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Encyclopedia > Standard gravitational parameter
Body μ (km3s-2)
Sun 132,712,440,000
Mercury 22,032
Venus 324,859
Earth 398,600
Mars 42,828
Jupiter 126,686,534
Saturn 37,931,187
Uranus 5,793,947
Neptune 6,836,529
Pluto 1,001

In astrodynamics, the standard gravitational parameter () of a celestial body is the product of the gravitational constant () and the mass : Astrodynamics is the study of the motion of rockets, missiles, and space vehicles, as determined from Sir Isaac Newtons laws of motion and his law of universal gravitation. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...

The units of the standard gravitational parameter are km3s-2


Small body orbiting a central body

Under standard assumptions in astrodynamics we have: For most of the problems in astrodynamics involving two bodies and standard assumptions are usually the following: A1: and are the only objects in the universe and thus influence of other objects is disregarded, A2: The orbiting body () is far smaller than central body (), i. ...

where:

and the relevant standard gravitational parameter is that of the larger body. In astrodynamics, an orbiting body () is a body that orbits central body (). Under standard assumptions in astrodynamics: it is orders of magnitude lighter than central body (i. ... In astrodynamics a central body () is a body that is being orbited by orbiting body(). Under standard assumptions in astrodynamics: it is orders of magnitude heavier than orbiting body (i. ...


For all circular orbits around a given central body: In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0. ...

where:


The last equality has a very simple generalization to elliptic orbits: The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body. ... Angular frequency is a measure of how fast an object is rotating In physics (specifically mechanics and electrical engineering), angular frequency ω (also called angular speed) is a scalar measure of rotation rate. ... The orbital period is the time it takes a planet (or another object) to make one full orbit. ... In astrodynamics or celestial mechanics a elliptic orbit is an orbit with the eccentricity greater than 0 and less than 1. ...

where:

  • is the semi-major axis.

For all parabolic trajectories rv² is constant and equal to 2μ. In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolas. ... In astrodynamics or celestial mechanics a parabolic trajectory is an orbit with the eccentricity equal to 1. ...


For elliptic and hyperbolic orbits μ is twice the semi-major axis times the absolute value of the specific orbital energy. In astrodynamics the specific orbital energy (or vis-viva energy) of an orbiting body traveling through space under standard assumptions is the sum of its potential energy () and kinetic energy () per unit mass. ...


Two bodies orbiting each other

In the more general case where the bodies need not be a large one and a small one, we define:

  • the vector r is the position of one body relative to the other
  • r, v, and in the case of an elliptic orbit, the semi-major axis a, are defined accordingly (hence r is the distance)
  • (the sum of the two μ-values)

where: In astrodynamics or celestial mechanics a elliptic orbit is an orbit with the eccentricity greater than 0 and less than 1. ... In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolas. ...

  • and are the masses of the two bodies.

Then:

In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0. ... In astrodynamics or celestial mechanics a elliptic orbit is an orbit with the eccentricity greater than 0 and less than 1. ... In astrodynamics or celestial mechanics a parabolic trajectory is an orbit with the eccentricity equal to 1. ... In astrodynamics the specific orbital energy (or vis-viva energy) of an orbiting body traveling through space under standard assumptions is the sum of its potential energy () and kinetic energy () per unit mass. ... Reduced mass is a concept that allows one to solve the two-body problem of mechanics as if it were a one body problem. ...

Terminology and accuracy

The value for the Earth is called geocentric gravitational constant and equal to 398 600.441 8 ± 0.000 8 km3s-2. Thus the uncertainty is 1 to 500 000 000, much smaller than the uncertainties in G and M separately (1 to 7000 each).


The value for the Sun is called heliocentric gravitational constant.


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Gravitation Summary (7851 words)
Gravitation is one of the four fundamental interactions in nature, the other three being the electromagnetic force, the weak nuclear force, and the strong nuclear force.
Moreover, gravitation is the reason for the very existence of the earth, the sun and other celestial bodies; without it matter would not have coalesced into these bodies and life as we know it would not exist.
Gravitation is also responsible for keeping the earth and the other planets in their orbits around the sun, the moon in its orbit around the earth, for the formation of tides, and for various other natural phenomena that we observe.
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The forces of gravitational compression will again exceed the forces of the internal pressure of substance, will begin collapse, in consequence of which enormous energy in the form of explosion is separated, and the surpluses of material leave star.
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