Abstract
Determination of the potential field in a fixed (inertial) system may be accomplished by the solution of a homogeneous linear partial differential equation when a family of orbits of a body moving in the field is given. This partial differential equation was presented and thoroughly analyzed earlier. The present paper discusses the same problem in a rotating system where the centrifugal and Coriolis effects render the pertinent partial differential equation in general non-homogeneous and non-linear. A linear, though non-homogeneous, partial differential equation for the determination of the synodic potential is obtained only in the special case of iso-energetic families of orbits.
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References
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Szebehely, V., Broucke, R. Determination of the potential in a synodic system. Celestial Mechanics 24, 23–26 (1981). https://doi.org/10.1007/BF01228791
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DOI: https://doi.org/10.1007/BF01228791