WSU Interiors of Rocky Planets Paper

Ref: NASA Space Science Data Center (NSSDC)

URL: http://nssdc.gsfc.nasa.gov/planetary/factsheet/index.html (Links to an external site.)

In this assignment we will assume that all metals (i.e., metallic refractory rock, like iron) have a density of 8000 kg/m3, and all non-metals (i.e., non-metallic refractory rock, like quartz) have a density of 3500 kg/m3.

We can use average densities to estimate the percentage composition of a planet’s interior.  Consider this example: if a planet is 50 percent metals and 50 percent non-metals, then its average density would be:

average density=density of metal×% metal+density of non-metal×% non-metal100

average density=8000×50+3500×50100

average density=5750 kg/m3

If a planet were 40 percent metals and 60 percent non-metals then its density would be:

average density=8000×40+3500×60100

average density=5300 kg/m3

In general, if a planet is f percent metals, then it is 100-f percent non-metals, and its average density would be:

average density=8000×f+3500×(100?f)100

In practice, planetary scientists measure average density and compute the percentage of metals and non-metals, i.e., solve for f.  Consider the following example:

The planet Mercury has a measured average density of 5427 kg/m3.  This density is in-between the densities of metallic rock and non-metallic rock.  Therefore Mercury is composed of a mixture of metallic rock and non-metallic rock.  Let f represent the percentage of metals.  Thus 100-f represents the percentage of non-metals.  We can form the equation for average density and compute the value of f.

5427=8000×f+3500×(100?f)100

f=42.82

Therefore, the planet Mercury is 42.82 percent metals and 57.18 percent non-metals.

Answer the following questions.

1. Compute the average density of a hypothetical planet whose composition is 65% metals and 35% non-metals.
2. Use the NASA Planetary Fact Sheets to obtain the average densities of Venus, Earth, and Mars.  Compute the percentage of metals and non-metals in each.  Present your reasoning and calculations by imitating the example paragraph above.
3. Discuss cause and effect: how did the clearing phase of planet formation lead to Mars having a lower percentage of metals than Venus and Earth?

Grading: [10] points for each of Q1, Q2, and Q3.  Calculations must be complete, including full algebra and units.  Paragraphs must be complete and correct. [30] points total.

attached below is appendix.