How Is the Orbital Period of a Chunk of Ice Calculated in Saturn-like Rings?

[sugarntwiligh]

Homework Statement

The rings of a Saturn-like planet are composed of chunks of ice that orbit the planet. The inner radius of the rings is 170,000 km. The mass of this planet is 5.7x10^26 kg.
Find the period of an orbiting chunk of ice at the inner radius.

Homework Equations

The force of gravity on the Saturn-like planet:
g=(G)(Mass of planet)/(radius squared)
Centripical velocity (can I do this using g from above as a?):
a=(squared V)/r
Then, use value of calculated v:
V=(2)(3.14)(r)/(T) to find T

The Attempt at a Solution

I was able to calculate g, and used the above equations:
g=1.3156m/ssq
g=a (centripical)
1.3156m=(squared v)/(1.7x10^8m)
v=2.236x10^8m/s
2.236x10^8m/s=(2)(3.14)(1.7x10^8m)/(T)
T=4.77s

The correct answer is 2x10^4s.
Christina

 

[sugarntwiligh]

Can someone please help me? Please I did really try to get it on my own but I just don't understand where to go after calculating the gravity. How do I relate gravity with period?

 

[sugarntwiligh]

Okay, so I did a little work on my own again and am still stuck. I derived the force by setting F=G*m1*m2/r^2 and plugging in the values:
G=6.67e-11
m1=6.14e26
m2=negligible
r=7.8e7 (in meters)

Then I set that answer equal to m*a, from F=ma, and used the m1 value from above to get a velocity of 8.167e-6m/s. Not the right answer.