Secular Effect of Evolution of the Orbits of Binaries Induced by the Variation of Gravitational Constant with Time (The Case for the Elliptical Orbit)

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Celestial Mechanics, Binaries: General

Scientific paper

The solutions of the equations with the variable gravitational constant are given by taking the eccentric anomaly as independent variable. The solutions include the secular and periodic variations in semi-major axis, and other orbital elements only exhibit periodic variations in the first-order solutions. The longitude of periastron and mean longitude exhibit secular variations in the second-order solutions. The numerical estimations for the case of evolution of the orbits of six binaries are given. The results are discussed and concluded.

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