Celestia Forums

Ok so I'm doing some revisions to my solar system spreadsheet, and I need to find a better way for calculating the period for planets with elliptical orbits. Anyway, the equation I'm using currently is as follows:

P=sqrt(D^3)/(8.965E+11)

where D = distance in miles

Now this particular equation is supplanted for another equation which I use for the moons of planets, this equation is as follows:

P=1.4*(sqrt(((D/6378.14)^3)/M))

In this case the Period is in hours, D = the distance to the moon in Kilometers, and Mp = the mass of the Planet related to Earth (M = Mp/Me)

So, that being said, I'm thinking I might want to revise or update these equations to be a little more exact, especially in the first case as the equation takes into account little except the SemiMajorAxis (D) in miles.

Any suggestions? And do I need to necessarilly have a different equation when finding the period for a planet and a moon?

Why not use the standard equation relating period to orbital radius, for all your calculations?

P = sqrt[4 * pi^2 * a^3 / (G * {M+m})]

Where P is the period in seconds, a is the semimajor axis in metres, M is the primary mass in kilograms, m is the secondary mass in kilograms, and G is the universal gravitational constant, 6.67e-11 N.m^2.kg^-2.
Gathering constants, you could make the above:

P = sqrt[5.92e11 * a^3 / (M+m)]

Grant

looks good to me, I'll plug in that data now.

Cheers.