# Homework Help: Exam review question about space shuttle orbits at differing radii

1. May 2, 2012

### npersons274

1. The problem statement, all variables and given/known data

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

2. Relevant equations

Force_centripetal=Force_gravity

v=(2piR)/T

T=period

3. 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.

2. May 2, 2012

### tiny-tim

welcome to pf!

hi npersons274! welcome to pf!

(try using the X2 and X2 buttons just above the Reply box )
hint: what is the equation balancing the centripetal acceleration with the gravitational acceleration?

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