# Sphere of influence (astrodynamics)

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Sphere of influence (astrodynamics)

A sphere of influence (SOI) in astrodynamics and astronomy is the spherical 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 our 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 $r_\left\{SOI\right\}$ of a planet:: $r_\left\{SOI\right\} = a_p\left(frac\left\{m_p\right\}\left\{m_s\right\}\right)^\left\{2/5\right\}$where: $a_p$ is the semimajor axis of the planet's orbit relative to the largest body in the system, usually the Sun: $m_p$ and $m_s$ are the masses of the planet and 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). Since the definition of rSOI relies on the presence of the Sun and a planet, the term is only applicable in a three body or greater system.

Table of planetary SOI radii

References

*cite book
last=Bate
first=Roger R.
coauthors= Donald D. Mueller, Jerry E. White
title= Fundamentals of Astrodynamics
year=1971
publisher=Dover Publications
location=New York
id=ISBN 0-486-60061-0
pages=333-334

*cite book
last=Sellers
first=Jerry J.
coauthors= Astore, William J., Giffen, Robert B., Larson, Wiley J.
editor=Kirkpatrick, Douglas H.
title= Understanding Space: An Introduction to Astronautics
edition=2
year=2004
publisher=McGraw Hill
id=ISBN 0-07-294364-5
pages= 228,738

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