On the effect of the eccentricity of a planetary orbit on the stability of satellite orbits |
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Authors: | S Ichtiaroglou G Voyatzis |
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Institution: | (1) Department of Physics, University of Thessaloniki, 54006, Greece |
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Abstract: | The effect of the eccentricity of a planet’s orbit on the stability of the orbits of its satellites is studied. The model
used is the elliptic Hill case of the planar restricted three-body problem. The linear stability of all the known families
of periodic orbits of the problem is computed. No stable orbits are found, the majority of them possessing one or two pairs
of real eigenvalues of the monodromy matrix, while a part of a family with complex instability is found. Two families of periodic
orbits, bifurcating from the Lagrangian points L1, L2 of the corresponding circular case are found analytically. These orbits are very unstable and the determination of their
stability coefficients is not accurate, so we compute the largest Liapunov exponent in their vicinity. In all cases these
exponents are positive, indicating the existence of chaotic motions |
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Keywords: | celestial mechanics periodic orbits stability Hill roblem |
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