Classical Mechanics Level 2

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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