Escape velocity/orbit velocity

Badger01

"Given a planet has mass M and radius R, find the speed it would have to be launched at. Compare this to the speed required to put the object in the circular orbit."

I understand the first half where E_p=E_k
i.e: GMm/r = 1/2 mv²
rearrange to find v

how ever, i'm unsure of what exactly the 'orbit velocity' is.
is the the value of v in centripetal force, F = mv²/r
is this the same as the speed needed to launch it in to orbit or what? i am rather stumped here..

gneill

The problem statement is a bit confusing. I suppose it could be asking you to compare the escape velocity for an object leaving the planet's surface (planet radius R) to the velocity of a hypothetical object orbiting the planet at the planet's surface. Obviously one would have to ignore the problem of terrain variations, such as mountains!

To answer your query, yes, the orbital velocity is the speed of the object along its orbital path. So it is indeed the 'v' in mv²/r.