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  2. Hill sphere - Wikipedia

    en.wikipedia.org/wiki/Hill_sphere

    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 ]

  3. Volume of an n-ball - Wikipedia

    en.wikipedia.org/wiki/Volume_of_an_n-ball

    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.

  4. Sphere of influence (astrodynamics) - Wikipedia

    en.wikipedia.org/wiki/Sphere_of_influence_(astro...

    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 ...

  5. Roche lobe - Wikipedia

    en.wikipedia.org/wiki/Roche_lobe

    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:

  6. Orbital mechanics - Wikipedia

    en.wikipedia.org/wiki/Orbital_mechanics

    The formula for an escape velocity is derived as follows. The specific energy (energy per unit mass) of any space vehicle is composed of two components, the specific potential energy and the specific kinetic energy. The specific potential energy associated with a planet of mass M is given by

  7. n-sphere - Wikipedia

    en.wikipedia.org/wiki/N-sphere

    The formula for the volume of the ⁠ ⁠-ball can be derived from this by integration. Similarly the surface area element of the ⁠ ( n − 1 ) {\displaystyle (n-1)} ⁠ -sphere of radius ⁠ r {\displaystyle r} ⁠ , which generalizes the area element of the ⁠ 2 {\displaystyle 2} ⁠ -sphere, is given by

  8. Spherical cap - Wikipedia

    en.wikipedia.org/wiki/Spherical_cap

    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.

  9. Spherical sector - Wikipedia

    en.wikipedia.org/wiki/Spherical_sector

    If the radius of the sphere is denoted by r and the height of the cap by h, the volume of the spherical sector is =. This may also be written as V = 2 π r 3 3 ( 1 − cos ⁡ φ ) , {\displaystyle V={\frac {2\pi r^{3}}{3}}(1-\cos \varphi )\,,} where φ is half the cone aperture angle, i.e., φ is the angle between the rim of the cap and the ...