Consider the earth–sun system as a gravitational analog to the hydrogen atom.
(a) What is the potential energy function (replacing Equation 4.52)? (Let m_E be the mass of the earth, and M the mass of the sun.)
(b) What is the “Bohr radius,” α_g, for this system? Work out the actual number.
(c) Write down the gravitational “Bohr formula,” and, by equating E_n to the classical energy of a planet in a circular orbit of radius r₀, show that From this, estimate the quantum number n of the earth.

(d) Suppose the earth made a transition to the next lower level (n-1). How much energy (in Joules) would be released? What would the wavelength of the emitted photon (or, more likely, graviton) be? (Express your answer in light years—is the remarkable a coincidence?)

Equation 4.52

Transcribed Image Text:

n = √ro/ag.