Problem: In analogy to the Bohr Theory of the hydrogen atom, develop a quantum theory of Earth satellites, obtaining expressions for the orbit radius (r) and the energy (E) in terms of the quantum number (n) and the other relevant parameters. A satellite of mass 1000 kg is in a circular orbit of radius 7000 km, to what value of n does this correspond? Equations and Constants: Bohr Model: E = -R*h/n^2 E = 1/2 * m * r^2 * ω*2 ω = v/r v^2 = G*M/r R = 1.0973 x 10^7 m^-1 h = 6.626x10^34 kg*m^2/s M = 5.972x10^24 kg G = 6.674x10^-11 m^3/(kg*s^2) Attempt: E = -R*h/n^2 1/2 * m * r^2 * ω*2 = -Rh/n^2 r^2 = -2*R*h/(n^2 * ω^2 * m) r^2 = -2*R*h*r^3/(n^2 * G* M * m) 1/r = -2*R*h/(n^2 * G* M * m) r = (n^2 * G* M * m) / (-2*R*h) Just by parsing the units I know I've taken a wrong turn. I've tried multiple times and I appear to be missing a velocity term somewhere with the (-2*R*h). I think I'm missing something simple, I just don't see it. Thanks.