1. The problem statement, all variables and given/known data Suppose an object of length “l” is located a distance “r” from a gravitating object of mass “M.” From physics you will learn that the gravitational acceleration is GM/r^2. Derive the difference in gravitational acceleration between distance “r” and distance “r+l” from the object. Show that as long as “l” is small compared to “r” (i.e., r >>l), the result is (2GM/r^3)l. Calculate this difference for the following two cases. What would happen to each person? a). A person of height l=170 cm located r=1000 km from a 1.5 MSun neutron star. b). The same person a distance 10^10 km (i.e., the width of a Solar System) from a 10^9 MSun black-hole as could be present in the nucleus of a typical galaxy. 2. Relevant equations GM/r^2 (2GM/r^3)l 3. The attempt at a solution I thought the difference would just be GM/(r+l)^2 - GM/r^2, and if l was small enough as compared to the other values the difference would be virtually 0. I don't know how the (2GM/r^3)l is derived and that's where I'm stuck. For the two people, would the given values be plugged into the regular gravitational acceleration equation or the one derived for the difference?