From Wikipedia, the free encyclopedia
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, such as a typical
planet or
star .
Explanation
According to
general relativity , in its weak-field and slow-motion 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
T
K
e
p
=
2
π
a
3
G
M
{\displaystyle T_{\rm {Kep}}=2\pi {\sqrt {\frac {a^{3}}{GM}}}}
where T Kep 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
T
=
T
K
e
p
+
T
G
v
m
=
T
K
e
p
±
S
M
c
2
,
{\displaystyle T=T_{\rm {Kep}}+T_{\rm {Gvm}}=T_{\rm {Kep}}\pm {\frac {S}{Mc^{2}}},}
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 T Gvm with opposite signs, so that the difference of their orbital periods would cancel the standard Keplerian terms and would add the
gravitomagnetic ones.
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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
References
^
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^
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^
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^
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^
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^
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^
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