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# Standard gravitational parameter

Body $mu$ (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 ($mu!,$) of a celestial body is the product of the gravitational constant ($G!,$) and the mass $M!,$:The units of the standard gravitational parameter are km3s-2

## Small body orbiting a central body

Under standard assumptions in astrodynamics we have:
$m_1 << m_2!,$
where:
• $m_1!,$ is the mass of the orbiting body,
• $m_2!,$ is the mass of the central body,
and the relevant standard gravitational parameter is that of the larger body.
For all circular orbits around a given central body:
$mu = rv^2 = r^3omega^2 = 4pi^2r^3/T^2!,$
where:
• $r!,$ is the orbit radius,
• $v!,$ is the orbital speed,
• $omega!,$is the angular speed,
• $T!,$ is the orbital period.

The last equality has a very simple generalization to elliptic orbits:
$mu=4pi^2a^3/T^2!,$
where:

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)
• $mu=\left\{G\right\}\left(m_1+m_2\right)!,$ (the sum of the two μ-values)
where:
• $m_1!,$ and $m_2!,$ are the masses of the two bodies.

Then:
• for circular orbits $rv^2 = r^3 omega^2 = 4 pi^2 r^3/T^2 = mu!,$
• for elliptic orbits: $4 pi^2 a^3/T^2 = mu!,$
• for parabolic trajectories $r v^2!,$ is constant and equal to $2 mu!,$
• for elliptic and hyperbolic orbits $mu$ 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.