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For such two- or restricted three-body problems as its simplest examples—e.g., one more massive primary astrophysical body, mass of m1, and a less massive secondary body, mass of m2—the concept of a Hill radius or sphere is of the approximate limit to the secondary mass's "gravitational dominance", [6] a limit defined by "the extent" of its ...
The most common base models to calculate the sphere of influence is the Hill sphere and the Laplace sphere, but updated and particularly more dynamic ones have been described. [ 2 ] [ 3 ] The general equation describing the radius of the sphere r SOI {\displaystyle r_{\text{SOI}}} of a planet: [ 4 ] r SOI ≈ a ( m M ) 2 / 5 {\displaystyle r ...
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular ...
In celestial mechanics, the Roche limit, also called Roche radius, is the distance from a celestial body within which a second celestial body, held together only by its own force of gravity, will disintegrate because the first body's tidal forces exceed the second body's self-gravitation. [1]
When calculating the length of a short north-south line at the equator, the circle that best approximates that line has a radius of (which equals the meridian's semi-latus rectum), or 6335.439 km, while the spheroid at the poles is best approximated by a sphere of radius , or 6399.594 km, a 1% difference. So long as a spherical Earth is assumed ...
The hill sphere of a celestial body describes the region in which the gravity of that body is dominant. The hill sphere radius of Venus is about 1 million kilometers; and as the cytherostationary orbital distance lies outside of it, no stable cytherostationary satellite can exist.
This article also states that it appears that stable satellite orbits exist only inside 1/2 to 1/3 of the Hill radius. The other article on the SoI gives a radius value of 925,000 km, which is about 575,000 miles, or about 62% of the radius of the Hill sphere. So: Hill radius = 1,500,000 km or 932,000 miles; SoI radius = 925,000 km or 575,000 miles
For example, one sphere that is described in Cartesian coordinates with the equation x 2 + y 2 + z 2 = c 2 can be described in spherical coordinates by the simple equation r = c. (In this system—shown here in the mathematics convention—the sphere is adapted as a unit sphere, where the radius is set to unity and then can generally be ignored ...