TABLE OF CONTENTS

            The University of Colorado's Laboratory for Atmospheric and Space Physics (LASP) has been chosen to provide mission operations support for ICESat (Ice, Cloud, and Land Elevation Satellite), a satellite that will study the growth or shrinkage of Greenland and Antarctica by taking laser altimetry measurements of ice sheets over these regions.  To effectively calibrate the spacecraft and its instruments, ICESat will fly in an 8-day repeat groundtrack calibration orbit for the first two to six months after its launch on December 19th, 2002.  Several orbit attainment burns will then be performed to decrease the spacecraft's semi-major axis and slightly increase its period to match the orbital parameters of ICESat's 183-day repeat groundtrack mission orbit.

            Because LASP will ultimately be responsible for ICESat's orbit attainment activities, this paper presents a proposal for a burn maneuver sequence that will transition ICESat from its calibration orbit to its frozen, mission orbit.  A search was first performed to investigate orbit attainment methods used by other satellites in frozen orbits.  Various orbital maneuvers were then compared, with fuel conservation upheld as a primary criterion for selection.  Finally, orbital mechanics equations, Satellite Tool Kit (STK) and the ICESat Orbit Control System (IOCS) software were used separately to generate a tentative burn maneuver sequence for mission orbit attainment.  These results were analyzed for their consistency with the IOCS results since the Ball Aerospace Flight Dynamics Subsystem Team will utilize this software system to generate the actual burn maneuver sequence for orbit attainment in an operational setting. 

            All results were similar to Matlab results obtained using simple orbital mechanics equations, with the exception of STK-generated delta V values, which showed significantly higher magnitudes than all other results.  Due to this fact, the STK burn maneuvers were deemed invalid.  The IOCS-simulated Hohmann Transfer method proved to be the most fuel efficient, although its delta V value was only slightly less than the result generated using IOCS's incremental error correction scheme.  However, the Hohmann Transfer-produced maneuvers also caused ICESat's groundtrack to leave its 800 m accuracy control band sooner than the other method, suggesting that the IOCS software's incremental error correction scheme might be better suited to conserve ICESat's fuel in view of the satellite's five year mission lifetime.

I.    INTRODUCTION

            The University of Colorado's Laboratory for Atmospheric and Space Physics (LASP) has been chosen to provide mission operations support for ICESat (Ice, Cloud, and Land Elevation Satellite), a satellite that will study the growth or shrinkage of Greenland and Antarctica by taking laser altimetry measurements of ice sheets over these regions.  To effectively calibrate the spacecraft and its instruments, ICESat will fly in an 8-day repeat groundtrack calibration orbit for the first two to six months after its launch on December 19th, 2002.  Several orbit attainment burns will then be performed to decrease the spacecraft's semi-major axis and slightly increase its period to match the orbital parameters of ICESat's 183-day repeat groundtrack mission orbit.²

            The Flight Dynamics Subsystem (FDS) Team, which is comprised of three University of Colorado (CU) graduate aerospace students from LASP, an FDS lead engineer from Ball Aerospace, and three software developers from the University of Colorado’s Center for Astrodynamics Research (CCAR) and Raytheon, will ultimately be responsible for the execution of ICESat’s orbit attainment activities.  However, the Ball Aerospace FDS lead engineer will be the only FDS team member in charge of designing the orbit lowering and orbit attainment maneuvers. The design of this maneuver sequence will be performed using the ICESat Orbit Control System (IOCS), a software program that utilizes an error correction scheme to incrementally correct ICESat’s orbit to ensure that the spacecraft maintains a precise control band of ±800 m along its reference groundtrack.
          
