In physics, the gravitomagnetic clock effect is a deviation from Kepler's third law that, according to the weak-field and low-velocity approximation of general relativity, will be suffered by a particle in orbit around a (slowly) spinning body, such as a typical planet or star.
Explanation
editAccording to general relativity, in its weak-field and low-velocity linearized approximation, a slowly spinning body induces an additional component of the gravitational field that acts on a freely-falling test particle with a non-central, gravitomagnetic Lorentz-like force.
Among its consequences on the particle's orbital motion there is a small correction to Kepler's third law, namely
where TKep is the particle's period, M is the mass of the central body, and a is the semimajor axis of the particle's ellipse. If the orbit of the particle is circular and lies in the equatorial plane of the central body, the correction is
- where S is the central body's angular momentum and c is the speed of light in vacuum.
Particles orbiting in opposite directions experience gravitomagnetic corrections TGvm with opposite signs, so that the difference of their orbital periods would cancel the standard Keplerian terms and would add the gravitomagnetic ones.[1][2][3][4][5][6][7][8][9][10][11][12][excessive citations]
Note that the + sign occurs for particle's corotation with respect to the rotation of the central body, whereas the − sign is for counter-rotation. That is, if the satellite orbits in the same direction as the planet spins, it takes more time to make a full orbit, whereas if it moves oppositely with respect to the planet's rotation its orbital period gets shorter.
See also
editReferences
edit- ^ Cohen, J.M.; Mashhoon, B. (October 1993). "Standard Clocks, Interferometry, and Gravitomagnetism". Physics Letters A. 181 (5): 353–358. Bibcode:1993PhLA..181..353C. doi:10.1016/0375-9601(93)90387-F.
- ^ Mashhoon, B.; Gronwald, F.; Theiss, D.S. (February 1999). "On measuring gravitomagnetism via spaceborne clocks: a gravitomagnetic clock effect". Annalen der Physik. 8 (2): 135–152. arXiv:gr-qc/9804008. Bibcode:1999AnP...511..135M. doi:10.1002/(SICI)1521-3889(199902)8:2<135::AID-ANDP135>3.0.CO;2-N. S2CID 17353038.
- ^ Tartaglia, A. (February 2000). "Detection of the gravitomagnetic clock effect". Classical and Quantum Gravity. 17 (4): 783–792. arXiv:gr-qc/9909006. Bibcode:2000CQGra..17..783T. doi:10.1088/0264-9381/17/4/304. S2CID 9356721.
- ^ Tartaglia, A. (September 2000). "Geometric Treatment of the Gravitomagnetic Clock Effect". General Relativity and Gravitation. 32 (9): 1745–1756. arXiv:gr-qc/0001080. Bibcode:2000GReGr..32.1745T. doi:10.1023/A:1001998505329. S2CID 119383886.
- ^ Lichtenegger, H.I.M.; Gronwald, F.; Mashhoon, B. (2000). "On detecting the gravitomagnetic field of the Earth by means of orbiting clocks". Advances in Space Research. 25 (6): 1255–1258. arXiv:gr-qc/9808017. Bibcode:2000AdSpR..25.1255L. doi:10.1016/S0273-1177(99)00997-7. S2CID 16542540.
- ^ Iorio, L. (August 2001). "Satellite Gravitational Orbital Perturbations and the Gravitomagnetic Clock Effect". International Journal of Modern Physics D. 10 (4): 465–476. arXiv:gr-qc/0007014. Bibcode:2001IJMPD..10..465I. doi:10.1142/S0218271801000925. S2CID 119426253.
- ^ Iorio, L. (October 2001). "Satellite non-gravitational orbital perturbations and the detection of the gravitomagnetic clock effect". Classical and Quantum Gravity. 18 (20): 4303–4310. arXiv:gr-qc/0007057. Bibcode:2001CQGra..18.4303I. doi:10.1088/0264-9381/18/20/309. S2CID 6342400.
- ^ Mashhoon, B.; Gronwald, F; Lichtenegger, H.I.M. (2001). "Gravitomagnetism and the Clock Effect". Gyros, Clocks, Interferometers ...: Testing Relativistic Gravity in Space. Lecture Notes in Physics. Vol. 562. pp. 83–108. arXiv:gr-qc/9912027. Bibcode:2001LNP...562...83M. doi:10.1007/3-540-40988-2_5. ISBN 978-3-540-41236-6. S2CID 32411999.
- ^ Mashhoon, B.; Iorio, L.; Lichtenegger, H.I.M. (December 2001). "On the gravitomagnetic clock effect". Physics Letters A. 292 (1–2): 49–57. arXiv:gr-qc/0110055. Bibcode:2001PhLA..292...49M. doi:10.1016/S0375-9601(01)00776-9. S2CID 14981533.
- ^ Iorio, L.; Lichtenegger, H.I.M.; Mashhoon, B. (January 2002). "An alternative derivation of the gravitomagnetic clock effect". Classical and Quantum Gravity. 19 (1): 39–49. arXiv:gr-qc/0107002. Bibcode:2002CQGra..19...39I. doi:10.1088/0264-9381/19/1/303. S2CID 5941537.
- ^ Iorio, L.; Lichtenegger, H.I.M. (February 2005). "On the possibility of measuring the gravitomagnetic clock effect in an Earth space-based experiment". Classical and Quantum Gravity. 22 (1): 119–132. arXiv:gr-qc/0210030. Bibcode:2005CQGra..22..119I. doi:10.1088/0264-9381/22/1/008. S2CID 118903460.
- ^ Lichtenegger, H.I.M.; Iorio, L.; Mashhoon, B. (December 2006). "The gravitomagnetic clock effect and its possible observation". Annalen der Physik. 15 (12): 868–876. arXiv:gr-qc/0211108. Bibcode:2006AnP...518..868L. doi:10.1002/andp.200610214. S2CID 9087843.