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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 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:
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 ...
An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane.It is also a spherical segment of one base, i.e., bounded by a single plane.
Mémoires de la section des sciences, Volume 1. Académie des sciences de Montpellier. pp. 243– 262. 2.44 is mentioned on page 258. Roche, Édouard (1850). "La figure d'une masse fluide soumise à l'attraction d'un point éloigné, part 2". Mémoires de la section des sciences, Volume 1. Académie des sciences de Montpellier. pp. 333– 348.
The volume of a n-ball is the Lebesgue measure of this ball, which generalizes to any dimension the usual volume of a ball in 3-dimensional space. The volume of a n-ball of radius R is , where is the volume of the unit n-ball, the n-ball of radius 1.
Thus, the segment volume equals the sum of three volumes: two right circular cylinders one of radius a and the second of radius b (both of height /) and a sphere of radius /. The curved surface area of the spherical zone—which excludes the top and bottom bases—is given by
Hart (2009) [3] states that the "volume of a spherical wedge is to the volume of the sphere as the number of degrees in the [angle of the wedge] is to 360". Hence, and through derivation of the spherical wedge volume formula, it can be concluded that, if V s is the volume of the sphere and V w is the volume of a given spherical wedge,