A moon orbits a planet of unknown mass with a period of 1.8 days. If the radius of the moon's orbit is 420,000,000 meters, find the mass of the planet.
For the speed of the moon I got: v=2 x pie x r / v
2 x pie x 420000000 / v = 1.8 days or 155520 seconds since speed is m/s.
v= 16968.5 m/s.
For the centripetal acceleration of the moon I got this: a= v^2/ r
16968.5 ^2 / 420000000 = .69 s
Now for the mass of the planet I am not quite sure how to figure out. If I know the speed and centripetal acceleration for the moon how do I use this to get the mass of the planet orbiting the moon??
The Attempt at a Solution
My attempt but was un successful:
v^2= G (Me/r)
16968.5 m/s^2= 6.67E-11 ( Me/420000000)