Edmund Hillary had it easy

Climbing to the top of Mount Everest is hard, but it's slightly easier than you might think as people weigh less as they climb to the top. Let \(W_E\) be a person's weight on top of Mount Everest and \(W_S\) be their weight at sea level. What is the value of \(1-W_E/W_S\)?

Details and assumptions

  • Assume the earth (other than Everest) is a sphere of mass \(6 \times 10^{24}~\mbox{kg}\) and radius \(6,370~\mbox{km}\).
  • The top of Mount Everest is \(8,848~\mbox{m}\) above the surface of the earth.
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