             Unfortunately, pre-launch, FDS-related activities for ICESat have proven to be excessively time-consuming.  As a result, a formal study to determine the most fuel-efficient method for lowering ICESat’s orbit from its calibration to mission phase has not been performed.  Instead, the FDS team has decided to rely completely upon the accuracy of the IOCS software, and its ability to determine the burns necessary to lower ICESat from its 8-day repeat groundtrack calibration orbit to its 183-day repeat groundtrack mission orbit.³  This paper details a formal comparison study that was performed to determine a burn maneuver sequence that will transition ICESat from its calibration orbit to its frozen, mission orbit.  Delta V calculations resulting from Satellite Tool Kit (STK), the IOCS software, and a Matlab program were compared, with fuel conservation upheld as a primary criterion for selection.  These results were then analyzed for their consistency with the IOCS results since the Ball Aerospace FDS lead engineer will utilize this software to generate the actual burn maneuver sequence for orbit attainment in an operational setting.

BACKGROUND: THE ICESAT MISSION

           
            The ICESat satellite, designed and constructed by Ball Aerospace, will provide ground-breaking data to the science community in the area of global warming by measuring the growth and/or shrinkage of ice regions near the Earth's poles.  The satellite’s main instrument, the Geoscience Laser Altimeter System (GLAS), will collect ice height data by firing laser pulses at positions on the Earth's surface and measuring the total time it takes for the reflected light pulse to bounce back to the satellite.  However, in order to fulfill GLAS's precise pointing requirements (the line of laser spots on a given ice sheet must repeat to ± 30 m, or 1 sigma), ICESat must maintain a repeat-groundtrack, frozen orbit of ±0.8 km.⁴

            In fact, ICESat will fly in two separate, repeat groundtrack orbits.  During the first 60-90 days of ICESat's mission, ICESat will remain in an 8-day repeat groundtrack calibration orbit.  This calibration orbit will overfly the White Sands ground station calibration site every 8 days with a 337 km spacing at the equator.  Once the satellite and its instruments have been commissioned and the 8-day repeat calibration orbit is no longer required, burns will be performed to attain ICESat's 183-day repeat groundtrack, mission orbit.  This mission orbit provides close groundtrack spacing for science observations with a 15 km spacing at the equator.²  Table 1 below shows some orbital parameters for ICESat’s two repeat groundtrack orbits.

Parameter	Calibration Orbit	Mission Orbit
Semi-major Axis, a	6971.5 km	6970.0 km
Eccentricity, e	0.0013	0.0013
Inclination, i	94o	94o
Argument of Periapse, ω	90o	90o
Repeat Period, P	119 revs in 8 days	2723 revs in 183 days
Groundtrack Repeat	± 800 m	± 800 m

Table 1:  Orbital Parameters for ICESat's Repeat Groundtrack Orbits

Satellite Tool Kit-generated 2-D maps of ICESat’s calibration and mission orbits are given as Figures 1 and 2 below:

 

Figure 1:  STK-Generated Image of ICESat’s 8-day Repeat Groundtrack Calibration Orbit

 

 

Figure 2:  STK-Generated Image of ICESat’s 183-day Repeat Groundtrack Mission Orbit

FOUNDATION:  THE FLIGHT DYNAMICS SUBSYSTEM

            To maintain ICESat’s mission/calibration orbit, as well as to transition between these orbits, the Flight Dynamics Subsystem was created.  Comprised of three University of Colorado (CU) graduate aerospace students from LASP, an FDS lead engineer from Ball Aerospace, and three software developers from the University of Colorado’s Center for Astrodynamics Research (CCAR) and Raytheon, the FDS Subsystem team will utilize three primary software programs to fulfill the ICESat mission’s science, attitude, and orbit determination requirements. 

