# Consider a small satellite moving in a circular orbit(radius) about a spherical planet(mass).Which expression gives this satellites orbital velocity?Multiple Choice: A) v=GM/r B) (GM/r)^1/2 C)...

Consider a small satellite moving in a circular orbit(radius) about a spherical planet(mass).Which expression gives this satellites orbital velocity?

Multiple Choice:

A) v=GM/r

B) (GM/r)^1/2

C) GM/r^2

D) (GM/r^2)^1/2

### 1 Answer | Add Yours

The gravitational acceleration between the satellite of mass m moving arround a spherical plannet of mass M and radius r is given by:

F = GMm/r^2, but this is also the centrepetal force due to the velocity v of the satellite which is mv^2/r

Therefore, mv^2/r = GMm/r^2 or

v = sqrt(GM/r) = (GM/r) ^(1/2).