Abstract
The present manuscript examines the circular restricted gravitational three-body problem (CRGTBP) by the introduction of a new approach through the power series method. In addition, certain computational algorithms with the aid of Mathematica software are specifically designed for the problem. The algorithms or rather mathematical modules are established to determine the velocity and position of the third body’s motion. In fact, the modules led to accurate results and thus proved the new approach to be efficient.
Highlights
The circular restricted gravitational three-body problem (CRGTBP) is a special case of the gravitational three-body problem which is one of the most important n-body problems
Certain computational algorithms with the aid of Mathematica software are designed for the problem
The modules led to accurate results and proved the new approach to be efficient
Summary
The circular restricted gravitational three-body problem (CRGTBP) is a special case of the gravitational three-body problem which is one of the most important n-body problems. Rabe [10] used a new computational and iteration method to determine a series of periodic Trojan orbits in the restricted problem of three bodies. We aim in this paper to employ an approach based on the power series to establish an algorithm or mathematical module using Mathematica to tackle this important problem of circular restricted gravitational dynamical problem.
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