On Planetary Orbits in Entropic Gravity

TL;DR

This paper derives a modified Newtonian gravity from an entropy model with volumetric, area, and length terms, analyzing planetary orbits and perihelion shifts to constrain the model's parameters.

Contribution

It introduces a novel entropy-based approach to gravity that incorporates volumetric and logarithmic terms, extending previous entropic gravity models.

Findings

Calculated perihelion shift of Mercury constrains model parameters.

Compared volumetric entropy contribution with galactic rotation and cosmological data.

Provided bounds on entropy parameters consistent with observations.

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.