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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 ...
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
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.
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]
It is the easiest way for the debris to commute between a Hill sphere (an inner circle of blue and light blue) and communal gravity regions (figure-eights of yellow and green in the inner side). Hill sphere and horseshoe orbit. L 2 and L 3 are gravitational perturbation equilibria points. Passing through these two equilibrium points, debris can ...
The projection is a diffeomorphism (a bijection that is infinitely differentiable in both directions) between the sphere (minus (0, 0, 1)) and the open disk of radius 2. It is an area-preserving (equal-area) map, which can be seen by computing the area element of the sphere when parametrized by the inverse of the projection. In Cartesian ...
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 ...