            Quaternion calculation software developed by Jason Staunch of CCAR will calculate pointing commands for the spacecraft in order to maximize scientific yield.  Microcosm Orbit Determination software developed by Cam Meek of CCAR will provide estimation and prediction of the satellite’s orbit to enable communication and antenna pointing, as well as the ability to monitor the satellite’s groundtrack location to meet science objectives.  Although this software package does not deliver precision orbit determination, it does fulfill relatively tight accuracy requirements:  5 m in along track, 5 m in across track, and 1 m in the radial direction for orbit determination; and 1 km in along track, 10 m in across track, and 10 m in the radial direction for orbit propagation.⁴  Finally, Raytheon’s IOCS software will maintain the required calibration/mission orbit by designing orbit-transition and station-keeping burns.  All three of these software programs will be used in conjunction on a daily basis by the FDS team to fulfill all attitude, orbit determination, and science requirements for the ICESat mission.

II.    AN OVERLOOKED PROBLEM:  TRANSITIONING BETWEEN ICESAT’S ORBITS

            Due to the hectic pace that precedes any satellite launch, several relatively important mission preparation activities that could be dealt with at a future time without harming the satellite have been postponed until after launch.  One such activity consists of a formal study to determine the most fuel efficient method for lowering ICESat’s orbit from its calibration to mission phase.  At this time, the FDS team has decided to rely completely upon the accuracy of the IOCS software, and its ability to determine the burns necessary to lower ICESat from its 8-day repeat groundtrack calibration orbit to its 183-day repeat groundtrack mission orbit.³  The question may then arise as to why total reliance upon the IOCS software constitutes a problem?

            The IOCS software is based upon an incremental error correction scheme.  Operationally, this methodology provides several benefits: the software runs quickly and efficiently, while more traditional groundtrack-monitoring software schemes might take hours to run.  However, recall that ICESat’s mission and science specifications will require numerous station-keeping burns throughout the satellite’s five-year mission to maintain ICESat’s frozen, mission orbit.  Minimum fuel usage during orbital maneuvers, specifically maneuvers designed to lower the satellite’s orbit, is a primary concern; the satellite’s fuel must be conserved for use during the life of the mission.  Thus, other methods for designing ICESat’s orbit-lowering burns should be considered. 

FUNDAMENTAL CONCEPTS:  ORBITAL MANEUVER SELECTION

            Table 1 indicates that very few differences actually exist between ICESat’s calibration and mission orbits.  Both orbits are nearly circular, with an eccentricity of 0.0013, and both orbits have inclinations and arguments of periapse of 94^o and 90^o, respectively.  However, the calibration orbit has a semi-major axis of 6971.5 km, while the mission orbit has a semi-major axis of 6970.0 km.  Given the fact that these orbits are nearly circular and lie within the same orbital plane, the obvious choice for an orbital maneuver that will effectively lower ICESat’s orbit while minimizing fuel usage is the Hohmann Transfer.⁵

            The Hohmann Transfer, developed by Walter Hohmann in 1925, uses two tangential burns to perform a minimum-energy (i.e. minimum fuel usage), co-planar transfer from one circular orbit to another.  Calculations for this maneuver are relatively simple, and are given by Equations 1 through 3 below⁵:

       

∆V1={2µRm/[Rc(Rc+Rm)]}½-(µ/Rc)½	(Eq. 1)
∆V2=(µ/Rm)½-{2µRc/[Rm(Rc+Rm)]}½	(Eq. 2)
∆VTotal=∆V1+∆V2	(Eq. 3)

Where,

µ = The Earth's Gravitational Parameter, 398600.44 km³/s²
R_c = Radius of ICESat's Calibration Orbit, 6971.5 km
R_m = Radius of ICESat's Mission Orbit, 6970.0 km
∆V₁ = Delta V of the first Hohmann Transfer burn
∆V₂ = Delta V of the second Hohmann Transfer burn
∆V_Total = Total Delta V for the Hohmann Transfer

