The influence of modified gravitational fields on motions of Keplerian objects at the far-edge of the Solar System

TL;DR

This study examines how three modified gravity theories affect the orbits of distant Solar System objects, revealing similar qualitative effects but distinct quantitative differences among the models.

Contribution

It compares the impact of Dark Matter, MOND, and a negative cosmological constant on the orbits of far-edge Solar System objects, highlighting differences in orbital parameters.

Findings

All modifications cause initial circular orbits to become elliptical with perihelion migration.

Quantitative differences are significant between MOND and the other two modifications.

Qualitative orbital behavior is similar across all three modified gravity models.

Abstract

We investigated the impact of three different modifications of Newtonian gravity on motions of Keplerian objects within the Solar System. These objects are located at distances of the order of the distance to the Oort cloud. With these three modifications we took into account a heliocentric Dark-Matter halo as was indicated by Diemand et al, Modified Newtonian Dynamics (MOND) and a vacuum-induced force due to a locally negative cosmological constant $\Lambda_-$ derived by Fahr & Siewert. In gravitationally bound systems it turns out that all three modifications deliver the same qualitative results: Initially circular orbits for the pure Newtonian case are forced to convert into ellipses with perihelion migrations. The quantitative consideration, however, of the orbital parameters showed strong differences between MOND on the one side, and Dark-Matter and $\Lambda_-$ effects on the other side.