Yukawa effects on the mean motion of an orbiting body

Abstract

In today’s gravity research there exist few modified gravitational theories which among other things predict the existence of a Yukawa-type correction to the classical gravitational potential. In this paper we study the Yukawa effect on the mean motion if any in a two-body scenario, assuming the influence of the existence of a possible Yukawa correction in the gravitational force of a primary. For that, we derive an equation in order to approximate the mean motion for secondary time rate of change of the orbiting body and its total variation over one revolution, under the influence of the non-Newtonian radial acceleration. Numerical results for Mercury and the companion star of the pulsar PSR 1913 + 16 are calculated. For specific values of the parameters α and λ, as given in the bibliography we have found that there is no corresponding Yukawa effect affecting the mean motion of the planet Mercury. On the other hand it appears that there is a periodic Yukawa effect that affects the mean motion of PSR + 16 whose maximum numerical value occurs when the eccentric anomaly is equal to 180 ∘.