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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 a more general sense, the patched conic approximation is only valid within the SOI.

The general equation describing the radius of the sphere $r_{SOI}$ of a planet:

$r_{SOI}=a{\left(\frac{m}{M}\right)}^{2/5}$

where

$a$ is the semimajor axis of the smaller object's (usually a planet's) orbit around the larger body (usually the Sun).

$m$ and $M$ are the masses of the smaller and the larger object (usually a planet and the Sun), respectively.

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_SOI relies on the presence of the Sun and a planet, the term is only applicable in a three-body or greater system. It 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.

Table of planetary SOI radii

Body	SOI radius	SOI radius
-	(km)	(body radii)
Mercury	$112\times 10^3$	45
Venus	$616\times 10^3$	100
Earth	$925\times 10^3$	145
Moon	$66.1\times 10^3$	38
Mars	$577\times 10^3$	170
Jupiter	$48.2\times 10^6$	677
Saturn	$54.8\times 10^6$	901
Uranus	$51.7\times 10^6$	2025
Neptune	$86.7\times 10^6$	3866

See also

• Hill sphere

References

• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
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• 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
  
  My blog: http://www.primaboinca.com/view_profile.php?userid=5889534