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

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.

arXiv commentLaTex2e, 22 pages, no tables, 1 figure, 38 references. Final version accepted for publication in Classical and Quantum Gravity

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• Satellite Motion in a Manev Potential with Drag
• Gravito-electromagnetic Effects of Massive Rings
• Numerical solution of Mathisson-Papapetrou-Dixon equations for spinning test particles in a Kerr metric
• Equilibria of a charged artificial satellite subject to gravitational and Lorentz torques
• Revisiting the gravitomagnetic clock effect
• Covariant Evolution of Gravitoelectromagnetism
• Constraining the relative inclinations of the planets B and C of the millisecond pulsar PSR B1257+12
• Review of the Gravitomagnetic Clock Effect