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	~~{{general relativity}}~~

	~~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]]~~.

	~~==Explanation==~~
	~~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.~~

	~~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~~>
	~~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~~
	~~:<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~~.

	~~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>~~
	~~{{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 }}~~
	<~~/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}}~~
	~~</ref><ref>~~
	{{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 }}
	~~</ref><ref>~~
	{{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 }}
	~~</ref><ref>~~
	~~{{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 }}~~
	<~~/ref~~><~~ref~~>
	~~{{cite journal \| last= Iorio\| first=L~~.~~\|title= SATELLITE GRAVITATIONAL ORBITAL PERTURBATIONS AND THE GRAVITOMAGNETIC CLOCK EFFECT~~
	~~\| 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 }}~~
	~~</ref><ref>~~
	{{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 }}
	~~</ref><ref>~~
	~~{{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}}~~
	~~</ref><ref>~~
	~~{{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 }}~~
	~~</ref><ref>~~
	~~{{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 }}~~
	~~</ref><ref>~~
	~~{{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 }}
	<~~/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 }}
	~~</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~~.

	~~==See also==~~

	*[[Introduction to general relativity]]
	*[[Gravitomagnetic time delay]]

	~~== References ==~~
	~~{{Reflist\|1}}~~

	~~{{DEFAULTSORT:Gravitomagnetic Clock Effect}}~~
	~~[[Category:Clocks]]~~

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