# ASTR 109 HOMEWORK #4 (Hamilton) Solutions

1. Solar System Collisions
• a) Lengths, if given, refer to Crater Diameters.  Impactor Diameter Mercury Venus Earth Mars 10cm 1.8m Shooting Star Shooting Star Shooting Star 1m 17.6m Shooting Star Shooting Star Airburst 10m 172m Shooting Star Airburst 162 m 100m 1.7km Shooting Star 1.3km 1.6km 1km 16.5km Airburst 12.5km 15.4km
• b)  Planet Impactor Diameter Crater Diameter Impact Rate Venus 6.6km 83.4km 24 million years Earth 65m 836m 370 years Mars 1.7m 28m 4.9 months
• c) (4.5 billion years) * (1 crater per 24 million years) = (4.5*109)/(2.4*106) = 188 craters. Since we see fewer craters of this size, i) perhaps the impact rate was much lower in the past, ii) perhaps Venus' atmosphere was much thicker in the past, or iii) perhaps craters have been erased by surface processes on Venus.
• d) A 22.5 rock impactor would create a 280km crater on Venus. Such an impact occurs about once every 460 million years. So since we see only one of these craters on Venus, the effective age of Venus' surface is about 500 million years. In addition, since craters on Venus are relatively pristine and undegraded, this argues against a slow erosional process and for a cataclysmic resurfacing of the planet about 500 million years ago. No one knows exactly what happened and why, but it must have been impressive!
2. Planetary Atmospheres.
• a) 128 = 27
So we reach Mars-like pressures 7*5km = 35km up in our atmosphere. Mt. Everest is about 10km high, so this is 3.5 times higher.
• b) 64 = 26
So we would reach Venus-like pressures in a hole that extends 6*5km = 30 km below Earth's surface. This is about two and a half times as deep as our deepest drilling hole, and reaches nearly to the mantle.
• c) A billion is 109
= 1000 * 1000 * 1000
= 210 * 210 * 210
= 230
It takes 30 doubling to reach from the edge of space to Earth's surface. 30 * 5km = 150km.
3. Planetary Formation.
• a) Since both Jupiter and Saturn both formed several Earth mass cores before they could capture gas, these cores had compositions of the solids in the Solar Nebula: ice, rock, and iron. The heavy rock and iron should still be at the center today.
• b) Mercury took a hit from a large protoplanet that stripped away its originally larger rocky mantle. The Moon formed in a similar impact on Earth - our satellite is made up of the stripped-away mantles of Earth and the impactor.
• c) Jupiter formed just beyond the "ice line" where it was cold enough that water vapor could freeze into solid ice. This meant that Jupiter's core of ice, rock, and ice grew much larger than the rock + iron terrestrial planets. Unlike the terrestrial planets, Jupiter's core became large enough to capture lots of Hydrogen and Helium gas from the Solar Nebula. Jupiter's core also grew faster than the cores of the more distant planets, and therefore it was able to accrete the most gas.

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