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.