PROBLEM SET  #6

ASTR  1030

Due in Lecture on Friday December 1, 2006

Think each problem through, and present your logic.

1. Why do the craters cover a larger fraction of the surface area on the far side of the Moon?

2. What is a continent?  Which bodies of the inner solar system show continent-like features?

3. What is continental drift?  Which bodies of the inner solar system show evidence of ongoing continental drift?

The remaining four questions involve using the Stefan-Boltzman Law.  The temperature of a planet can be estimated by assuming that it absorbs radiation from the Sun at a rate epR²F, where e is the fraction of radiation absorbed (as opposed to reflected back into space), R is the radius of the planet, and F is the Flux from the Sun in ergs/cm²/s. F can be expressed as L/4pD², where L is the luminosity of the Sun and D is the distance from the Sun to the planet. The planet re-radiates the heat into space according to 4pR²sT⁴. 

4. Derive a formula for the temperature of a planet in terms of its distance from the Sun.

5. Earth currently has a temperature of 300K at the equator. When the solar system was younger the Sun was 20% lower luminosity. What would be the temperature? Would this freeze the oceans? (I'll do this one for you --  T=300 x fourth root of 0.8 )

6. If the Earth were to be enveloped in ice, then the absorption efficiency would drop to 0.3 from its current value of 0.7.  Would the Earth remain covered in ice?

7. Mars may, in the distant past, have been been tilted over with the pole pointing at the Sun during summer. In that case the area which re-radiates to space drops by a factor of 2.  If the temperature of Mars is now 225K, what would be its temperature tilted over?  Could this explain the presence of water on the surface?