Symmetric and Asymmetric Librations in Planetary and Satellite Systems at the 2/1 Resonance |
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| Authors: | George Voyatzis John D Hadjidemetriou |
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| Institution: | (1) Department of Physics, University of Thessaloniki, 54124 Thessaloniki, Greece |
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| Abstract: | Families of asymmetric periodic orbits at the 2/1 resonance are computed for different mass ratios. The existence of the asymmetric
families depends on the ratio of the planetary (or satellite) masses. As models we used the Io-Europa system of the satellites
of Jupiter for the case m1>m2, the system HD82943 for the new masses, for the case m1=m2 and the same system HD82943 for the values of the masses m1<m2 given in previous work. In the case m1≥ m2 there is a family of asymmetric orbits that bifurcates from a family of symmetric periodic orbits, but there exist also an
asymmetric family that is independent of the symmetric families. In the case m1<m2 all the asymmetric families are independent from the symmetric families. In many cases the asymmetry, as measured by
and by the mean anomaly M of the outer planet when the inner planet is at perihelion, is very large. The stability of these asymmetric families has
been studied and it is found that there exist large regions in phase space where we have stable asymmetric librations. It
is also shown that the asymmetry is a stabilizing factor. A shift from asymmetry to symmetry, other elements being the same,
may destabilize the system. |
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| Keywords: | asymmetric librations asymmetric periodic orbits three body problem planetary systems |
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