# Mu (GM) for calculations

1. Oct 14, 2004

### kepler

Hi again,

I was able to solve the previous problems I had, with some study over the net and some books.
Now I have a different problem: I have a routine that uses Mu (GM) for calculations; for the planets, Mu = GaussK * GaussK * ( 1 + mass ), where GaussK is the Gaussian constant (0.01720209895) and mass is the mass of the planet divided by the mass of the sun ( for earth, mass = 1/328900.56, for example ).
Now, I want to use the same routine, but for the orbit of the moon around the earth. Wich value of Mu must I use to maintain the proportion and the functionality of the routine?

Kepler

Last edited: Oct 14, 2004
2. Oct 15, 2004

### Jenab

I don't do canonical units for anything except sun-relative orbits. For orbit simulations and transfer calculations in the Earth-moon system, I'd stay with MKS units. In fact, there's so much perturbing going on throughout most of this volume that I'd probably use rotating coordinates and include the centrifugal, coriolis and torquey force terms, as well as a time-dependent force vector for the solar perturbation. The rotating system would have a varying angular speed, in order to keep the Earth and moon on the X axis, hence the need for the torquey force term.

But if you confine yourself to low Earth orbits, your new Mu would be the gravitational constant (G) multiplied by the mass of Earth. As for your new GaussK, remember that the Gaussian constant for sun-relative orbits is equal to 2 pi / 365.256898326. It's a handy number for getting other planets' orbits scaled in comparison to Earth's orbit.

Jerry Abbott

Last edited: Oct 15, 2004