Equations of motion of the mass centers in a scalar theory of gravitation: Expansion in the separation parameter

TL;DR

This paper develops an asymptotic framework within a scalar theory of gravitation to derive post-Newtonian equations of motion for extended bodies, highlighting the influence of internal structure on their dynamics.

Contribution

It introduces an asymptotic expansion scheme for deriving high-order post-Newtonian equations of motion in a scalar gravitational theory, accounting for internal structure effects.

Findings

Internal structure affects equations of motion due to the asymptotic scheme.

Explicit PN equations truncated beyond eta^3 order.

Assumption of spherical bodies simplifies calculations.

Abstract

An asymptotic framework is defined for the small parameter eta which quantifies a good separation between the extended bodies that make a weakly gravitating system. This is introduced within an alternative scalar theory of gravitation, though it may be defined similarly in other theories. This framework allows one to truncate the translational equations of motion at any well-defined order. Here, the post-Newtonian (PN) equations valid in the scalar theory are truncated beyond the order eta^3. The PN approximation scheme used is the asymptotic scheme, that expands all fields. To get the explicit form of the equations of motion for the mass centers, the bodies are assumed spherical, merely for calculating the PN corrections. It is found that, due to the use of the asymptotic PN scheme, the internal structure of the bodies does play a role in the equations of motion.