Effects of zonal harmonics on the out-of-plane equilibrium points in the generalized Robe's circular restricted three-body problem |
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| Institution: | 1. Theory Group, Department of Physics and Texas Cosmology Center, The University of Texas at Austin, TX 78712, USA;2. Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA;1. Physics Department, University of Rijeka, Radmile Matejčić, 51000 Rijeka, Croatia;2. INAF Astronomical Observatory of Padova, via dell’Osservatorio 8, Asiago (VI) 36012, Italy;1. Division of Theoretical Astronomy, National Astronomical Observatory of Japan,2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan;2. Department of Natural Science, Kochi University, 2-5-1 Akebono-cho, Kochi 780-8520, Japan;3. Department of Human Informatics, Aichi Shukutoku University, 2-9 Katahira, Nagakute, Aichi 480-1197, Japan |
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| Abstract: | This article examines the effects of the zonal harmonics on the out-of-plane equilibrium points of Robe's circular restricted three-body problem when the hydrostatic equilibrium shape of the first primary is an oblate spheroid, the shape of the second primary is an oblate spheroid with oblateness coefficients up to the second zonal harmonic, and the full buoyancy of the fluid is considered. It is observed that the size of the oblateness and the zonal harmonics affect the positions of the out-of-plane equilibrium points L6 and L7. It is also observed that these points within the possible region of motion are unstable. |
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