Journal Article

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

Lin-Sen Li

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 419, issue 3, pages 1825-1832
Published in print January 2012 | ISSN: 0035-8711
Published online January 2012 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.19652.x
Influence of the time variation of the gravitational constant on the orbital elements of planets

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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 . The eccentricity exhibits periodic variation, but there is no secular variation in the first and second orders for . The longitude of perihelion and the mean longitude at the epoch exhibit periodic variation but no secular variation in the first order for . However, they do exhibit secular variation in the second order for . 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.

Keywords: gravitation; celestial mechanics; planets and satellites: dynamical evolution and stability; planets and satellites: general

Journal Article.  2594 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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