Sphere of influence (astrodynamics)

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For the term relating to black holes, see sphere of influence (astronomy).

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}


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 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[edit]

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[edit]


  • 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.