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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. (From -To) REPORT DATE (DD-MM-YYYY) 20-03-2004 REPORT TYPE Final Report DATES COVERED SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)Air Force Office of Scientific Research SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION / AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTES ABSTRACTRecent developments have indicated that it is possible to express the relative equations of motion for space objects in non-circular orbits using mean Keplerian elements and low order expansions. This report provides the initial derivation of one such effort known as the Cluster Orbits With Perturbations Of Keplerian Elements (COWPOKE) equations. Given mean Keplerian elements and element differences, the COWPOKE equations describe spherical radial, cross-track, and along-track separations of the satellites as an explicit function of time. The framework of the equations allows for very high eccentricity reference orbits and for the inclusion of dynamic perturbations. Test cases using two-body dynamics show the utility of this approach. SUBJECT TERMSRelative motion, satellite formation flying, astrodynamics

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