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The standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of that body. For two bodies, the parameter may be expressed as G ( m 1 + m 2 ) , or as GM when one body is much larger than the other: μ = G ( M + m ) ≈ G M . {\displaystyle \mu =G(M+m)\approx GM.}
Gravity well (or funnel) is a metaphorical concept for a gravitational field of a mass, with the field being curved in a funnel-shaped well around the mass, illustrating the steep gravitational potential and its energy that needs to be accounted for in order to escape or enter the main part of a sphere of influence. [11]
The gravitational constant is a physical constant that is difficult to measure with high accuracy. [7] This is because the gravitational force is an extremely weak force as compared to other fundamental forces at the laboratory scale. [d] In SI units, the CODATA-recommended value of the gravitational constant is: [1]
The Hill sphere for Earth thus extends out to about 1.5 million km (0.01 AU). The Moon's orbit, at a distance of 0.384 million km from Earth, is comfortably within the gravitational sphere of influence of Earth and it is therefore not at risk of being pulled into an independent orbit around the Sun.
Escape speed at a distance d from the center of a spherically symmetric primary body (such as a star or a planet) with mass M is given by the formula [2] [3] = = where: G is the universal gravitational constant (G ≈ 6.67 × 10 −11 m 3 ⋅kg −1 ⋅s −2 [4])
In the case of a spherically symmetric mass distribution we can conclude (by using a spherical Gaussian surface) that the field strength at a distance r from the center is inward with a magnitude of G/r 2 times only the total mass within a smaller distance than r. All the mass at a greater distance than r from the center has no resultant effect.
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]
The ends of the diameter indicate the apsides, the points of closest and farthest distance. The Kepler problem derives its name from Johannes Kepler, who worked as an assistant to the Danish astronomer Tycho Brahe. Brahe took extraordinarily accurate measurements of the motion of the planets of the Solar System.