figure 6. Maneuver Results -- Thrust Scale Factors
Maneuver Planning Error vs. Burn Duration
-7.00
-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
4.00
050 100 150 200 250 300 350 400
Burn Duration (seconds)
Post Calibration Maneuver Planning Error (%)
LOI1
P1
P2C
Rotation Trim
1st Month LOC
P1C
LOI2trim
P2
LRT1
LRT2
LOI2
Figure 7. Maneuver Results -- Maneuver Planning Errors
22
LESSONS LEARNED
Of the many lessons learned in flying this mission, this section highlights those that seemed
especially significant to the authors who hope they will be useful for planning future missions.
The technique of modeling maneuvers as impulsive burns worked very well for this spacecraft and
simplified long-range mission planning and prelaunch maneuver analysis. Modeling the
pressure-regulated bipropellant engine simply with a constant Thrust and Isp also worked well, and no
trim or error correction maneuvers were needed because of modeling errors.
The assumptions made during prelaunch mission analysis that the trajectory could be treated in distinct
phasesLEO, phasing loops, lunar orbit, and transfer to Geographos–proved to be valid. Even though
the late TTI caused the phasing loops to change, the changes did not affect the maneuvers after LOI.
This phased approach was a great help in premission analysis because it isolated the studies and
allowed several analysts to work on different phases simultaneously.
The prelaunch projections of the operational maneuver planning activities for the Clementine mission
were fairly accurate. Although there were some changes, the risk mitigation strategies compensated for
them. All the maneuvers fell within the predicted error margins except TTI, which had a pointing error
greater then expected but was still corrected well within the V budget. The TTI was performed a day
late, but this delay was compensated for easily using the phasing loops.
Due to the contingency in LEO, the amount of work done in LEO was well above expectations.
Running operations with two 13-hour shifts got to be tiresome for the team but did allow continuity
during maneuver support. Having both shifts fully trained for all maneuver planning and contingency
support was very important and helpful.
Detailed procedures were useful for prelaunch training and as a reference document during operations.
Single-page checklists of details for procedures common to all maneuvers were very useful in
operations, especially for quality assurance of data.
Truncating maneuvers to 4 or 5 significant digits identified possible correction maneuvers during
preluanch mission analysis, and simplified the interface with the control center (DMOC) during
operations.
Determining a consistent TSF for the short maneuvers was not possible, but had little effect on the V
budget because even a large percentage of a small maneuver has a small effect. Error analysis, fuel
budget creation, and trajectory design should account for the number of maneuvers needed to
determine a good TSF. The TSF’s possible relationship to the duration of the maneuvers should also
be considered. Using a differential corrector to solve for the TSF based on Keplerian elements worked
extremely well, and took less than two minutes to run.
CONCLUSION
Because of Clementine’s fast track approach and restricted budget, activities and procedures were
only performed to reduce the mission risks to acceptable levels. The constant challenge was to balance the
mission needs against the risks. While innovation was sometimes to come up with a new, advanced method
for some activity, more often it was to establish that a simple method would work just as well, costing less
or taking less time. Most of the methods described in this paper are not necessarily unique, but they were
worth mentioning because they got the job done.
23
The maneuver planning for Clementine was challenging, requiring solutions to interesting orbit
mechanics problems involving sensitive multibody trajectories. Each maneuver was new and unique—
techniques used for previous maneuvers were not always applicable to the current situation. When
problems arose, the team members had to use their ingenuity as much as their analytic skills. Like the rest
of the Clementine project, every team member was given the opportunity and freedom to make critical and
influential decisions. The resulting accountability created a challenging work atmosphere, and a rewarding
experience.
ACKNOWLEDGMENTS
The authors would like to acknowledge and thank the only member of the maneuver team not in
the author list, Craig Roberts. We look forward to reading the paper he is currently writing on Clementine’s
lunar orbit design6. In addition, we would like to express our appreciation to Darrel Conway, Don
Dichmann, and Robert Sperling, who assisted us behind the scenes in many ways, especially by developing
numerical algorithms.
REFERENCES
1. D. Carrington et al., “Trajectory Design for the Deep Space Program Science Experiment (DSPSE)
Mission,” AAS 93-260, presented at the AAS/NASA International Symposium, Greenbelt, Maryland,
April 1993
2. J. Carrico et al., “Rapid Design of Gravity Assist Trajectories,” presented at the ESA Symposium on
Spacecraft Flight Dynamics, Darmstadt, Germany, October 1991
3. J. Carrico et al., “An Interactive Tool for Design and Support of Lunar, Gravity Assist, and Libration
Point Trajectories,” AIAA 93-1126, presented at the AIAA/AHS/ASEE Aerospace Design Conference,
Irvine, California, February 1993
4. D. Conway et al, “Operational Use of Swingby–an Interactive Trajectory Design and Maneuver
Planning Tool–for Missions to the Moon and Beyond,” not yet published
5. W. Kizner, “A Method of Describing Miss Distances for Lunar and Interplanetary Trajectories,”
Ballistic Missile and Space Technology, III, 1961
6. C. Roberts et al, “Lunar Orbit Mission Design and Orbit Maneuver Computation for the Clementine
Mission,” to be presented at the CNES International Symposium on Space Dynamics to be held in
Toulouse, France in June, 1995.
7. D. F. Lawden, “Impulsive Transfer Between Elliptical Orbits”, Optimization Techniques, edited by
G. Leitman, Academic Press, New York, 1962, pp. 323-351.
8. D. F. Lawden, “Optimal Transfer Between Coplanar Elliptical Orbits”, J. Guidance Control and
Dynamics 15, 3 (1991), pp. 788-791.
