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

(a) Suppose that we increase from our distance from the center of the Earth by a distance . Use a linear approximation to find an approximation to the resulting change in , as a fraction of the original acceleration:

(Your answer will be a function of and .)

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

(c) What is the percentage change in 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 =

You can earn partial credit on this problem.