Question

What is the standard gravitational parameter (GM)?

There's really no clear definition of standard gravitational parameter - just that its G times M, and that's really not helpful.

If someone could give me a clear and easier definition, that would really be helpful!

Thanks!

Answer 1

The gravitational parameter for a body `GM` is the gravitational constant `G` multiplied by the mass of the body.

Explanation:

When doing calculations involving gravity, the gravitational constant `G` is required. It is however difficult to measure the value of `G` to high degrees of accuracy.

The known value of `G=6.674 08 \times 10^-11 m^3 kg^-1 s^-2` but the uncertainty in the value is `0.000 31 \times 10^-11`. So, effectively we only know the value of `G` to four decimal places.

Calculating the mass `M` of a body, such as a planet or the Sun, is also difficult. To do so accurately would require knowledge of the body's volume and density which we can't know accurately.

Fortunately, in gravitational equations the quantities `G` and `M` are multiplied together to form the gravitational parameter `\mu=GM`.

Using data from measurements of the orbits of planets, moons and satellites it is possible to measure the value of the gravitational parameter for bodies with a high degree of accuracy. The values of the gravitational parameter for the Sun, Earth and other planets have been carefully measured.

So, if you want to calculate the orbital parameters of a satellite orbiting the Earth, you don't get the values for `G` and `M` and multiply them together. Instead you get the much more accurate gravitational parameter `\mu` for the Earth.