Orbital KE of a satellite - need to know formula only.?

Question

What is the orbital KE of a satellite of mass 560 kg in circular orbit about a planet of mass 21 * 10 ^ 24 kg, orbiting at a distance of 47700 km from the center of the planet?
(G = 6.67 * 10 ^ -11 N m ^ 2 / kg ^ 2)

It also asked what would be the PE.

My question is pertaining to my formulas.
To determine the velocity I used
V = square root of ( G * M * m / radius )
KE = .5 * M * m * v ^2
PE = - G* M * m / R

M = mass of planet, (21 e 24 kg)
m = mass of satellite 560 kg
R = 47700 km

NET energy = - G * M * m / 2 r

Answer 1

Your formula for KE is incorrect. (One clue is that it does not have the correct units for energy--there's an extra "mass" in there). Likewise, your formula for "v" is incorrect for a similar reason.

To derive the formula for KE, consider this:

a = F/m = GM/r² [Newton's 2nd law]

a = v²/r [formula for acceleration in a circle]

So:

v²/r = GM/r²
v² = GM/r

Therefore:

KE = (1/2)mv²
= (1/2)m(GM/r)
= GMm/(2r)

So actually, you don't even need to know the velocity to determine the KE -- it cancels out of the equation.