Velocity Extrema in Keplerian Relative Motion: A Gröbner Basis Approach

This paper analyzes the relative motion between two spacecraft in orbit. Specifically, the paper provides bounds for relative spacecraft velocity- based measures which impact spacecraft formation-flight mission design and analysis. The relative speed metric, and velocity components for formation-fli...

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Bibliographic Details
Published inThe Journal of the astronautical sciences Vol. 68; no. 4; pp. 785 - 804
Main Authors Allgeier, Shawn E., Fitz-Coy, Norman G., Erwin, R. Scott
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2021
Springer Nature B.V
Subjects
Aerospace Technology and Astronautics
Engineering
Formation flying
Intersatellite communications
Mathematical Applications in the Physical Sciences
Mission planning
Original Article
Satellite communications
Satellite constellations
Space Exploration and Astronautics
Space Sciences (including Extraterrestrial Physics
Spacecraft
Gröbner Basis
Satellite Proximity Operations
Relative Motion
Motion Extrema
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Summary:This paper analyzes the relative motion between two spacecraft in orbit. Specifically, the paper provides bounds for relative spacecraft velocity- based measures which impact spacecraft formation-flight mission design and analysis. The relative speed metric, and velocity components for formation-flight are presented for general Keplerian elliptic orbits along with the range rate metric for certain special cases. A methodology for bounding the metrics is presented. The extremal equations are formulated as an affine variety and solved using a Gröbner basis reduction. The metrics have utility to the mission designer of formation flight architectures, with relevance to Earth observation constellations and inter-satellite communications systems.
ISSN:0021-9142
2195-0571
DOI:10.1007/s40295-021-00274-z