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For planet Earth, which can be approximated as an oblate spheroid with radii 6 378.1 km and 6 356.8 km, the mean radius is = (( ) ) / = . The equatorial and polar radii of a planet are often denoted r e {\displaystyle r_{e}} and r p {\displaystyle r_{p}} , respectively.
In a two planet system, the mutual hill radius of the two planets must exceed to be stable. Multi-planet systems of three or more with semi-major-axis differences of less than ten mutual hill radii are always unstable. This is due to the loss of angular momentum due to perturbations by a third planet. [11]
The most common base models to calculate the sphere of influence is the Hill sphere and the Laplace sphere, but updated and particularly more dynamic ones have been described. [ 2 ] [ 3 ] The general equation describing the radius of the sphere r SOI {\displaystyle r_{\text{SOI}}} of a planet: [ 4 ] r SOI ≈ a ( m M ) 2 / 5 {\displaystyle r ...
For the giant planets, the "radius" is defined as the distance from the center at which the atmosphere reaches 1 bar of atmospheric pressure. [ 11 ] Because Sedna and 2002 MS 4 have no known moons, directly determining their mass is impossible without sending a probe (estimated to be from 1.7x10 21 to 6.1×10 21 kg for Sedna [ 12 ] ).
Coordinate systems in astronomy can specify an object's relative position in three-dimensional space or plot merely by its direction on a celestial sphere, if the object's distance is unknown or trivial. Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate system used on the surface of Earth.
Jupiter is the biggest planet in our solar system, according to NASA. Jupiter’s radius is over 11 times the equatorial radius of the Earth.
If a planet has a radius and/or mass between that of Earth and Neptune, then there is a question about whether the planet is rocky like Earth, a mixture of volatiles and gas like Neptune, a small planet with a hydrogen/helium envelope (mini-Jupiter), or of some other composition.
An infinite universe (unbounded metric space) means that there are points arbitrarily far apart: for any distance d, there are points that are of a distance at least d apart. A finite universe is a bounded metric space, where there is some distance d such that all points are within distance d of each other.