In principle, and in the absence of electromagnetic or any other non-gravitational interactions, an electron and a proton should form a ?gravitational atom,? bound by the force of gravity. We know that the energy of the ground state of the ordinary hydrogen atom is given by eq. (14.4)

Show that the ground state energy of gravitationally bound ?hydrogen? is given by E_grav = ?1/2G²_Nm²_pm³_e/?² and evaluate this numerically.

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2 met 1 -13.6 eV, EBohr 2 ( 47 E0