III.    ORBIT TRANSITION METHODS ON PREVIOUS MISSIONS

            One only need look at other missions’ methods for altering a satellite’s orbit to recognize that thorough analysis must be performed to ensure that mission constraints (minimum time, minimum fuel usage, etc.) are met.  The TOPEX/POSEIDON⁶ satellite, designed to fly in a frozen, nearly circular orbit, required orbit raising maneuvers after launch, because its injection orbit was 14 km too low.  Fortunately, TOPEX/POSEIDON's ground team had planned for this possibility, and had designed a series of six maneuvers using the Orbit Acquisition Maneuver Software (OAMS), a computer package derived from JPL's GTARG groundtrack monitoring code.  Similar to ICESat's IOCS software, OAMS utilizes an error correction scheme to design burn maneuvers.  By combining this software package and human analysis, the TOPEX/POSEIDON team was able to raise the satellite to its mission orbit within one month of launch.⁶  The GEOSAT Follow-on (GFO)⁷  mission team also used customized Matlab programs, JPL-produced GTARG software, and a self-imposed error-correction philosophy to design a burn maneuver sequence to lower the satellite from its injection orbit to its 41 km lower (semi-major axis) mission orbit.  To attain GFO's exact repeat operational orbit, the ground team designed "a series of maneuvers of decreasing magnitude, subsequent errors correcting for errors in the execution of preceding maneuvers."⁷  This method produced a sequence of 13 maneuvers ranging in magnitude from 0.11 m/s to 7.0 m/s that allowed the satellite to reach its mission orbit in approximately two months.⁷

            Unlike TOPEX/POSEIDON and GFO, the QuikSCAT⁸ and Landsat-7⁹ missions primarily chose human analysis over computer programs for their orbit attainment burn sequence design.  Prior to QuikSCAT's launch, a group of individuals that collectively became known as the Orbit Raising Working Group (ORWG) brainstormed to develop a plan for raising QuikSCAT from its injection orbit to its 800 km frozen mission orbit.  Once the first cluster of five burns was developed, the ORWG used Microcosm orbit determination software and the QuikSCAT Software Test Bench to verify their maneuver calculations and select the next set of burns.  This process resulted in QuikSCAT performing a series of 24 burns in order to attain its frozen mission orbit in 18 days.⁸  Landsat-7 relied even more heavily upon human analysis for its maneuver sequence design due to the complicated constraints posed by the mission requirements.  Not only was the satellite's final mission orbit a sun-synchronous, frozen, polar orbit, but Landsat-7 was also required to fly under Landsat-5 during the satellite's calibration phase.  Using custom-designed code algorithms and manual calculations, the mission team developed a  sequence of eight maneuvers, each less than 2.5 m/s each, that would allow Landsat-7 to reach its desired orbit in just two weeks.⁹

            It is interesting to note that while all of the missions mentioned above performed orbit transition comparison studies prior to launch, ground teams for these missions also combined several different design and analysis options for creating a burn maneuver sequence instead of relying on one calculation source.  This comparison study hopes to provide ICESat's mission team with a similar analysis regarding the reliability of the IOCS software to design orbit lowering burns after ICESat's launch.

IV.    COMPARISON STUDY

            A comparison study was performed to determine the reliability of the IOCS software, which will be utilized operationally to design the orbit lowering maneuvers that will transfer ICESat from its 8-day repeat groundtrack calibration orbit to its 183-day repeat groundtrack mission orbit.  As mentioned previously, the Hohmann Transfer was selected as the orbital maneuver of choice to lower ICESat’s orbit since it provides a minimum-energy (and thus minimum fuel-usage), co-planar transfer between ICESat’s two nearly-circular orbits.   However, the IOCS software relies upon an incremental correction scheme to design burn sequences.  This comparison study analyzed whether or not the IOCS software effectively designs orbit-lowering burns, or if its underlying correction scheme would ultimately waste ICESat’s fuel with unnecessary burn maneuvers.  To accomplish this comparison, calculations for a Hohmann Transfer to lower ICESat’s orbit from its calibration to mission phase were performed using Matlab and STK.  The IOCS software was then used to design two separate orbit-lowering burn maneuver sequences.  The first sequence relied solely upon IOCS’s incremental correction scheme.  The second sequence simulated a Hohmann Transfer by forcing two equal but separate burns at the northernmost and southernmost points of ICESat’s orbit.

