How do you calculate the period of a satellite in orbit around a planet?

R = Center to center distance (the distance between the satellite and the planet, measured in meters)

T = The period of orbit (time it take to do one orbit)

G = Universal gravitational constant (6.67x10^-11)

M = Mass of planet

P = Pi (Sorry, couldn't type the pi symbol on my keyboard)

The formula is:

R^3/T^2 = G x M/4 x P^2

Rearrange to make T (Period) the subject:

T^2 = R^3 x 4 x P^2/G x M (make sure to square root it)

The formula is 'kepler's law of periods'

the formula should be right, just ignore me if it isn't

hope that helped : )

So you know the satellites orbit radius which is R

You also know the Mass M of the planet and gravitational constant

There are two forces acting on the Satellite

Gravitational force Fg=G*M*m/R2 (n2 means n squared)

and centrifugal force

Fc=m*R*w2

( w is the angular speed .unit rad/s this is related to normal speed as v=w*R)

These must be equal or the orbit would change

m*R*w2=G*M*m/R2

where

w2=G*M/R3

Lets say that the satellite makes a full circle around the earth in T seconds which is also the period.

In that time the satellite has travelled an angular distance of 2*pi (which in degrees would be 360 deg). So

w*T=2*pi

T=2*pi/w

put in w and you get

T=2*pi/(root(G*M/R3))

which is the formula you are looking for