ASTR 109 HOMEWORK #4 (Hamilton)
due Wednesday August 13

1. Craters in the Solar System.
Go to the Solar System Collisions program at a) Bits of rocky and icy debris continually strike the inner planets at high speeds. Launch your own rocky impactors at Mercury, Venus, Earth and Mars. Chooses sizes of 10cm, 1m, 10m, 100m and 1km and record what happens (shooting star, atmospheric explosion also called an airburst, or surface crater) for each planet. For craters, record the crater diameter as well. Make a table that summarizes all of your results.
b) For Venus, Earth, and Mars, work out the smallest rocky body that can penetrate the planet's atmospheric shield. Get the diameter to two significant figures (e.g. 9.1 not 9.08). Record the diameter of the impactor, the diameter of the crater that it creates, and how often this happens. (Note, we actually do see smaller craters on Venus, but these are from debris thrown up by the largest impacts.)
c) If Venus is 4.5 billion years old and all quantities remain unchanged over time (i. impact rate, ii. atmosphere of Venus, iii. surface of Venus), then roughly how many of these smallest craters should we see on its surface? We actually see far fewer than expected. How might you imagine changing each of the three factors to explain the observed number of craters on Venus?
d) Finally, evidence from the Moon shows that the flux of debris to the planets was larger in the past and a study of crater sizes on Venus shows that its atmosphere was probably never dramatically denser than it is today. This suggests that the surface of Venus has been altered somehow. Take the largest crater on Venus (Mead Crater, diameter 280km) and use the Collision Calculator to work out the size of the rocky impactor and how often such events occur. What age do you infer for the surface of Venus?

2. Planetary Atmospheres
A planetary atmosphere has a characteristic height at which the atmosphere pressure (and density) roughly halves. On Earth, this height is around 5 km, so 5km up there is only 1/2 as much atmosphere, 10km up there is only 25% as much, etc.
a) To experience the pressure in Mars' atmosphere (assume 128 times less than Earth), how high should we go in our atmosphere? Compare to the height of Mt. Everest.
b) Inside deep mineshafts, the atmospheric pressure is greater than at sea-level because of this effect. If we wished to experience the atmospheric pressure of Venus (assume 64 times that of Earth), how deep a hole would we need to dig into the Earth? Compare to the deepest borehole ever drilled (12.2 km by the Russians) and the thickness of continental crust (about 35 km)
c) Roughly how far up is the edge of space, if we define this as the point where the atmosphere is only one billionth (10-9) that of Earth's surface? Make the approximation 210 = 1024 ~ 1000 = 103.

3. Planetary Formation. (3-4 sentences each)
a) From the most likely scenario of Solar System formation discussed in class, do you expect rock and iron cores for Jupiter and Saturn? Why or why not?
b) Explain the leading theories for why Mercury has a large iron core and the Moon has almost no iron.
c) Explain the theory for why Jupiter is the most massive of all of the planets.

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