Chapter 12, Problem 44PCE

Predict/Explain Suppose the Earth were to suddenly shrink to half its current diameter, with its mass remaining constant. (a) Would the escape speed of the Earth increase, decrease, or stay the same? (b) Choose the best explanation from among the following

1. I.                    Since the radius of the Earth would be smaller, the escape speed would also be smaller.
2. II.                  The Earth would have the same amount of mass, and hence its escape speed would be unchanged.
3. III.               The force of gravity would be much stronger on the surface of the compressed Earth, leading to a greater escape speed.