Gravity assist as a test of relativistic gravity

TL;DR

This paper explores using gravity assist maneuvers to test relativistic gravity by analyzing how variations in Eddington parameters affect spacecraft trajectories near planets.

Contribution

It proposes a novel method to evaluate the post-Newtonian parameters $eta$ and $\gamma$ through gravity assist trajectory analysis.

Findings

A $10^{-4}$ change in $eta$ or $\gamma$ causes a 50 km shift in probe's aphelion.

Relativistic corrections influence impact parameters during planetary flybys.

Gravity assist maneuvers can serve as precise tests for relativistic gravity theories.

Abstract

We consider the gravity assist maneuver, that is, a correction of spacecraft motion at its passing near a planet, as a tool for evaluating the Eddington post-Newtonian parameters $\beta$ and $\gamma$, characterizing vacuum spherically symmetric gravitation fields in metric theories of gravity. We estimate the effect of variation in $\beta$ and $\gamma$ on a particular trajectory of a probe launched from the Earth's orbit and passing closely near Venus, where relativistic corrections slightly change the impact parameter of probe scattering in Venus's gravitational field. It is shown, in particular, that a change of $10^{-4}$ in $\beta$ or $\gamma$ leads to a shift of about 50 km in the probe's aphelion position.