Sphere of influence (astrodynamics)
A sphere of influence (SOI) in astrodynamics and astronomy is the spherical region (actually is an oblate sphere) 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 
of a planet:
where
is the semimajor axis of the planet's orbit relative to the largest body in the system, usually the Sun
and 
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. 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 |  |
45 |
| Venus |  |
100 |
| Earth |  |
145 |
| Moon |  |
38 |
| Mars |  |
170 |
| Jupiter |  |
677 |
| Saturn |  |
901 |
| Uranus |  |
2025 |
| Neptune |  |
3866 |
See also
References
- Bate, Roger R.; Donald D. Mueller, Jerry E. White (1971). Fundamentals of Astrodynamics. New York: Dover Publications. pp. 333–334. ISBN 0-486-60061-0.
- Sellers, Jerry J.; Astore, William J., Giffen, Robert B., Larson, Wiley J. (2004). Kirkpatrick, Douglas H.. ed. Understanding Space: An Introduction to Astronautics (2 ed.). McGraw Hill. pp. 228,738. ISBN 0-07-294364-5.