• 107328  Infos

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:
    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 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.