(i) State the universal law of gravitation, writing the expression for the magnitude of the force between two point masses.
(ii) For two given masses, the force of attraction is F when their centres are separated by a distance r. If the separation is reduced to 0.99r, show that the new force F′ is approximately 1.020F. Hence obtain the percentage change in the force produced by the 1 % decrease in separation.
(iii) Explain physically why even a very small percentage change in the distance between two bodies produces a comparatively larger percentage change in the gravitational force between them.