Sphere of influence (astrodynamics)

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A sphere of influence (SOI) in astrodynamics and astronomy is the spherical region around a celestial body where the primary gravitational influence of 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 rSOI of a planet:

r_{SOI} = a_p(\frac{m_p}{m_s})^{2/5}

where

ap is the semimajor axis of the planet's orbit relative to the largest body in the system, usually the Sun
mp and ms 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.

[edit] Table of planetary SOI radii

Body SOI Radius SOI Radius
- (km) (body radii)
Mercury 112 × 103 45
Venus 616 × 103 100
Earth 925 × 103 145
Moon 66,1 × 103 38
Mars 577 × 103 170
Jupiter 48.2 × 106 677
Saturn 54.8 × 106 901
Uranus 51.7 × 106 2025
Neptune 86.7 × 106 3866
Pluto 3.31 × 106 2753

[edit] References

  • Bate, Roger R., Donald D. Mueller, Jerry E. White (1971). Fundamentals of Astrodynamics. New York: Dover Publications, 333-334. ISBN 0-486-60061-0.
  • Sellers, Jerry J., Astore, William J., Giffen, Robert B., Larson, Wiley J. (2004). Kirkpatrick, Douglas H.: Understanding Space: An Introduction to Astronautics, 2, McGraw Hill, 228,738. ISBN 0-07-294362-5.
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