Deep space experiment to measure $G$

TL;DR

This paper proposes a deep space experiment using a gravity train mechanism to measure the gravitational constant G with significantly improved accuracy, leveraging laser ranging and harmonic motion of a retroreflector.

Contribution

It introduces a novel deep space setup employing a layered sphere and retroreflector to measure G more precisely than current Earth-based methods.

Findings

Potential to measure G with nearly three orders of magnitude higher accuracy

Requires engineering advances in release mechanisms and system stability analysis

Utilizes existing laser ranging technology for precise measurements

Abstract

Responding to calls from the National Science Foundation (NSF) for new proposals to measure the gravitational constant $G$, we offer an interesting experiment in deep space employing the classic gravity train mechanism. Our setup requires three bodies: a larger layered solid sphere with a cylindrical hole through its center, a much smaller retroreflector which will undergo harmonic motion within the hole and a host spacecraft with laser ranging capabilities to measure round trip light-times to the retroreflector but ultimately separated a significant distance away from the sphere-retroreflector apparatus. Measurements of the period of oscillation of the retroreflector in terms of host spacecraft clock time using existing technology could give determinations of $G$ nearly three orders of magnitude more accurate than current measurements here on Earth. However, significant engineering advances in the release mechanism of the apparatus from the host spacecraft will likely be necessary. Issues with regard to the stability of the system are briefly addressed.