What is the Correct Way to Calculate the Period of Io?

[Sheneron]

[SOLVED] Universal Gravitation

Homework Statement

Jupiter's closest moon, Io has a mass of 8.90 x 10^22 kg. The mean radius of Jupiter is 6.99 x 10^7m, the mean distance from the center of Jupiter to the center of Io is 4.22 x 10^8m, and the mass of Jupiter is 1.90 x 10^27.

A) Determine the gravitational froce
B)Find the period of Io

The Attempt at a Solution

I solved for F_G and got = 6.334 x 10^22

Then I set up my equation like so:

F_G = \frac{m_{Io}4\pi^2(R)}{T^2}

My question is, for R in the above equation would I just use the distance between the center of masses, or the distance between the center of mass minus the radius of Jupiter? I am sure it is the center of masses, but why is Jupiter's radius in the problem then...

 

[Dick]

Probably to tempt you to make the mistake of NOT using the center to center distance. Resist that temptation.

 

[Sheneron]

Tricky indeed. Thanks