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It's within your reach too if you'll just use a little logical common
sense, and realize that Newton was not the genious he was made out to
be; he was mistaken about several things: Orbits are not elliptical;
not _Ptolemaic_ epicycles either, but are spiral whorling vortexes.
The rate of free fall is not 32'/sec^2; but 16'/sec^2; as Galileo had
already discovered.

Just wondering--do you know how to integrate x dx? (Or, in this case,
with more standard notation for variable, t dt?)

Or are you just like, oh... say... my physics professors who drop
factors of 2, 3, 1/2, pi, whatever, on the grounds that they are only
making an order-of-magnitude estimate? But, you know, they know the
_correct_ final answer, so that they can drop the _appropriate_
factors to make the final answer of the guess come out right.

Best wishes,

Andrew