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A sphere of influence (SOI) in astrodynamics and astronomy is the oblate spheroid-shaped region where a particular celestial body exerts the main gravitational influence on an orbiting object. 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 ...
The Hill sphere is a common model for the calculation of a gravitational sphere of influence. It is the most commonly used model to calculate the spatial extent of gravitational influence of an astronomical body ( m ) in which it dominates over the gravitational influence of other bodies, particularly a primary ( M ). [ 1 ]
The radius of the sphere of influence is called the "(gravitational) influence radius". There are two definitions in common use for the radius of the sphere of influence. The first [ 1 ] is given by r h = G M BH σ 2 {\displaystyle r_{h}={\frac {GM_{\text{BH}}}{\sigma ^{2}}}} where M BH is the mass of the black hole, σ is the stellar velocity ...
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Again, if the mass of the smaller object (M 2) is much smaller than the mass of the larger object (M 1) then L 2 is at approximately the radius of the Hill sphere, given by: The same remarks about tidal influence and apparent size apply as for the L 1 point.
The length A is the orbital separation of the system and r 1 is the radius of the sphere whose volume approximates the Roche lobe of mass M 1. This formula is accurate to within about 2%. [ 2 ] Another approximate formula was proposed by Eggleton and reads as follows:
The patch point between the hyperbolic trajectory relative to the departure planet and the heliocentric transfer orbit occurs at the planet's sphere of influence radius relative to the Sun, as defined above in Orbital flight. Given the Sun's mass ratio of 333,432 times that of Earth and distance of 149,500,000 kilometers (80,700,000 nautical ...
The sphere therefore appears in nature: for example, bubbles and small water drops are roughly spherical because the surface tension locally minimizes surface area. The surface area relative to the mass of a ball is called the specific surface area and can be expressed from the above stated equations as