On the Possibility of Measuring the Gravitomagnetic Clock Effect in an Earth Space-Based Experiment

TL;DR

This paper investigates the feasibility of measuring the gravitomagnetic clock effect using Earth satellites, focusing on the required precision and technological challenges for detecting a tiny time shift caused by gravitomagnetism.

Contribution

It proposes a method to measure the gravitomagnetic clock effect with Earth satellites and analyzes the technological requirements for such a measurement.

Findings

The gravitomagnetic time shift for Earth is approximately 5×10^{-7} seconds.

Precise control of orbital parameters is essential, with semimajor axis differences limited to 10^{-2} cm.

Drag-free control and advanced tracking are necessary to achieve measurement accuracy.

Abstract

In this paper the effect of the post-Newtonian gravitomagnetic force on the mean longitudes $l$ of a pair of counter-rotating Earth artificial satellites following almost identical circular equatorial orbits is investigated. The possibility of measuring it is examined. The observable is the difference of the times required to $l$ in passing from 0 to 2$\pi$ for both senses of motion. Such gravitomagnetic time shift, which is independent of the orbital parameters of the satellites, amounts to 5$\times 10^{-7}$ s for Earth; it is cumulative and should be measured after a sufficiently high number of revolutions. The major limiting factors are the unavoidable imperfect cancellation of the Keplerian periods, which yields a constraint of 10$^{-2}$ cm in knowing the difference between the semimajor axes $a$ of the satellites, and the difference $I$ of the inclinations $i$ of the orbital planes which, for $i\sim 0.01^\circ$, should be less than $0.006^\circ$. A pair of spacecrafts endowed with a sophisticated intersatellite tracking apparatus and drag-free control down to 10$^{-9}$ cm s$^{-2}$ Hz$^{-{1/2}}$ level might allow to meet the stringent requirements posed by such a mission.