Gravitomagnetic clock effect: Difference between revisions
Content deleted Content added
No edit summary |
No edit summary |
||
| Line 2: | Line 2: | ||
==Explanation== |
==Explanation== |
||
According to general relativity, a spinning body induces an additional component of the [[gravitational field]] which acts on a freely-falling test particle with a non-central, [[gravitomagnetic]] Lorentz-like force. |
According to [[general relativity]], a spinning body induces an additional component of the [[gravitational field]] which 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 |
Among its consequences on the particle's orbital motion there is a small correction to [[Kepler's third law]], namely |
||
:<math>T_{\rm Kep}=2\pi\sqrt{a^3/GM}</math> |
:<math>T_{\rm Kep}=2\pi\sqrt{a^3/GM}</math> |
||
where ''T''<sub>Kep</sub> is the particle's period, and ''M'' is the [[mass]] of the central body. The correction is |
where ''T''<sub>Kep</sub> is the particle's period, and ''M'' is the [[mass]] of the central body. The correction is |
||
Revision as of 23:35, 30 December 2009
The gravitomagnetic clock effect is a deviation from Kepler's third law that, according to general relativity, will be suffered by a particle in orbit around a spinning body endowed with angular momentum , such as a typical planet or star.
Explanation
According to general relativity, a spinning body induces an additional component of the gravitational field which 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, and M is the mass of the central body. The correction is
- where S is the central body's angular momentum and c is the the speed of light in vacuum.
Interestingly, 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]
References
- ^
Cohen, J.M. (1993). ""Standard Clocks, Interferometry, and Gravitomagnetism". Physics Letters A. 181 (5): 353–358. doi:10.1016/0375-9601(93)90387-F.
{{cite journal}}: Unknown parameter|coauthors=ignored (|author=suggested) (help); Unknown parameter|month=ignored (help) - ^
Mashhoon, B. (1999). "On measuring gravitomagnetism via spaceborne clocks: a gravitomagnetic clock effect". Annalen der Physik. 8 (2): 135–152. doi:10.1002/(SICI)1521-3889(199902)8:2.
{{cite journal}}: Unknown parameter|coauthors=ignored (|author=suggested) (help); Unknown parameter|month=ignored (help) - ^
Tartaglia, A. (2000). "Detection of the gravitomagnetic clock effect". Classical and Quantum Gravity. 17 (4): 783–792. doi:10.1088/0264-9381/17/4/304.
{{cite journal}}: Unknown parameter|month=ignored (help) - ^
Tartaglia, A. (2000). "Geometric Treatment of the Gravitomagnetic Clock Effect". General Relativity and Gravitation. 32 (9): 1745–1756. doi:10.1023/A:1001998505329.
{{cite journal}}: Unknown parameter|month=ignored (help) - ^
Lichtenegger, H.I.M. (2000). "On detecting the gravitomagnetic field of the Earth by means of orbiting clocks". Advances in Space Research. 25 (6): 1255–1258. doi:10.1016/S0273-1177(99)00997-7.
{{cite journal}}: Unknown parameter|coauthors=ignored (|author=suggested) (help) - ^
Iorio, L. (2001). "SATELLITE GRAVITATIONAL ORBITAL PERTURBATIONS AND THE GRAVITOMAGNETIC CLOCK EFFECT". International Journal of Modern Physics D. 10 (4): 465–476. doi:10.1142/S0218271801000925.
{{cite journal}}: Unknown parameter|month=ignored (help) - ^
Iorio, L. (2001). "Satellite non-gravitational orbital perturbations and the detection of the gravitomagnetic clock effect". Classical and Quantum Gravity. 18 (20): 4303–4310. doi:10.1088/0264-9381/18/20/309.
{{cite journal}}: Unknown parameter|month=ignored (help) - ^
Mashhoon, B. (2001). "Gravitomagnetism and the Clock Effect". Lecture Notes in Physics: 83–108. doi:10.1007/3-540-40988-2_5.
{{cite journal}}: Unknown parameter|coauthors=ignored (|author=suggested) (help) - ^
Mashhoon, B. (2001). "On the gravitomagnetic clock effect". Physics Letters A. 292 (1–2): 49–57. doi:10.1016/S0375-9601(01)00776-9.
{{cite journal}}: Unknown parameter|coauthors=ignored (|author=suggested) (help); Unknown parameter|month=ignored (help) - ^
Iorio, L. (2002). "An alternative derivation of the gravitomagnetic clock effect". Classical and Quantum Gravity. 19 (1): 39–49. doi:10.1088/0264-9381/19/1/303.
{{cite journal}}: Unknown parameter|coauthors=ignored (|author=suggested) (help); Unknown parameter|month=ignored (help) - ^
Iorio, L. (2005). "On the possibility of measuring the gravitomagnetic clock effect in an Earth space-based experiment". Classical and Quantum Gravity. 22 (1): 119–132. doi:10.1088/0264-9381/22/1/008.
{{cite journal}}: Unknown parameter|coauthors=ignored (|author=suggested) (help); Unknown parameter|month=ignored (help) - ^
Lichtenegger, H.I.M. (2006). "The gravitomagnetic clock effect and its possible observation". Annalen der Physik. 15 (12): 868–876. doi:10.1002/andp.200610214.
{{cite journal}}: Unknown parameter|coauthors=ignored (|author=suggested) (help); Unknown parameter|month=ignored (help)
