Sphere of influence (astrodynamics)
The Sphere of Influence ( SOI short, . Engl for sphere of influence ) is one among others in astrodynamics and aerospace usual size. It indicates the range in which the gravity of a planet has an impact on other celestial bodies (which must be necessarily included in invoices ). Outside the SOI, the influence of the celestial body is opposite the Sun as viewed the negligible.
Due to the introduction
Without the instrument of the SOI would be movements of celestial bodies, especially of space ships and space stations, extremely difficult to calculate, as every body on each other has a gravitational influence: already a three-body problem can be described only by a system of differential equations, which are not generally more is releasable. For the solar system with all included sky objects you are then in a system to determine the equations of motion - if it is at all possible - requires vast amounts of time and computer use.
By applying the SOI the complexity of the system is therefore significantly reduced, and of a multi-body problem is usually a two-body problem which can be solved without computer assistance.
Calculation
Usually one assumes that the SOI is a sphere whose radius can be calculated using the following formula use:
It is
- The semi-major axis of the planetary path (which is the distance from the sun, which is the radius of the orbit around the sun at corresponding circular paths )
- The respective mass.
That is, the Sphere of Influence is the greater, the farther the planet from the Sun and the heavier it is.