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 (vshuttleabove)?

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.

Question 6 options:

We can't say without knowing the inital velocity of the shuttle.

The shuttle should increase its velocity.

The shuttle should decrease its velocity.

We can't say without knowing the inital velocity of the shuttle.

The shuttle should increase its velocity.

The shuttle should decrease its velocity.

Explanation / Answer

force will remain constant between earth and shuttle

given by =GMm/r^2=mv^2/r

where M is mass of earth,m is mass of shuttle,r is radius of orbit,v is velocity ,G is gravitational constant

solving it we get

GM/r=v^2

v^2*r=constant

assuming shuttle is away from earth than station

so to decrease r ,the velocity of shuttle should increase

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