Effect of a large-scale distance variation of gravitational constant on the orbital elements of celestial bodies

The effects of the variation of the gravitational constant with distance on the variation of the orbital elements of celestial objects are examined. The theoretical results show clearly that the large distance variation of the gravitational constant results in the periodic variation of the semi-major axis, eccentricity, longitude of the perihelion and the mean longitude, but it results in the secular variation of the longitude of the perihelion and the mean longitude, no secular variation for other orbital elements. As an example, the effects on four planets are estimated. Discussion and conclusion are drawn.