On planetary orbits in entropic gravity

Abstract

Starting with an entropy that includes volumetric, area and length terms as well as logarithmic contributions, we derive the corresponding modified Newtonian gravity and derive the expression for planetary orbits. We calculate the shift of the perihelion of Mercury to find bounds to the parameters associated to the modified Newtonian gravity. We compare the parameter associated to the volumetric contribution in the entropy-area relationship with the value derived for galactic rotation curves and the value obtained from the cosmological constant.