An oblate spheroid is ellipsoid having a shorter axis and two equal longer axes. A spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. ... 3D rendering of an ellipsoid In mathematics, an ellipsoid is a type of quadric that is a higher dimensional analogue of an ellipse. ...

An oblate spheroid

The oblateness, ellipticity, or flattening is a measure for a planet that is a spheroid in shape, bulging outward in the center due to its rotation. Earth is slightly oblate. Oblate Spheroid This image was made by AugPi using Mathematica. ... The flattening, ellipticity, or oblateness of an oblate spheroid is the relative difference between its equatorial radius a and its polar radius b: The flattening of the Earth is 1:298. ... A planet is generally considered to be a relatively large mass of accreted matter in orbit around a star that is not a star itself. ... Rotation of a plane, seen as the rotation of the terrain relative to the plane (exposure time 1. ... Earth, also known as Terra, and Tellus mostly in the 19th century, is the third-closest planet to the Sun. ...

Gravity tends to contract celestial bodies into a perfect sphere, the shape where all the mass is as close to the center of gravity as possible. Perfect spherical shape is the shape of least gravitational potential energy, the oblate shape corresponds to a higher gravitational potential energy than that. For a rotating planet relaxing to the state of a perfect sphere is not available. A sphere is a perfectly symmetrical geometrical object. ... In geometry, two objects are of the same shape if one can be transformed to another (ignoring color) by dilating (that is, by multiplying all distances by the same factor) and then, if necessary, rotating and translating. ... Potential energy (U, or Ep), a kind of scalar potential, is energy by virtue of matter being able to move to a lower-energy state, releasing energy in some form. ...

To get a feel for the type of equilibrium that is involved, an interested person can take place in a swivel chair, with weights in in their hands, and someone brings the chair into rotation. If they pull the weights toward them, their rotation rate goes up (by conservation of angular momentum), which means that additional contraction requires a stronger force than before. In physics the angular momentum of an object with respect to a reference point is a measure for the extent to which, and the direction in which, the object rotates about the reference point. ...

Something analogous to that happens in planet formation. Matter is first coalescing into a slow rotating disk-shaped distribution, and collisions and friction convert kinetic energy to heat, allowing the disk to self-gravitate into an oblate spheroid.

As long as the proto-planet is still too oblate to be in equilibrium, gravitational potential energy is released as it contracts. The contraction increases the rotation rate, making further contraction more demanding. There is a point where further contraction would result in more increase in rotational kinetic energy than the amount of gravitational potential energy that is released by the contraction. The contraction process halts at that point.

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 has ceased. In that sense the equilibrium state is a state of lowest possible energy.

Mathematically, for flattening we have

where a is the equatorial radius, b is the polar radius and b:a is the aspect ratio. The approximation is valid in the case of a fluid planet of uniform density; it is a function of the Newtonian constant of gravitation G, the rotation period T and the density ρ. The equator is an imaginary circle drawn around a planet (or other astronomical object) at a distance halfway between the poles. ... For other uses of the word pole, see Pole (disambiguation). ... The aspect ratio of a two-dimensional shape is the ratio of its longest dimension to its shortest dimension. ... Density (symbol: ρ - Greek: rho) is a measure of mass per unit of volume. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... In astronomy, a rotation period is the time an astronomical object takes to complete one revolution around its rotation axis. ...

See Also

• Spheroid