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npersons274
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Homework Statement
The space shuttle makes 1 revolution around the Earth in 1.5 hours when it is in an orbit 200 km above the Earth’s surface. The radius of the Earth Re is 6.5 × 10^6m. If the shuttle moves to a new orbit such that it makes 1 revolution per day (24 hours), what is the radius of the new orbit?
(1) 6.2Re (2) 12Re (3) 24.8Re (4) 16Re (5) 0.38Re
Homework Equations
Force_centripetal=Force_gravity
v=(2piR)/T
T=period
The Attempt at a Solution
My professor said:
"Yes, the centripetal force is provided by gravity. The tangential velocity v=2piR/T where T is the period. Thus show that T is proportional to R^2 and solve. For orbit 2, R_2=R_1sqrt(T_2/T_1)"
...but I still can't understand what he's talking about. What does he mean that period T is proprtional to r^2? And what does any of this have to do with balancing the centripetal force with the force of gravity?
Thank you. This forum is the best.