Stability of 2-body orbits in retarded gravitation theory (RGT)

TL;DR

This paper demonstrates that the retarded gravitation theory (RGT) produces stable two-body orbits similar to Newtonian gravity, addressing concerns about potential instabilities and supporting RGT as a viable alternative explanation for galactic rotation curves.

Contribution

The study provides the first stability analysis of RGT in a two-body system, showing it closely matches Newtonian predictions and is free from instabilities.

Findings

RGT orbits are stable in a two-body planetary model.

RGT solutions closely resemble Newtonian solutions in stability.

Instabilities are not responsible for high galactic rotation velocities.

Abstract

The recently formulated retarded gravitation theory (RGT) explains the non-Newtonian velocities of stars in spiral galaxies, *without any new hypothesis*, and may hence be tested even in the laboratory. However, doubts have been expressed that those higher rotation velocities in RGT may be due to instabilities. We resolve these doubts by solving the full functional differential equations of RGT for a model 2-body planetary system. The solution is stable and closely agrees with the Newtonian solution for this planetary case. Thus, the big difference between RGT and Newtonian gravity for a spiral galaxy is not due to any instability in RGT.