Question: If M is the mass of the earth and G is a constant, the acceleration due to gravity, g, at a distance r from the center of the earth is given by
g = GM/r2
(a) Find dg/dr.
(b) What is the practical interpretation (in terms of acceleration) of dg/dr? Why would you expect it to be negative?
(c) You are told that M = 6·1024 and G = 6.67·10-20 where M is in kilograms and r in kilometers. What is the value of dg/dr at the surface of the earth (r = 6400 km)?
(d) What does this tell you about whether or not it is reasonable to assume g is constant near the surface of the earth?