Consider the earth moon system quantum mechanically! Treat the earth and moon as point masses. Write down...

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Physics

Consider the earth moon system quantum mechanically! Treat theearth and moon as point masses.
Write down the potential energy function for the earth/moon.Compare it to the potential energy function for the hydrogenatom.
What is the â€œBohrâ€ radius for the earth/moon system?
Estimate the principle quantum number (n) of the earth/moonsystem.

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SolutionTwobody systems like the earthmoon system of celestialmechanics or the protonelectron hydrogen atom of quantummechanics can be analyzed more simply using reduced massIn this note both a classical and a quantum derivation will begiven The quantum derivation will need to anticipate someresults on multiparticle systemsIn twobody systems the two bodies move around their combinedcenter of gravity However in examples such as the onesmentioned one body is much more massive than the other In thatcase the center of gravity almost coincides with the heavybody earth or proton Therefore in a naive firstapproximation it may See Answer

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