Science Fair Project Encyclopedia
Standard gravitational parameter
The units of the standard gravitational parameter are km3s-2
Small body orbiting a central body
Under standard assumptions in astrodynamics we have:
and the relevant standard gravitational parameter is that of the larger body.
For all circular orbits around a given central body:
The last equality has a very simple generalization to elliptic orbits:
- is the semi-major axis.
For all parabolic trajectories rv² is constant and equal to 2μ.
For elliptic and hyperbolic orbits μ is twice the semi-major axis times the absolute value of the specific orbital energy.
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)
- and are the masses of the two bodies.
- for circular orbits
- for elliptic orbits:
- for parabolic trajectories is constant and equal to
- for elliptic and hyperbolic orbits μ is twice the semi-major axis times the absolute value of the specific orbital energy, where the latter is defined as the total energy of the system divided by the reduced mass.
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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