# Asteroid Belt Mass Distribution Analysis

## Introduction

The meteor explosion over Russia really interests me and I have been reading as much about it as I can. While reading about meteors and asteroids, I encountered the following statement.

The total mass of the asteroid belt is estimated to be 2.8×1021 to 3.2×1021 kilograms, which is just 4% of the mass of the Moon.

I like to fact check things I read on the web or in the news. Checking this statement is a nice application of simple data analysis in Excel. Let's do a quick fact check here.

## Background

The Wikipedia has a great article on the asteroid belt and I cannot improve on their article for basic information. What I need is data on all the known objects in the asteroid belt. It turns out that the folks at the Jet Propulsion Laboratory (JPL) have a great database of all the known asteroid belt objects. I will use that database to generate a list of all the known asteroid belt objects with a diameter greater than or equal to 1 km. I chose the 1 km lower bound to keep the amount of data small.

## Analysis

My analysis is approximate -- think of it as a Fermi problem-type analysis. My analysis approach is simple:

• Download a paper that contains asteroid densities and compute a weighted average density to use for my analysis -- see the Appendix of this post for my average density analysis analysis
• Download all the main belt objects with diameters (D) greater than or equal to 1 km from JPL website
• Determine the volume of each asteroid using the formula $latex M=\frac{4}{3}\cdot \pi \cdot {{\left( \frac{D}{2} \right)}^{2}}\cdot \rho$, where ρ is my estimate of the average density of an asteroid (2.46 gm/cm3)
• Put all the data into a table and sort them by mass
• Compute the percentage of mass that each asteroid represents in the asteroid belt

Table 1 shows the first 10 entries of my table. There are actually 2039 asteroids in my complete table. Understand that I only have a very approximate analysis here. If you want to see a list of the most massive 18 asteroids using the most accurate numbers known, see the Wikipedia. I have included the whole Excel file in the Appendix for this post.

Table 1: Top Ten Asteroids in Terms of Mass.
Name Diameter(km) Estimated Mass(1019 kg) Main Belt Mass(%)
Ceres 952.40 111.32 41.1%
Pallas 545.00 20.86 7.7%
Vesta 530.00 19.18 7.1%
Hygiea 407.12 8.70 3.2%
Davida (1903 LU) 326.06 4.47 1.6%
Interamnia (1910 KU) 316.62 4.09 1.5%
Europa 302.50 3.57 1.3%
Euphrosyne 255.90 2.16 0.8%
Eunomia 255.33 2.14 0.8%
Psyche 253.16 2.09 0.8%

When I added up all the masses in my list, I got a number slightly less than 4% of the mass of the Moon -- fact confirmed.

## Conclusion

I was a bit surprised that the asteroid belt contains so little material. Think about -- the total mass in the asteroid belt is less than 4% of the Moon's mass. That really is not very much.

## Appendix

I put my Excel file out here for the curious.

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