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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]
This so-called sphere of influence is loosely defined by, up to a Q-like fudge factor , / (+) /, hence for a Sun-like star we have, = (+) / > [,] = (), i.e., stars will neither be tidally disrupted nor physically hit/swallowed in a typical encounter with the black hole thanks to the high surface escape speed = / = / from any solar ...
The blue path in this image is an example of a hyperbolic trajectory. A hyperbolic trajectory is depicted in the bottom-right quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the hyperbolic trajectory is shown in red.
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 simplification is achieved by dividing space into various parts by assigning each of the n bodies (e.g. the Sun, planets, moons) its own sphere of influence.When the spacecraft is within the sphere of influence of a smaller body, only the gravitational force between the spacecraft and that smaller body is considered, otherwise the gravitational force between the spacecraft and the larger ...
The formula for escape velocity can be derived from the principle of conservation of energy. For the sake of simplicity, unless stated otherwise, we assume that an object will escape the gravitational field of a uniform spherical planet by moving away from it and that the only significant force acting on the moving object is the planet's gravity.
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 ...