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
, 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.
| 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.