Kinematics - Uniform Circular Motion

AI Thread Summary
The discussion focuses on calculating the period, T, of a satellite's orbit using gravitational and centripetal force equations. The user attempts to derive the formula but encounters issues with the angular velocity leading to confusion about the relationship between T and the radius, Rs. It is clarified that T should indeed be proportional to R^(3/2), aligning with Kepler's Third Law. The correct formula for T is confirmed as T = 2πRs/√(GMe). The conversation emphasizes the importance of understanding the relationship between gravitational force and orbital motion.
nahanksh
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Homework Statement


What is the period, T, of the satellite's orbit (G is the gravitational constant, 6.7 × 10-11 m3 kg-1 s-2) ?
(The picture is attached)http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/oldexams/exam1/sp08/fig18.gif


Homework Equations


a = w^2*r
w=2pi/period
F = -Gm1m2/(R^2)

The Attempt at a Solution



Using the force equation and "a=F/m",

I got a = GMe/Rs^2

And using a = w^2*Rs,

GMe/Rs^2 = w^2*Rs

Then, the angular velocity keeps having Rs^3 which doesn't seem to be right when compared to the answer...

What's wrong with my attempt?
Please help me out here...


The answer should be "T= 2*pi*Rs/sqrt(GMe)
 
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nahanksh said:
The answer should be "T= 2*pi*Rs/sqrt(GMe)


No, T should definitely be proportional to R3/2, that's where Kepler's Third Law comes from.
 
Oh, so you think what i was doing was right..?
 

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