Body | $mu$ (km^{3}s^{-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 km

^{3}s

^{-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:

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)
- $mu=\{G\}(m\_1+m\_2)!,$ (the sum of the two μ-values)

where:

- $m\_1!,$ and $m\_2!,$ are the masses of the two bodies.

Then:

## Terminology and accuracy

The value for the Earth is called

**geocentric gravitational constant** and equal to 398 600.441 8 ± 0.000 8 km

^{3}s

^{-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**.