MATLAB PROCEDURE

            A Matlab program, Hohmann_Transfer, was created using Equations 1, 2, and 3.  By inputting the radius of the initial orbit (in this case the calibration orbit’s radius), the radius of the final (mission) orbit, and the gravitational parameter of the central body (Earth), the user was able to calculate the delta V’s of the two Hohmann Transfer burns, the total delta V for the entire Hohmann Transfer, and the time of transfer in both seconds and days.  Note that this method of calculation is fairly simplistic since it does not take into account space environmental effects such as drag and solar radiation pressure, perturbations that could effect the accuracy of a Hohmann Transfer.

SATELLITE TOOL KIT PROCEDURE

            A scenario was created in Satellite Tool Kit (STK) to simulate ICESat’s calibration orbit.  A Hohmann Transfer to lower ICESat to its mission orbit was then simulated using directions available on CU’s Spaceflight Dynamics (ASEN 5050) course website.¹⁰  Figures 3 through 10 show the window associated with each step created in STK's Astrogator propagation tool to simulate a Hohmann Transfer.  

Figure 3:  Initial State Step of STK's Astrogator Propagation Tool  Used to Simulate a Hohmann Transfer



Figure 4:  Initial State Propagation Step of STK's Astrogator Tool Used to Simulate a Hohmann Transfer



Figure 5:  Start Transfer Step of STK's Astrogator Tool Used to Simulate a Hohmann Transfer

Figure 6:  Delta V1 Step of STK's Astrogator Tool Used to Simulate a Hohmann Transfer

Figure 7:  Delta V1 Propagation Step of STK's Astrogator Tool Used to Simulate a Hohmann Transfer

Figure 8:  Stop Transfer Step of STK's Astrogator Tool Used to Simulate a Hohmann Transfer

Figure 9:  Delta V2 Step of STK's Astrogator Tool Used to Simulate a Hohmann Transfer

Figure 10:  Delta V2 Propagation Step of STK's Astrogator Tool Used to Simulate a Hohmann Transfer

ICESAT ORBIT CONTROL SYSTEM SOFTWARE PROCEDURE

            Simulated ephemeris data for both ICESat’s calibration and mission orbits was available for this study.  To model an operational IOCS software run, the program was initialized; the IOCS initialization screen is given as Figure 11. 
 

 

Figure 11:  IOCS Initialization Screen

            An input orbit file was selected to place the spacecraft in ICESat’s calibration orbit, and the 183-day repeat reference groundtrack ephemeris file was selected in the “Reference Node File” field.  This field designates on which reference groundtrack the user would like the spacecraft to fly.  By specifying the calibration ephemeris file as ICESat’s current orbit and the mission ephemeris file as the spacecraft’s desired orbit, the user has told the IOCS software to design a burn maneuver sequence that will lower ICESat from its calibration orbit to its mission orbit.  Notice also that the button labeled “Next Approaching Track” was selected.  By choosing this option, the user has notified the IOCS software that a burn maneuver sequence to transition between orbits must be designed, instead of the usual station-keeping burns.

            Once the program has been initialized, the user must select the “Update” button, which will initiate the burn maneuver design sequence.  After the IOCS software has completed all calculations, the “Maneuvers” section of the screen should contain information pertaining to a burn maneuver sequence.  An example IOCS screen containing calculated maneuvers for this case is given as Figure 12:

Figure 12: IOCS Screen Containing Calculated Burn Maneuvers

Notice that the user has allowed all elements of this burn maneuver sequence to be estimated, relying entirely upon the IOCS software’s underlying incremental correction scheme.  Although several maneuvers appear in Figure 12, only the first delta V would be used operationally.  All other maneuvers may be catagorized as "future, suggested maneuvers".
   
