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## Murphy's Mangled Math

17 Feb 2012, 06:53 UTC
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In his blog Stranded Resources Tom Murphy argues that space resources will likely remain beyond our reach. He concludes humanity should learn to live within its means and conserve our resources. This sound advice is the theme for most of his Do The Math blogs.But the math on which he builds his argument is wrong.To calculate delta V from earth to Mars he adds 3 quantities:Earth escape velocity (~11 km/s),Earth to Mars velocity (~6 km/s)Mars escape velocity (~5 km/s)Which totals ~22 km/s.But you donâ€™t simply add these three quantities. Break the Earth to Mars velocity into two parts. These parts form legs of two right triangles. The other legs being Earth escape velocity and Mars escape velocity. Add each hypotenuse for the actual delta V.So the total delta V is around 17 km/s, not 22 km/s.But wait. Murphy did generously round his 22 km/s to 20 km/s.And there is also a ~2 km/s gravity loss incurred during vertical ascent. Add this 2 km/s to 17 km/s and you get 19 km/s. Murphy isn't shy about mentioning gravity loss. But he doesn't include it in his calculations, giving the impression that he's being quite generous to the addled space cadets. Including ...