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[SOLVED] Universal Gravitation
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
I solved for F_G and got = 6.334 x 10^22
Then I set up my equation like so:
[tex]F_G = \frac{m_{Io}4\pi^2(R)}{T^2}[/tex]
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...
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:
[tex]F_G = \frac{m_{Io}4\pi^2(R)}{T^2}[/tex]
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...