The acceleration due to gravity, $g$, is given by $$g = \frac{G M}{r^2},$$ where $M$ is the mass of the Earth, $r$ is the distance from the center of the Earth, and $G$ is the uniform gravitational constant.

(a) Suppose that we increase from our distance from the center of the Earth by a distance $\Delta r = x$. Use a linear approximation to find an approximation to the resulting change in $g$, as a fraction of the original acceleration:
$\Delta g \approx$ $g \times$
(Your answer will be a function of $x$ and $r$.)

(b) Is this change positive or negative?
$\Delta g$ is ? positive negative
(Think about what this tells you about the acceleration due to gravity.)

(c) What is the percentage change in $g$ when moving from sea level to the top of Mount Elbert (a mountain over 14,000 feet tall in Colorado; in km, its height is 4.36 km; assume the radius of the Earth is 6400 km)?
percent change =