Consider two solid, uniform spherical planets A and B that rotate slowly so that their rotation can be neglected. Planet A has mass MA and radius RA. Planet B has twice the mass of planet A but also twice its radius.
Answer the following:
a. (i) State Newton’s law of universal gravitation.
b. (ii) Starting from the law stated in part (i), show how the magnitude of the acceleration due to gravity g at the surface of a spherical planet depends on its mass and radius.
c. (iii) Using the result of part (ii), obtain the ratio gAgB for the two planets described above and give a brief qualitative explanation of the numerical value you obtain.