            To simulate a Hohmann Transfer using the IOCS software, it is possible to force the program to perform two separate burn maneuvers, equal in magnitude but located at the southernmost and northernmost portions of ICESat’s orbit.  Once again, the IOCS software was initialized as represented in Figure 11.  However, for this case the “Maneuver Type” field in the “Maneuvers” section of the main screen was set to North/South prior to updating the program’s maneuver calculations.  Because the user indicated the “Maneuver Type” option, the IOCS software would only use these first two North/South burns to transition ICESat from its calibration orbit to its mission orbit, although other possible burn maneuvers would appear in the “Maneuvers” window below these first two burns.  An IOCS screen representing the North/South burn maneuver design case prior to burn calculation is given as Figure 13.

 

 

Figure 13:  IOCS Screen Representing a Split North/South (Simulated Hohmann Transfer) Burn Maneuver Sequence

V.    RESULTS

            Burn maneuver sequences were generated to transition ICESat from its calibration orbit to its mission orbit using orbital mechanics equations in Matlab, Satellite Tool Kit and the ICESat Orbit Control System.  In all instances, calculations for a Hohmann Transfer were used or simulated.  However, since the FDS team has decided to rely completely upon the accuracy of the IOCS software to design the burns necessary to lower ICESat from its 8-day repeat groundtrack calibration orbit to its 183-day repeat groundtrack mission orbit³, one run of the IOCS software was performed that allowed the program to design burn maneuvers using its internal incremental error correction scheme.  All software programs did successfully design burn maneuver sequences to lower ICESat from its calibration orbit to its mission orbit, although several of these results differed significantly.  Table 2 gives delta V results for each of the four software cases.

Software Case	Delta V1 (m/s)	Delta V2 (m/s)	Total DeltaV (m/s)
Matlab	0.440679	0.406811	0.813600
Satellite Tool Kit	2.116720	1.700000	3.81627
IOCS Using Error Correction Scheme	0.762340	---	0.762340
IOCS Using Simulated Hohmann Transfer	0.381153	0.381153	0.762306

Table 2:  Delta V Results for Each Software Case

            Notice that the IOCS software produced slightly smaller total delta V results than the other two software programs, most likely because the IOCS software takes space environmental factors such as atmospheric drag into account.  Given ICESat's low calibration orbit, atmospheric drag would actually help lower the spacecraft into its mission orbit, thus decreasing the total delta V required of the orbit-lowering burn maneuvers.  Notice also that when IOCS was allowed to use only its internal, incremental error correction scheme, the software produced one large delta V burn instead of two separate burn maneuvers.  

            In this study, the Matlab results were used primarily as a sanity check for the other software programs, and its inclusion was extremely helpful, especially since it made pinpointing STK's results as erroneous fairly simple.  Unfortunately, it is unknown why STK produced such large delta V results.  Burns of the magnitude suggested by STK seem decidedly unrealistic when compared with the results of the other software programs.  Still, the STK software did produce an animation, represented by the snapshot given as Figure 14, which indicated that, at least according to STK's internal algorithm, the burn maneuvers in Table 2 would transition ICESat from its calibration to mission orbit correctly.  

Figure 14:  Snapshot of STK Animation Showing ICESat Transitioning from its Calibration to Mission Orbit

            Despite STK's visual confirmation that its large burn maneuvers would effectively transition ICESat's orbit, common sense indicates that burns as large as those produced by STK should not be used onboard ICESat for relatively small orbit adjustments.

VI.    ERROR ANALYSIS

            Although the IOCS delta V results presented in the previous section look favorable, no conclusions regarding their acceptability may be made without a thorough error analysis.  Fortunately, the IOCS program automatically produces East-West and North-South groundtrack error plots.  Within these plots, dashed blue lines represent the 800 m control box that ICESat's groundtrack must maintain to accurately satisfy its stringent pointing requirements.  The red line represents the new groundtrack produced after burn maneuvers have been performed, and the black line represents the groundtrack without burn maneuvers.  Figures 15 and 16 give the North/South and East/West groundtrack error plots for the unconstrained IOCS case in which the software was allowed to use its internal incremental error correction scheme to produce a burn maneuver sequence.  Figures 17 and 18 give the North/South and East/West groundtrack error plots for the simulated Hohmann Transfer using IOCS.

