Resonance in the Restricted Problem of Three Bodies with Short-Period Perturbations in the Elliptic Case
This is a generalization of the paper by Bhatnagar and Beena Gupta ‘Resonance in the restricted problem of three bodies with short-periodic perturbations’. The motion of an asteroid moving in the gravitational field of Jupiter is considered. In the original paper it was assumed that Jupiter is moving in a circular orbit around the Sun. In the present paper we consider the orbit to be elliptic. The series occurring in the problem are expanded in powers of a small parameter ε, which represents the ratio of the mass of Jupiter to that of the Sun. The perturbations in the osculating elements are obtained up to O(ε).
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