Sphere of influence (astronomy)

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The sphere of influence (SOI for short) is a u. a. Quantity commonly used in astrodynamics and space travel . It indicates the area in which the gravity of a planet has effects on other celestial bodies (which must be included in calculations). Outside the SOI, the influence of the celestial body is considered to be negligible compared to that of the sun .

Reason for introduction

Without the SOI instrument, the movements of celestial bodies, especially spaceships and space stations , would be extremely difficult to calculate, since every body has a gravitational influence on everyone else: even a three-body problem can only be described using a system of differential equations , which is generally no longer possible is solvable. For the solar system with all the celestial bodies it contains, one is then with a system whose equations of motion - if it is possible at all - require vast amounts of time and use of computers.

Applying the SOI significantly reduces the complexity of the system, and a multi-body problem usually becomes a two-body problem that can be solved without computer support.

calculation

Mostly one assumes that the SOI is a sphere , the radius of which can be calculated using the following formula:

.

It is

  • the major semi-axis of the planet's orbit (which corresponds to the distance from the sun, i.e. the radius of the orbit around the sun, in the case of circular orbits)
  • the respective mass .

That is, the further the planet is from the sun and the heavier it is, the larger the sphere of influence is.

values

planet SOI radius
(in km)		 SOI radius
(in radii of the celestial body)
Mercury 112,000 45
Venus 616,000 100
earth 925,000 145
moon 66,000 38
Mars 577,000 170
Jupiter 48,200,000 677
Saturn 54,800,000 901
Uranus 51,700,000 2,025
Neptune 86,700,000 3,866

literature

  • Bate, Roger R., Donald D. Mueller, Jerry E. White: Fundamentals of Astrodynamics. New York: Dover Publications, 1971, ISBN 0-486-60061-0 .
  • Sellers, Jerry J., Astore, William J., Giffen, Robert B., Larson, Wiley J., Kirkpatrick, Douglas H .: Understanding Space: An Introduction to Astronautics (2 ed.). McGraw Hill, 2004, ISBN 0-07-294364-5 .
  • Walter, Ulrich: Astronautics , Wiley-VCH, 2008, ISBN 3-527-40685-9

See also