Dynamical history of coplanar two-satellite systems |
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Authors: | E L Ruskol E V Nikolajeva A S Syzdykov |
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Institution: | (1) O. J. Schmidt Institute of Physics of the Earth and Institute of Space Research, U.S.S.R. Acad. Sci., Moscow, U.S.S.R. |
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Abstract: | One of the possible early states of the Earth-Moon system was a system of several large satellites around the Earth. The dynamical
evolution of coplanar three-body systems is studied; a planet (Earth) and two massive satellites (proto-moons) with geocentric
orbits of slightly different radii. Such configurations may arise in multiple satellite systems receding from a planet due
to tidal friction. The numerical integration of the equations of motion shows that initially circular Keplerian orbits are
soon transformed into disturbed elliptic orbits which are intersecting. The life-time of such a coplanar system between two
probable physical collisions of satellites is roughly from one day to one year for satellite systems with radii less than
20R⊕, and may reach 100 yr for three-dimensional systems. This time-scale is short in comparison with the duration of the removal
of satellites due to tides raised on the planet, which is estimated as 106–108 yr for the same orbital dimensions. Therefore, the life-time of a system of several proto-moons is mainly determined by their
tidal interactions with the Earth. For conditions which we have considered, the most probable result of the evolution was
coalescence of satellites as the consequence of the collisions. |
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