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High Order Resonances in the Evolution of the Lunar Orbit

  • J. Kovalevsky (a1)

Abstract

This paper deals with the long term evolution of the motion of the Moon or any other natural satellite under the combined influence of gravitational forces (lunar theory) and the tidal effects. We study the equations that are left when all the periodic non-resonant terms are eliminated. They describe the evolution of the-mean elements of the Moon. Only the equations involving the variation of the semi-major axis are considered here. Simplified equations, preserving the Hamiltonian form of the lunar theory are first considered and solved. It is shown that librations exist only for those terms which have a coefficient in the lunar theory larger than a quantity A which is function of the magnitude of the tidal effects. The solution of the general case can be derived from a Hamiltonian solution by a method of variation of constants. The crossing of a libration region causes a retardation in the increase of the semi-major axis. These results are confirmed by numerical integration and orders of magnitude of this retardation are given.

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Copyright

References

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