1. The problem statement, all variables and given/known data If the angular momentum of Earth in its motion around the Sun were quantized like a hydrogen electron, what would Earth's quantum number be? How much energy would be released in a transition to the next lowest level? Would that energy release be detectable? What would be the radius of that orbit? 2. Relevant equations L = mvr = nħ F = GMm/r2 = mv2/r En = -E0/n2 3. The attempt at a solution I found Earth's quantum number by solving mvr = nħ for n, with m = 5.972 x 1024 kg, r = 149.7 x 109 m and v = 29.78 x 103 m/s. n = 2.523 x 1074 The second part is what gets me. In order to express the energy of a energy level in terms of a planet, I used F = GMm/r2 = mv2/r and E = KE + PEg = mv2/2 - GMm/r to get: E = -GMm/2r I then plugged in v = (GM/r)1/2 to r = nħ/mv getting r = n2ħ2/m2GM And then plugged this into E getting: E = -G2M2m3/2n2ħ2 The energy of a transition would equal: En+1 - En = -E0/(n+1)2 + E0/n2 Which I could solve with a super huge/super small online calculator. I already assume that the energy will be super small and the orbit won't noticeably change. My issue is...what do I plug in for m? Or should I do it a completely different way? Please help!