Geometric interpretation of the Tschauner-Hempel solutions for satellite relative motion
Abstract
The fundamental solutions of the Tschauner-Hempel equations, which describe the motion of a deputy satellite relative to a chief satellite with arbitrary eccentricity, are interpreted geometrically as generalizations of the drifting two-by-one ellipse that describes relative motion in circular orbits. General solutions are formed by taking linear combinations of these fundamental solutions. The amplitudes of these fundamental solutions are proposed as a parameterization of relative motion in elliptic orbits. A simple maneuver scheme is also developed to achieve arbitrary desired changes in the fundamental-solution amplitudes.
- Publication:
-
Advances in Space Research
- Pub Date:
- May 2015
- DOI:
- 10.1016/j.asr.2015.01.032
- Bibcode:
- 2015AdSpR..55.2268S
- Keywords:
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- Satellite formation flying;
- Relative motion;
- Elliptic orbits