Problem set 4 for ASTR 221: Stars and Planets
Due Wednesday Oct 16 at 5pm.
1. Scale heights of planetary atmospheres.
Kutner problems P25.1, P25.6, P25.10
Kutner problems P23.8, P23.9
Kutner Problems P24.4, P24.8
Roche Limit Problem (from Prof Mihos)
In notes we saw that the different planetary atmospheres, despite huge variations in atmospheric composition and planetary properties, are fairly similar. By calculating the relative scale heights of the atmospheres of Venus, Earth and Jupiter, explain why this is the case, and why the Earth's atmosphere has the lowest scale height of the three.
In class we calculated
the Roche limit, which showed how close a moon could get to its
parent planet before it will be tidally disrupted.
Saturn's
moons are mostly icy bodies, with densities of about 1.2
g/cm3. Calculate the Roche limit for these moons. Compare this to
the size of Saturn's rings, most of which lie within 120,000 km from
the planet's center. Noting that all of Saturn's moons lie outside
of 130,000 km from the planet' center, what does this suggest as one
possible formation mechanism for Saturn's rings?
Calculate the
Roche limit for the Moon. Is it in any danger of being disrupted any
time soon?