The acceleration due to gravity, g, is given by gm r2 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 δr = x. use a linear approximation to find an approximation to the resulting change in g, as a fraction of the original acceleration: your answer will be a function of x and r,)
(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 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 4.28 km; assume the radius of the earth is 6400 km)?