ASTR 100 (McGaugh)
Homework #3 solutions

Chapter 3, Problem # 9

Chapter 5, Problem # 4

Chapter 6, Problem # 5

The larger the number of impact craters, the older the surface. When a surface shows relatively few craters, this means that the older craters must have been erased by geological processes which created a new surface on the planet - i.e. the surface is young.

From youngest surface to oldest surface: Earth, Venus, Mars, Mercury

Chapter 7, Problem #2

Hydrogen and helium were very abundant in the early Solar System, thus one would initially expect all planets to have a lot of hydrogen and helium in their atmospheres. However, since the Earth is much closer to the Sun than the giant planets, it is hotter. Thus the gases in its atmosphere have higher velocities than those in the atmospheres of the giant planets. Since hydrogen and helium are the two lightest gases, they have the highest velocities of all. Also, since the Earth is smaller than the giant planets, the escape velocity is smaller for gases in the Earth's atmosphere than for gases in the atmospheres of the giant planets. The Earth is hot enough and small enough that the high velocities of the hydrogen and helium particles in its atmosphere allowed them to escape into space. Thus much of the original hydrogen and helium was lost and so the Earth does not have a hydrogen and helium atmosphere today. The slower velocities of the hydrogen and helium particles in the atmospheres of the colder and larger giant planets were too small to allow much of these gases to escape, thus the giant planets have retained their hydrogen and helium atmospheres.