Do the following two problems from chapter 9 (p. 268) of Moons and Planets. The first one requires thinking and reflection and writing a couple of sentences for each part. The second one requires a little arithmetic and then a sentence or two of explanation.

3. Compare surface rock types that you might expect on an imaginary, 5000-km diameter planet of bulk composition like the Earth given the following conditions:

(a) The planet had never melted.

(b) The planet had a magma ocean with very little convection or vigorous stirring.

(c) The planet had a magma ocean in which there had been vigorous convection and efficient differentiation of siliceous and basic minerals.

(d) The events in (c) had occurred but were followed by extensive volcanism that tapped magmas in the planet's upper mantle.

15. Suppose you were going to dig a 10-km-diameter hemispherical crater in such a way as to throw the material out of the hole (shovelful by shovelful or all at once) about 10 crater diameters upward into the air, allowing the material to disperse outside the rim. (a) Calculate the potential energy consumed in this operation. (b) Compare this figure with the kinetic energy indicated to be necessary to create a 10-km-diameter crater and comment on the similarity or difference.