Abstract
The general properties of certain differential systems are used to prove the existence of periodic orbits for a particle around an oblate spheroid.
In a fixed frame, there are periodic orbits only fori=0 andi near π/2. Furthermore, the generating orbits are circles.
In a rotating frame, there are three families of orbits: first a family of periodic orbits in the vicinity of the critical inclination; secondly a family of periodic orbits in the equatorial plane with 0<e<1; thirdly a family of periodic orbits for any value of the inclination ife=0.
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Stellmacher, I. Periodic orbits around an oblate spheroid. Celestial Mechanics 23, 145–158 (1981). https://doi.org/10.1007/BF01229550
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DOI: https://doi.org/10.1007/BF01229550