### Description

**Moons and planets and mass ratios**

In this exercise we will look at one statistic that purports to make a clear separation between major planets and minor planets. The solar system has 8 major planets. These planets are in one group because they resemble each other in a great many statistical ways, in spite of some obvious differences. One of those ways is the masses of their moons. Major planets are much, much more massive than their companion moons. Some minor planets have companion moons; Pluto is one. Pluto is NOT much more massive than its moons.

To compare a planet with its moons, we will divide the planet’s mass by its moon’s mass to form a ratio. Then we will compare these ratios with each other and see if there are any trends and/or outliers.

We collect data from the NASA Planetary Fact Sheets:

https://nssdc.gsfc.nasa.gov/planetary/planetfact.htmlLinks to an external site.

- Complete the table of masses below. The first few rows are completed for you so you can check your arithmetic and make sure you know how to perform the computations. We will restrict ourselves to only a few moons per planet, otherwise we will have a vast amount of data to compile.
- When you are done the first table, then count how many ratios are in each range (called a “bin”).
- Use the information from the second table to form a histogram (also called a bar chart): number of ratios in each bin (y-axis) versus range (x-axis). The ratios are spread over a large number range, so to compare them most easily we will compare factors of 10.
- Is Pluto an outlier on this histogram? How do you know it is an outlier?
- Are any of the major planets outliers? If not then this statistic is self-consistent. If so then this statistic is inconsistent. What do you think, is this statistic consistent? Why or why not?

Table 1:

**Planet-moonPlanet mass (kg)Moon mass (kg)Ratio planet/moon**Earth-Moon5.97e240.0735e2481.2Jupiter-Callisto1898e240.10759e2417600Jupiter-Europa1898e240.048e2439500Jupiter-Ganymede1898e240.14819e2412800Jupiter-IoSaturn-DioneSaturn-EnceladusSaturn-IapetusSaturn-MimasSaturn-RheaSaturn-TethysSaturn-TitanUranus-ArielUranus-MirandaUranus-OberonUranus-TitaniaUranus-UmbrielNeptune-NereidNeptune-ProteusNeptune-TritonPluto-Charon

Table 2:

**Range of ratioNumber of ratios**0 to less than 1010 to less than 100100 to less than 10001000 to less than 10 00010 000 to less than 100 000100 000 to less than 1 000 0001 000 000 to less than 10 000 00010 000 000 to less than 100 000 000100 000 000 to less than 1 000 000 000

Grading: Each question is worth 6 points. Total = 30 points. Passing grade = 18.