The acceleration due to gravity, $g,$ is constant at sea level on the Earth's surface. However, the acceleration decreases as an object moves away from Earth's surface due to the increase in distance from the center of Earth.

Derive an expression for the acceleration due to gravity $g_h$ at a distance $h$ above the surface of Earth.

Enter your expression in terms of the radius $R$ of Earth, $g,$ and $h.$

Suppose a $91\mathrm{.}75kg$ hiker has ascended to a height of $1841m$ above sea level in the process of climbing Mt$.$ Washington.

Use $g=9\mathrm{.}807\frac{m}{s^2}$ and $R=6\mathrm{.}371{10}^{6}m.$

By what percent $P$ has the hiker's weight changed from its value at sea level as a result of climbing to this elevation?

$P=$

$\%$

Enter your answer as a positive value.