Artificial Horseshoe Orbits Using Low Thrust Propulsion

Horseshoe orbits, occurring naturally in three-body systems, can be generated artificially in a two-body system with the application of continuous low thrust. In this paper, the Clohessy-Wiltshire equations are presented in cylindrical polar form, and with the addition of continuous low thrust they are used to generate artificial horseshoe orbits around a circular reference orbit. Two solutions using simple thrust commands are derived and tested numerically. It is shown that the thrust magnitude and v requirements for artificial horseshoe orbits are modest and achievable for certain Earth orbiting cases, and that the applications for such novel spacecraft constellations are potentially diverse. Finally, a discussion of phased constellations of spacecraft, considering constellations on nested horseshoe orbits around the same reference orbit and those on displaced-plane non-Keplerian orbits, is also presented