Generalized gravitomagnetic clock effect

Abstract

In General Relativity, the rotation of a gravitating body like the Earth influences the motion of orbiting test particles or satellites in a non-Newtonian way. This causes, e.g., a precession of the orbital plane known as the Lense-Thirring effect and a precession of the spin of a gyroscope known as the Schiff effect. Here, we discuss a third effect first introduced by Cohen and Mashhoon called the gravitomagnetic clock effect. It describes the difference in proper time of counterrevolving clocks after a revolution of $2\pi$. For two clocks on counterrotating equatorial circular orbits around the Earth, the effect is about $10^{-7}$ seconds per revolution, which is quite large. We introduce a general relativistic definition of the gravitomagnetic clock effect which is valid for arbitrary pairs of orbits. This includes rotations in the same direction and different initial conditions, which are crucial if the effect can be detected with existing satellites or with payloads on nondedicated missions. We also derive the post-Newtonian expansion of the general relativistic expression and calculate the effect for the example of a satellite of a Global Navigation Satellite System compared to a geostationary satellite.

9 pages, 1 figure; v2: minor corrections to match published version

References in corpus (14)

• Gravity Probe B: Final Results of a Space Experiment to Test General Relativity
• Perturbative Approach to an orbital evolution around a Supermassive black hole
• Celestial mechanics in Kerr spacetime
• Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
• On the gravitomagnetic clock effect
• Fundamental Physics and General Relativity with the LARES and LAGEOS satellites
• Detection of the gravitomagnetic clock effect
• Gravitomagnetism and Relative Observer Clock Effects
• Observables for bound orbital motion in axially symmetric space-times
• On the Possibility of Measuring the Gravitomagnetic Clock Effect in an Earth Space-Based Experiment
• The gravitomagnetic clock effect and its possible observation
• Satellite gravitational orbital perturbations and the gravitomagnetic clock effect
• Satellite non-gravitational orbital perturbations and the detection of the gravitomagnetic clock effect
• Gravity Probe C(lock) - Probing the gravitomagnetic field of the Earth by means of a clock experiment

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• Post-Keplerian corrections to the orbital periods of a two-body system and their measurability
• Definition of the relativistic geoid in terms of isochronometric surfaces
• Normal gravity field in relativistic geodesy
• Revisiting the gravitomagnetic clock effect
• Potentials for general-relativistic geodesy
• Review of the Gravitomagnetic Clock Effect