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The Hill radius or sphere (the latter defined by the former radius [citation needed]) has been described as "the region around a planetary body where its own gravity (compared to that of the Sun or other nearby bodies) is the dominant force in attracting satellites," both natural and artificial.
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 ...
This article also states that it appears that stable satellite orbits exist only inside 1/2 to 1/3 of the Hill radius. The other article on the SoI gives a radius value of 925,000 km, which is about 575,000 miles, or about 62% of the radius of the Hill sphere. So: Hill radius = 1,500,000 km or 932,000 miles; SoI radius = 925,000 km or 575,000 miles
The Hill sphere (gravitational sphere of influence) of the Earth is about 1,500,000 kilometers (0.01 AU) in radius, or approximately four times the average distance to the Moon. [12] [nb 2] This is the maximal distance at which the Earth's gravitational influence is stronger than the more distant Sun and planets. Objects orbiting the Earth must ...
The size of the "neighborhoods" (or spheres of influence) vary with radius : r S O I = a p ( m p m s ) 2 / 5 {\displaystyle r_{SOI}=a_{p}\left({\frac {m_{p}}{m_{s}}}\right)^{2/5}} where a p {\displaystyle a_{p}} is the semimajor axis of the planet's orbit relative to the Sun ; m p {\displaystyle m_{p}} and m s {\displaystyle m_{s}} are the ...
In celestial mechanics, the Roche limit, also called Roche radius, is the distance from a celestial body within which a second celestial body, held together only by its own force of gravity, will disintegrate because the first body's tidal forces exceed the second body's self-gravitation. [1]
A sphere (top), rotational ellipsoid (left) and tri-axial ellipsoid (right) The mean radius in astronomy is a measure for the size of planets and small Solar System bodies . Alternatively, the closely related mean diameter ( D {\displaystyle D} ), which is twice the mean radius, is also used.
It is the easiest way for the debris to commute between a Hill sphere (an inner circle of blue and light blue) and communal gravity regions (figure-eights of yellow and green in the inner side). Hill sphere and horseshoe orbit. L 2 and L 3 are gravitational perturbation equilibria points. Passing through these two equilibrium points, debris can ...