Abstract
We have applied the method of Liapounov Characteristic Numbers (LCN) to the planar restricted three-body problem with various mass ratios μ and Jacobi constantsC, for various cases of satellite and asteroidal motion. Some results on the LCN's for both ordinary and regularized coordinate systems are obtained. The results indicate that there exists a maximum valueC* ofC, depending on μ, such that all the LCN's are zero within computational accuracy whenC>C*. The meaning of this is that all orbits whose initial conditions are located in the region for whichC>C* are effectively stable.
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Jefferys, W.H., Yi, ZH. Stability in the restricted problem of three bodies with Liapounov Characteristic Numbers. Celestial Mechanics 30, 85–95 (1983). https://doi.org/10.1007/BF01231104
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DOI: https://doi.org/10.1007/BF01231104