Influence of the time variation of the gravitational constant on the orbital elements of planets

Abstract

In this paper, using the expansion of the true anomaly, we examine how the time variation of the gravitational constant influences the variation of the orbital elements of planets. The theoretical results show that the semimajor axis exhibits secular and periodic variation in the first order for u G/G. The eccentricity exhibits periodic variation, but there is no secular variation in the first and second orders for u G/G. The longitude of perihelion and the mean longitude at the epoch exhibit periodic variation but no secular variation in the first order for u G/G. However, they do exhibit secular variation in the second order for u G/G. The inclination and ascending node exhibit no variation. The bounds on the values of the secular variation of the semimajor axis and the orbital period, which result from the time variation of the gravitational constant, are estimated for five planets. The results are discussed and conclusions are made.