Physics centripetal acceleration/ mass

[astru025]

Homework Statement

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.

Homework 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??

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

 

[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.

 

[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.