Derivation of the formula describing this curve is left as an exercise for the reader
Eeek - that sounds rather hard. Have you read A Fall of Moondust? There's a bit in that where a ship takes off from the moon and lands less than a hundred miles away, something that nobody had bothered to do before. Arthur C. Clarke, in his narratorial voice, says that the mathematicians would probably have taken great delight in working out the optimal trajectory using the calculus of variations, but of course the captain doesn't do that - he goes 100 miles straight up, thus qualifying for deep space rates, and then orbits to the right point and drops straight down :-)
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Eeek - that sounds rather hard. Have you read A Fall of Moondust? There's a bit in that where a ship takes off from the moon and lands less than a hundred miles away, something that nobody had bothered to do before. Arthur C. Clarke, in his narratorial voice, says that the mathematicians would probably have taken great delight in working out the optimal trajectory using the calculus of variations, but of course the captain doesn't do that - he goes 100 miles straight up, thus qualifying for deep space rates, and then orbits to the right point and drops straight down :-)