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## Asteroid densities

### The CASt dataset

asteroid_dens.dat

Astronomical background

Asteroids are the billions of rocky bodies in the Asteroid Belt lying between the orbits of Mars and Jupiter.  Spectra and reflectivity show several types of surfaces. However, the internal structure of asteroids has been largely unknown.  A crucial clue is provided by the density; for example, an asteroid made of solid water ice will have density 1 g/cm3, solid rock will have densities around 3-5 g/cm3, and porous structures will have lower density.  To calculate asteroid densities one needs measurements of the radius (obtainable from astronomical information) and the mass (which cannot be obtained from their orbits or spectra).  Masses can only be measured by examining the orbit of some smaller body, a man-made probe or a natural companion asteroid.

To date, masses and radii -- and thus densities -- have been measured for only a handful of asteroids.  Each density has an estimated measurement error depending on the accuracy of the orbital information of the companion and other problems.  Data for 22 along with detailed discussion of asteroid composition and porosity are presented by Britt et al. (2002, online at http://homepage.mac.com/brother_guy/.Public/Asteroid%20Densities.pdf). Five additional measurements were recently reported (Behrend et al. 2006; Marchis et al. 2006). We have collected these into the dataset here.

Dataset

The dataset has 27 rows and the following columns:

1. Asteroid name
2. Density in units of g/cm3
3. Uncertainty of the density (s.d.)

Statistical exercises

• Establish the distribution of asteroid densities, with and without weighting by the measurement errors.  (Note that the sample is not random so it will not accurately reflect the true population distribution.)  Parametric modelling (mean, variance, kurtosis) and nonparametric density estimation.  Look for bimodality (e.g. solid rock vs. ice vs. porous interior).