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| {{main|gravitoelectromagnetism}}
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| {{general relativity}}
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| In physics, the '''gravitomagnetic clock effect''' is a deviation from [[Kepler's third law]] that, according to the weak-field and slow-motion approximation of [[general relativity]], will be suffered by a particle in orbit around a (slowly) spinning body endowed with angular momentum ''S'', such as a typical [[planet]] or [[star]].
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| ==Explanation==
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| According to [[general relativity]], in its weak-field and slow-motion linearized approximation, a slowly spinning material 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.
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| Among its consequences on the particle's orbital motion there is a small correction to [[Kepler's third law]], namely
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| :<math>T_{\rm Kep}=2\pi\sqrt{a^3/GM}</math>
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| where ''T''<sub>Kep</sub> 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
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| :<math>T=T_{\rm Kep}+T_{\rm Gvm}=T_{\rm Kep}\pm{S}/{Mc^2},</math> where ''S'' is the central body's [[angular momentum]] and ''c'' is the [[speed of light]] in vacuum.
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| Interestingly, particles orbiting in opposite directions experience [[gravitomagnetic]] corrections ''T''<sub>Gvm</sub> with opposite signs, so that the difference of their orbital periods would cancel the standard Keplerian terms and would add the [[gravitomagnetic]] ones.<ref>
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| {{cite journal | last=Cohen| first=J.M.| coauthors=Mashhoon, B.|title= “Standard Clocks, Interferometry, and Gravitomagnetism| journal= Physics Letters A| year=1993 |volume=181| issue=5| month=October|pages= 353–358| doi=10.1016/0375-9601(93)90387-F |bibcode = 1993PhLA..181..353C }}
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| </ref><ref> | |
| {{cite journal | last = Mashhoon | first = B. | coauthors = Gronwald, F.; Theiss, D.S. | title = On measuring gravitomagnetism via spaceborne clocks: a gravitomagnetic clock effect | month = February| journal = Annalen der Physik | year = 1999 | volume = 8 | issue=2 | pages = 135–152 | doi=10.1002/(SICI)1521-3889(199902)8:2}}
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| </ref><ref>
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| {{cite journal | last=Tartaglia |first= A. |title = Detection of the gravitomagnetic clock effect|journal= Classical and Quantum Gravity| volume= 17| issue=4| month=February | pages= 783–792| year=2000| doi=10.1088/0264-9381/17/4/304 | bibcode=2000CQGra..17..783T|arxiv = gr-qc/9909006 }}
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| </ref><ref>
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| {{cite journal | last=Tartaglia |first= A. |title = Geometric Treatment of the Gravitomagnetic Clock Effect |journal= General Relativity and Gravitation| volume= 32| issue=9| month=September | pages= 1745–1756| year=2000| doi=10.1023/A:1001998505329|arxiv = gr-qc/0001080 |bibcode = 2000GReGr..32.1745T }}
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| </ref><ref>
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| {{cite journal | last = Lichtenegger| first = H.I.M. |coauthors = Gronwald, F.; Mashhoon, B.|title = On detecting the gravitomagnetic field of the Earth by means of orbiting clocks | journal = Advances in Space Research| volume = 25 | issue=6| pages=1255–1258 | year=2000|doi=10.1016/S0273-1177(99)00997-7 |bibcode = 2000AdSpR..25.1255L }}
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| </ref><ref> | |
| {{cite journal | last= Iorio| first=L.|title= SATELLITE GRAVITATIONAL ORBITAL PERTURBATIONS AND THE GRAVITOMAGNETIC CLOCK EFFECT
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| | journal= International Journal of Modern Physics D|date=August 2001| volume= 10| issue= 4| pages= 465–476 |doi= 10.1142/S0218271801000925 |arxiv = gr-qc/0007014 |bibcode = 2001IJMPD..10..465I }}
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| </ref><ref>
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| {{cite journal | last= Iorio| first=L.|title= Satellite non-gravitational orbital perturbations and the detection of the gravitomagnetic clock effect | journal= Classical and Quantum Gravity|date=October 2001| volume= 18| issue= 20| pages= 4303–4310 |doi= 10.1088/0264-9381/18/20/309 |arxiv = gr-qc/0007057 |bibcode = 2001CQGra..18.4303I }}
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| </ref><ref>
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| {{cite journal| last=Mashhoon |first=B.|coauthors= Gronwald, F; Lichtenegger, H.I.M.|title=Gravitomagnetism and the Clock Effect|journal=Lecture Notes in Physics |year=2001|pages=83–108|doi=10.1007/3-540-40988-2_5| volume=562}}
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| </ref><ref>
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| {{cite journal | last= Mashhoon| first=B.|coauthors= Iorio, L.; Lichtenegger, H.I.M.|title= On the gravitomagnetic clock effect | journal= Physics Letters A|date=December 2001| volume= 292| issue= 1–2| pages= 49–57 |doi= 10.1016/S0375-9601(01)00776-9|ref=Gclock1|arxiv = gr-qc/0110055 |bibcode = 2001PhLA..292...49M }}
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| </ref><ref>
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| {{cite journal | last= Iorio| first=L.|coauthors= Lichtenegger, H.I.M.; Mashhoon, B.|title= An alternative derivation of the gravitomagnetic clock effect| journal= Classical and Quantum Gravity|date=January 2002| volume= 19| issue= 1| pages= 39–49 |doi= 10.1088/0264-9381/19/1/303|ref=Gclock2 |arxiv = gr-qc/0107002 |bibcode = 2002CQGra..19...39I }}
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| </ref><ref>
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| {{cite journal | last= Iorio| first=L.|coauthors= Lichtenegger, H.I.M.| title= On the possibility of measuring the gravitomagnetic clock effect in an Earth space-based experiment | journal= Classical and Quantum Gravity|date=February 2005| volume= 22| issue= 1| pages= 119–132| doi= 10.1088/0264-9381/22/1/008|ref= Gclock4|arxiv = gr-qc/0210030 |bibcode = 2005CQGra..22..119I }}
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| </ref><ref> | |
| {{cite journal | last= Lichtenegger| first=H.I.M.| coauthors= Iorio, L.; Mashhoon, B.|title= The gravitomagnetic clock effect and its possible observation | journal= Annalen der Physik|date=December 2006| volume= 15| issue= 12| pages= 868–876 | doi=10.1002/andp.200610214|ref=Gclock3 |arxiv = gr-qc/0211108 |bibcode = 2006AnP...518..868L }}
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| </ref> Note that the '''+''' sign occurs for particle's co-rotation with respect to the rotation of the central body, whereas the '''−''' sign is for counter-rotation. That is, if the satellite revolves in the same direction as the planet spins, it takes more time to describe a full orbital revolution, whereas if it moves oppositely with respect to the planet's rotation its orbital period gets shorter.
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| ==See also==
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| *[[Introduction to general relativity]]
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| *[[Gravitomagnetic time delay]]
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| == References ==
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| {{Reflist|1}}
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| {{DEFAULTSORT:Gravitomagnetic Clock Effect}}
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| [[Category:Clocks]]
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