Physics centripetal acceleration/ mass

1. Sep 27, 2013

astru025

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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??

3. 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)
1.03E10

2. Sep 27, 2013

Delphi51

Looks pretty good! The first bit confuses me because you use v for velocity and also for period (usually T), but I agree with your velocity number. I also agree with the a = .69, but the units are m/s², not seconds. I don't quite see how you are getting the mass in the last part. It appears you forgot to square the velocity.

Astru, I would like to offer you a hot tip. Whenever you see the word "orbit" in a problem, immediately write down "centripetal force equals gravitational force" or Fc = Fg. Then replace the Fg with your big G formula and Fc with either the formula with v in it or the one with T in it. In this case, you are given the period, so use the one with the T and don't bother to calculate the velocity. (If you only have Fc = mv²/R, then replace the v with 2πR/T to get Fc = 4π²mR/T²)
You'll soon have an equation where you can cancel the mass of the moon and solve for the mass of the planet in terms of period and radius - only one calc instead of three so less chance for error! For me, the mass works out to roughly 10 to the 15th kg.

3. Sep 27, 2013

nasu

You forgot to square the speed, haven't you?

The parameters are pretty close to those of Jupiter's satellite Io. So I expect you'll get a mass close to Jupiter's mass. Order of magnitude 10^27 kg.

Last edited: Sep 27, 2013
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