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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