The last of the fundamental forces to evade unification, deep mysteries remain in our understanding of gravity. Get started at the beginning with the Newtonian description of gravity.

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.

Assume that the earth and the moon are both perfect spheres and the earth-moon distance is constant.

A neutron star has a mass equal to that of the sun, which is \(2.1 \times 10^{30}\text{ kg},\) but has a radius of only \(7\text{ km}.\) What is the approximate gravitational acceleration at the surface of the star?

**Assumptions and details**

- The universal gravitational constant is \(G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.\)

- The universal gravitational constant is \(G=6.67 \times 10^{-11} \text{ N }\cdot\text{m}^2\text{/kg}^2.\)
- \(R = 5.5\times10^6\) m.

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