Sphere of influence (astrodynamics)
Body SOI radius ( 10 km ) SOI radius ( body radii )
Mercury 0.112 46
Venus 0.616 102
Earth 0.929 145
Moon 0.0661 38
Mars 0.578 170
Jupiter 48.2 687
Saturn 54.5 1025
Uranus 51.9 2040
Neptune 86.8 3525
Table of selected SOI radii
Dependence of Sphere of influence rSOI/a on the ratio m/M The table shows the values of the sphere of gravity of the bodies of the solar system in relation to the Sun ( with the exception of the Moon which is reported relative to Earth ) : [ 1 ]
A sphere of influence (SOI) in astrodynamics and astronomy is the oblate-spheroid-shaped region around a celestial body where the primary gravitational influence on an orbiting object is that body. This is usually used to describe the areas in the Solar System where planets dominate the orbits of surrounding objects such as moons, despite the presence of the much more massive but distant Sun. In the patched conic approximation, used in estimating the trajectories of bodies moving between the neighbourhoods of different masses using a two body approximation, ellipses and hyperbolae, the SOI is taken as the boundary where the trajectory switches which mass field it is influenced by. The general equation describing the radius of the sphere formula_1 of a planet:
where
In the patched conic approximation, once an object leaves the planet's SOI, the primary/only gravitational influence is the Sun (until the object enters another body's SOI). Because the definition of r relies on the presence of the Sun and a planet, the term is only applicable in a three-body or greater system and requires the mass of the primary body to be much greater than the mass of the secondary body. This changes the three-body problem into a restricted two-body problem.