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I present a simplified version of the problem I have been toying
with. Suppose we get rid of the sun and instead put the earth at the
end of a string (whose length equals the usual earth-sun distance)
and whirl it around so that it matches earth's usual orbital speed of
v_orbit = 29.8 km/s. Also suppose that the earth does not spin on its
axis.
Got it? Okay here's the question: With what speed (relative to the
earth) must you launch a stone so that it just escapes to infinity?