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. Astrodynamics is the study of the motion of rockets, missiles, and space vehicles, as determined from Sir Isaac Newtons laws of motion and his law of universal gravitation. ... For other uses, see Astronomy (disambiguation). ... A sphere is a symmetrical geometrical object. ... See lists of astronomical objects for a list of the various lists of astronomical objects in Wikipedia. ... Gravity is a force of attraction that acts between bodies that have mass. ... Two bodies with a slight difference in mass orbiting around a common barycenter. ... This article is about the Solar System. ... A planet (from the Greek πλανήτης, planetes or wanderers) is a body of considerable mass that orbits a star and that produces very little or no energy through nuclear fusion. ... A natural satellite is an object that orbits a planet or other body larger than itself and which is not man-made. ... Sol redirects here. ... Astrodynamics is the study of the motion of rockets, missiles, and space vehicles, as determined from Sir Isaac Newtons laws of motion and his law of universal gravitation. ...

The general equation describing the radius of the sphere r_SOI of a planet: Remote Authentication Dial In User Service (RADIUS) is an AAA (authentication, authorization and accounting) protocol for applications such as network access or IP mobility. ...

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 r_SOI relies on the presence of the Sun and a planet, the term is only applicable in a three body or greater system. In geometry, the semi-major axis (also semimajor axis) a applies to ellipses and hyperbolas. ... This article or section is in need of attention from an expert on the subject. ... This article is about the n-body problem in classical mechanics. ...

Table of planetary SOI radii

“km” redirects here. ... This article is about the planet. ... Adjectives: Venusian or (rarely) Cytherean Atmosphere Surface pressure: 9. ... This article is about Earth as a planet. ... This article is about Earths moon. ... Adjectives: Martian Atmosphere Surface pressure: 0. ... For other uses, see Jupiter (disambiguation). ... This article is about the planet. ... For other uses, see Uranus (disambiguation). ... For other uses, see Neptune (disambiguation). ... Adjectives: Plutonian Atmosphere Surface pressure: 0. ...

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). in Kirkpatrick, Douglas H.: Understanding Space: An Introduction to Astronautics, 2, McGraw Hill, 228,738. ISBN 0-07-294364-5.