 
Figure 15:  North/South Groundtrack Error Plot for Unconstrained IOCS-calculated Burn Maneuver Sequence




 
Figure 16:  East/West Groundtrack Error Plot for Unconstrained IOCS-Calculated Burn Maneuver Sequence



 

Figure 17:  North/South Groundtrack Error Plot for North/South Split (Simulated Hohmann Transfer) Maneuver

 

 

Figure 18:  East/West Groundtrack Error Plot for North/South Split (Simulated Hohmann Transfer) Maneuver

            Both IOCS cases produced similar total delta V results, and the errors associated with each case are similar as well.  Unfortunately, the blue dashed lines indicating ICESat's groundtrack control band are absent in Figures 15 and 16, but this omission may be the result of electronic transfer errors.  Analysis of Figures 15 through 18 reveals that the simulated Hohmann Transfer burn maneuvers allow the satellite's groundtrack to leave its 800 meter control band significantly earlier than the burn sequence produced by the IOCS's incremental error correction scheme.  In fact, while the error correction scheme-related burns maintain ICESat's necessary groundtrack accuracy for at least 90 days, the simulated Hohmann Transfer-related burn sequence allows ICESat's groundtrack to leave its 800 m control band in 83 days for the East/West direction and in 52 days for the North/South direction.

            In this study, the Matlab results were used primarily as a sanity check for the other software programs.  Since Matlab's results proved to be consistent with the results generated by IOCS, no formal error analysis was performed for the orbital mechanics equations used in the Matlab program, Hohmann_Transfer.  However, because the STK results differed so extensively from the other software programs' results, common sense (and a knowledge of acceptable values from previous experience with burn maneuvers) suggests that the delta V maneuvers produced by STK should simply be discarded.

VII.    CONCLUSIONS AND RECOMMENDATIONS

            The primary objective of this study was to provide a comparison of methods for designing a burn maneuver sequence to lower ICESat's orbit from its calibration to mission phase.  Fuel conservation was upheld as a primary concern, and thus delta V results produced using a Hohmann Transfer method were compared with delta V results generated using the IOCS software's incremental error correction scheme.  All results were similar to Matlab results obtained using simple orbital mechanics equations, with the exception of STK-generated delta V values, which showed significantly higher magnitudes than all other results.  Due to this fact, the STK burn maneuvers were deemed invalid.  

            The IOCS-simulated Hohmann Transfer method proved to be the most fuel-efficient, although its delta V value was only slightly less (0.000036 m/s) than the result generated using IOCS's incremental error correction scheme.  Surprisingly, the Hohmann Transfer-produced maneuvers also caused ICESat's groundtrack to leave its 800 m accuracy control band sooner than the other method, suggesting that the IOCS software's incremental error correction scheme might be better suited to conserve ICESat's fuel in view of the satellite's five year mission lifetime.  Further work is suggested in order to definitively conclude which method (simulated Hohmann Transfer or incremental error correction) would consume less fuel during the long-term life of the mission.  

            In addition, it is recommended that members of ICESat's FDS team perform this study again after the satellite's launch on December 19, 2002.  Using actual satellite ephemeris data instead of the simulated data used in this study might provide a better indication of which method is optimal when lowering ICESat's orbit.  Finally, because the IOCS software does not actually use an orbit propagation technique, it may prove beneficial to propagate ICESat's orbit and the effects of  the IOCS software's proposed burns using the FDS subsystem's orbit determination software package.  The orbit determination software's output ephemeris could then be compared with the desired mission reference groundtrack ephemeris.