Using Density to Investigate the Solar System
Part 1
Table 3 of ‘The mean density of the Earth” (Hughes, 2006, p. 23 lists the mean density and the uncompressed density fore variety of objects in the solar system. In Figure 2 (Hughes, 2006), the uncompressed densities in Table 3 are plotted against their heliocentric distance (i.e., their average distance from the sun) in astronomical units.
Hughes (2006) plots the base-10 logarithm of the distances instead of the actual distances. Your first task is to re-plot the uncompressed densities using a linear distance scale. You may use software such as Microsoft Excel or matiab if you wish. Your plot should take up the majority of a standard 8. 5″ x 11″ page.
On your plot, do the following:
1. Use a linear scale for the x-axis that rang. from 0 AU to 4000. point)
2. Use a linear scale for the y-axis that rang. from 0 kg/ma.6000 kg/n0. (1 point)
3. Label the ax., including units, so that it is clear what you are plotting. (2 points)
4. Use three different symbols to plot the uncompressed densities: one for the terrestrial planets, one for the moon, and one for the asteroids and other moons listed in the table. Include a legend with your plot. (5 points)
5. Draw a vertical line to indicate the position of the asteroid belt Label the line or include it in your legend. (2 points)
B. Using the coned astronomical symbols, label the terrestrial planets and Pluto. (1 point)
7. After you have plotted the asteroids and moons, use the correct astronomical symbols to indicate on your plot which planets the moons orbit. Hint: The moons will cluster at distances that correspond to those in Table 2-1 (Ha.ann, 2005, p. 12). (2 paints)
8. Take a look et the plot and record your first impressions. What trends, if any, do you see in the date? (2 points)
Part 2
Use Hughes (2006) to answer the following questions.
1. What is the ,now line,’ and what is its significance? where was the snow line located? (3 points)
2. How does Hughes moo explain the density of the Moon? (1 paint)
3. How does Hughes (2006) explain the density of Mercury? What does he think the density should have been? (2 poi.)
4. Does Hughes (zoos) identify any trends in uncompressed density with distance from the sun? Explain. (3 points)
Part 3
The tends one does or does not see in uncompressed density data depend substantially on which data points one chooses to include. For example, Hughes (2006) only considers the uncompressed densities of Earth, Venus, and Mars when looking for trends in the uncompressed densities of the terrestrial planets. He discards Mercury, the moon, and the asteroids. Perhaps he does this based on his expectations about how the position of the snow line should affect the compositions of materials in the solar system.
1. Let us assume indeed that the asteroids are relevant in determining density trends. Inducting this assumption, fit a line to the data within 10 AU of the sun, while still leaving art Mercury and the moon. Draw your line so that it has approximately the same number of data points above Ras below R. According to your line, what would be the uncompressed density of a planet at Mercury’s position of 0.4 AU? (3 points)
2. Using the uncompressed density you’ve just found, calculate the percentage of iron making up the planet Use the densities listed in Hughes woo of 1000 kg/n0 for laboratory iron and 2700 kg/ma for crust rook. Show your work. (3 points)
3. Perform the calculation for the percentage of iron making up Mercury again, this time using the uncompressed density of Mercury. Show your work. How do the two values compare? (4 points)
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