There is a mistake in the beginning of the hint ... the first expression for velocity v(y) is inverted.
I will fix that and clean it up a bit in the next hour. The proper expression for velocity is
v(y) = (const)*sqrt[y/(R+y)]
where "const" involves G's, M's, and R's. Possibly even a 2.
Keep an eye out here for the revision soon.
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