Further ex 7.4.8:

8. The force of gravity exerted on Earth by the Moon is responsible for many phenomena that have a significant impact on biological systems, such as the level and frequency of high and low tides. This force is f(M, R) = 398600 M R2 where M is the mass of the Moon and R is its distance from Earth. Currently, M = 73480 x 1018 kg and R = 384400 km (on average), and these haven't changed much in several million years. But suppose an asteroid of mass 250 x 1018 kg collides with the Moon, causing its mass to increase by that amount and shifting the Moon's orbit so that it is 400 km closer to Earth! Using a linear approximation to estimate how much the Moon's gravitational pull on Earth will change