Mean Orbital Separation Question

[hulkster1988]

So it was basic to figure out the masses and such, but I'm not exactly sure what the "orbital separation" really is? Can someone enlighten me? Here is the question for reference:

A moon with a mass one quarter that of its parent planet orbits that
planet with a period of 12 days. The mass of the planet is twice that of
Pluto. What is the mean orbital separation of the planet and its moon?

Thanks for any help.

 

[tony873004]

planet = 2Pluto
moon = .25 * 2Pluto = 0.5Pluto
total system mass = 2.5 Pluto

Google for Pluto's mass

Once you have it, you can algebraically re-write the Period formula P=2pi*sqrt(a³)/GM) to solve for a, the semi-major axis, which should equal to your orbital separation in a circular orbit, or your average orbital distance when averaged over longitude rather than time. There's a couple of calculators on this page: http://orbitsimulator.com/formulas/ that will do it for you. The 3rd one is the Period formula, and the 4th one is this formula re-written to solve for "a".

 

[hulkster1988]

Great, thanks a lot ...that link is very helpful