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{{Short description|Outward bulge around a planet's equator due to its rotation}}
{{for|the feature on some of
{{More citations needed|date=April 2023}}
An '''equatorial bulge''' is a difference between the [[equator]]ial and polar [[diameter]]s of a [[planet]], due to the [[centrifugal force]] exerted by the [[Rotation around a fixed axis|rotation]] about the body's axis. A rotating body tends to form an [[oblate spheroid]] rather than a [[sphere]].
[[File:Sphere-OblateSpheroidComparison.jpg|thumb|Comparison between an oblate spheroid and sphere.]]
==On Earth==
{{main|Earth
{{further|Earth ellipsoid|Figure of the Earth}}
The planet [[Earth]] has a rather slight equatorial bulge
The difference of the [[radius|radii]] is thus about {{cvt|21
More precisely,
== The equilibrium as a balance of energies ==
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When spun, the spring-metal band bulges at its equator and flattens at its poles in analogy with the Earth.]]
[[Gravity]] tends to contract a celestial body into a [[sphere]], the shape for which all the mass is as close to the center of gravity as possible.
A way for one to get a feel for the type of equilibrium involved is to imagine someone seated in a spinning swivel chair and holding a weight in each hand; if the individual pulls the weights inward towards them, [[Work (physics)|work]] is being done and their rotational kinetic energy increases. The increase in rotation rate is so strong that at the faster rotation rate the required [[centripetal force]] is larger than with the starting rotation rate.
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Something analogous to this occurs in planet formation. Matter first coalesces into a slowly rotating disk-shaped distribution, and collisions and friction convert kinetic energy to heat, which allows the disk to self-gravitate into a very oblate spheroid.
As long as the proto-planet is still too oblate to be in equilibrium, the release of [[gravitational energy|gravitational potential energy]] on contraction keeps driving the increase in rotational kinetic energy. As the contraction proceeds, the rotation rate keeps going up, hence the required force for further contraction keeps going up. There is a point where the increase of rotational kinetic energy on further contraction would be larger than the release of gravitational potential energy. The contraction process can only proceed up to that point, so it halts there.
As long as there is no equilibrium there can be violent convection, and as long as there is violent convection friction can convert kinetic energy to heat, draining rotational kinetic energy from the system. When the equilibrium state has been reached then large scale conversion of kinetic energy to heat ceases. In that sense the equilibrium state is the lowest state of energy that can be reached.
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== Effect on gravitational acceleration ==
{{main|Theoretical gravity}}
[[
Red arrow: gravity
Green arrow
Blue arrow: the resultant force
<br/>
The resultant force provides required centripetal force. Without this centripetal force frictionless objects would slide towards the equator.
<br/>
In calculations, when a coordinate system is used that is co-rotating with the Earth, the vector of the notional [[
Because of a planet's rotation around its own axis, the [[gravitational acceleration]] is less at the [[equator]] than at the [[geographical pole|poles]]. In the 17th century, following the invention of the [[pendulum clock]], French scientists found that clocks sent to [[French Guiana]], on the northern coast of [[South America]], ran slower than their exact counterparts in Paris. Measurements of the acceleration due to gravity at the equator must also take into account the planet's rotation. Any object that is stationary with respect to the surface of the Earth is actually following a circular trajectory, circumnavigating the Earth's axis. Pulling an object into such a circular trajectory requires a force. The acceleration that is required to circumnavigate the Earth's axis along the equator at one revolution per [[sidereal day]] is 0.0339 m/s
At the poles, the gravitational acceleration is 9.8322 m/s<sup>2</sup>. The difference of 0.0178 m/s<sup>2</sup> between the gravitational acceleration at the poles and the true gravitational acceleration at the
In summary, there are two contributions to the fact that the effective gravitational acceleration is less strong at the equator than at the poles. About 70
The diagram illustrates that on all latitudes the effective gravitational acceleration is decreased by the requirement of providing a centripetal force; the decreasing effect is strongest on the
== Effect on satellite orbits ==
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|bibcode=2011PhRvD..84l4001I
|doi=10.1103/PhysRevD.84.124001
|s2cid=118305813
|last1=Renzetti
|first1=G.
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|bibcode=2013JApA...34..341R
|doi=10.1007/s12036-013-9186-4
|s2cid=120030309
|last1=Renzetti
|first1=G.
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|bibcode=2014Ap&SS.352..493R
|doi=10.1007/s10509-014-1915-x
|s2cid=119537102
|last1=King-Hele
|first1=D. G.
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|doi=10.1139/p2012-081
}}</ref> because the much smaller relativistic effects are qualitatively indistinguishable from the oblateness-driven disturbances.
== Formulation ==
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*<math>G</math> is the universal [[gravitational constant]],
*<math>a</math> is the mean radius,
*<math>a_e = a\, (1 + \tfrac{f}{3})</math> and <math>a_p = a\,(1 - \tfrac{2f}{3})</math> are respectively the equatorial and polar radius,{{Dubious|date=April 2023}}
*<math>T</math> is the rotation period and <math>\omega = \tfrac{2 \pi}{T}</math> is the [[angular velocity]],
*<math>\rho</math> is the body density and <math>M \simeq \tfrac{4}{3} \pi \rho a^3</math> is the total body mass.
Real flattening is smaller due to mass concentration in the center of celestial bodies.
{| class="wikitable"
|+ [[Giant planet]]s of the [[Solar System]]
|-
! !! a<sub>e</sub> [km] !! a<sub>p</sub> [km] !! f<sub>real</sub> !! T [h] !! M [10<sup>26</sup> kg] !! f<sub>formula</sub>
|-
| [[Jupiter]] || 71,492 || 66,854 || 0.066 || 9.9 || 18.98 || 0.104
|-
| [[Saturn]] || 60,268 || 54,364|| 0.108 || 10.6 || 5.68 || 0.178
|-
| [[Uranus]] || 25,559 || 24,973 || 0.023 || 17.2 || 0.87 || 0.036
|-
| [[Neptune]] || 24,764 || 24,341 || 0.017 || 16.1 || 1.02 || 0.032
|}
== See also ==
|