1. The problem statement, all variables and given/known data Both Newton's gravitational law and Coulomb's law are inverse-square laws: The force of attraction between the sun (S) and Earth(E) has (G*m_S*m_E)/r^2, whereas the force of attraction between an electron and a proton in a hydrogen atom is (e^2)/(4*pi*epsilon_0*r^2). Derive an expression for the equivalent of the Bohr radius for the gravitational case. What is the value of the quantum number of Earth's orbit? Would distance differences between individual quantum states in the solar system be observable? 2. Relevant equations F = (G*m_S*m_E)/r^2 F= (e^2)/(4*pi*epsilon_0*r^2) KE = 1/2 * m*v^2 PE = -e^2 / (4*pi*epsilon_0*r) U=(G*m_S*m_E)/r E_total = nhv 3. The attempt at a solution My attempt was to use the virial theorem, that total energy is equal to one of half of the potential energy. Therefore, since U=-(G*m_S*m_E)/r, then E_total = -(G*m_S*m_E)/2r. Then I equated E_total = -(G*m_S*m_E)/2r = nhv, and solved for v to get v = -(G*m_S*m_E)/(2rnh). I then used F = (G*m_S*m_E)/r^2 = (m*v^2) / r and substituted what I got for v, and solved for r. This yielded: r = (G*m_S*(m_E^2))/(4n^2*h^2). Is this the correct way to get the Bohr radius? I also solved for n to get n = sqrt((G*m_S*m_E^2)/(4*h^2*r)) which gave me n=3.533x10^63, which seems to be off by a factor of 10^11 from the actual answer. Any direction would be valuable, and I thank you in advance!