A space shuttle is 200 m below the International Space Station. Both are in circ

Question

A space shuttle is 200 m below the International Space Station. Both are in circular orbits around the Earth. The crew of the shuttle would like be in the same orbit at the station. Should they increase or decrease their their orbital velocity (vshuttle above)? This question is not asking about the velocity of the shuttle up or down, only the velocity tangential to its orbit. Also, assume that the acceleration due to gravity does not change between the orbit of the shuttle and the orbit of the space station.

Explanation / Answer

If M is mass of earth and m is mass of revolving object,
use:
Gravitational force = centrepetal force
G*M*m/R^2= m*V^2/R
V= sqrt (G*M/R)

So greater the value of R, less will be the velocity required
R is distance from centre of earth

SPace shuttle is closer to earth as it is 200m below space station
So, R for shuttle is less than R for space station

So, V shuttle will be more than velocity of space station

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