Question

A satellite orbiting Earth at an orbital radius r has a velocity v. What would the velocity be if the satellite is moved to an orbital radius of 6r?
Responses

6v
6 v - no response given

16v
1 sixth v - no response given

6–√v
square root of 6 v - no response given

16√v

Answer 1

For a circular orbit v = sqrt(GM/r). At radius 6r,

v' = sqrt(GM/(6r)) = sqrt(1/6)·sqrt(GM/r) = v / sqrt(6) ≈ 0.408 v.

So the correct new speed is v/√6. (If you must pick from the given choices, choose the one that means 1/√6·v; none of the other listed values match.)