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{{for|the term relating to black holes|sphere of influence (astronomy)}}
 
A '''sphere of influence''' ('''SOI''') in [[astrodynamics]] and [[astronomy]] is the [[oblate spheroid|oblate-spheroid]]-shaped region around a [[celestial body]] where the primary [[gravity|gravitational]] influence on an [[orbit]]ing 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 [[natural satellite|moon]]s), 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 <math>r_{SOI}</math> of a planet:
: <math>r_{SOI} = a\left(\frac{m}{M}\right)^{2/5}</math>
where
: <math>a</math> is the [[semimajor axis]] of the smaller object's (usually a planet's) orbit around the larger body (usually the Sun).
: <math>m</math> and <math>M</math> are the [[mass]]es 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 r<sub>SOI</sub> relies on the presence of the Sun and a planet, the term is only applicable in a [[n-body problem|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==
{| cellpadding="2" cellspacing="0" style="margin:1px; border:1px solid black;width:220px; font-size:100%; font-family:Arial,Helvetica" align="center"
|colspan="1" | Body ||colspan="1"| SOI radius||colspan="1"|SOI radius
|-
|align="center" style="border-bottom:1px solid"| - ||style="border-bottom:1px solid" align="center" | ([[kilometre|km]]) ||style="border-bottom:1px solid" align="center" | (body radii)
|-
| [[Mercury (planet)|Mercury]] ||align="right" | <math>112 \times 10^3</math>||align="right" | 45
|-
| [[Venus]] ||align="right" | <math>616 \times 10^3</math>||align="right" | 100
|-
| [[Earth]] ||align="right" | <math>925 \times 10^3</math>||align="right" | 145
|-
| [[Moon]] ||align="right" | <math>66.1 \times 10^3</math>||align="right" | 38
|-
| [[Mars]] ||align="right" | <math>577 \times 10^3</math>||align="right" | 170
|-
| [[Jupiter]] ||align="right" | <math>48.2 \times 10^6</math>||align="right" | 677
|-
| [[Saturn]] ||align="right" | <math>54.8 \times 10^6</math>||align="right" | 901
|-
| [[Uranus]] ||align="right" | <math>51.7 \times 10^6</math>||align="right" | 2025
|-
| [[Neptune]] ||align="right" | <math>86.7 \times 10^6</math>||align="right" | 3866
|-
|}
 
==See also==
* [[Hill sphere]]
 
==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
|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
|isbn=0-07-294364-5
|pages= 228,738}}
 
[[Category:Astrodynamics]]
[[Category:Orbits]]

Latest revision as of 12:52, 13 December 2013

28 year-old Painting Investments Worker Truman from Regina, usually spends time with pastimes for instance interior design, property developers in new launch ec Singapore and writing. Last month just traveled to City of the Renaissance.

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 rSOI of a planet:

rSOI=a(mM)2/5

where

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

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

See also

References

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  • 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534