The acceleration due to gravity, [math], is given by [math] where [math] is the mass of the Earth, [math] is the distance from the center of the Earth, and [math] is the uniform gravitational constant.

(a) Suppose that we increase from our distance from the center of the Earth by a distance [math]. Use a linear approximation to find an approximation to the resulting change in [math], as a fraction of the original acceleration:
[math] [math]
(Your answer will be a function of [math] and [math].)

(b) Is this change positive or negative?
[math] is
(Think about what this tells you about the acceleration due to gravity.)

(c) What is the percentage change in [math] 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 =