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# What is the Least Dense Exoplanet?

In order to calculate a crude, average density we need a mass and radius estimate or measurement for an exoplanet (and a spherical geometry is usually assumed). However, the majority of exoplanets do not have radius (or any kind of size) measurement. For example, on 3 August, 2012, out of 777 confirmed exoplanets, only 252 (just over 32%) had a radius measurements, and only 241 had both mass and radius measurements. Therefore, if we ask “What is the least dense exoplanet?” we must remember that we can only answer this question for a fraction of the confirmed exoplanets. Using the same example, on that date, the least dense exoplanet in the Extrasolar Planets Encylopedia catalog was WASP-17 b. This planet has about half of the mass of Jupiter contained within a size that is about twice that of Jupiter, so we could expect the density to be about a sixteenth of Jupiter. Using the exact numbers give a density of $0.0616$ times that of Jupiter, or about $0.0148$ times that of Earth. This translates into about $0.082 \ {\rm g \ cm}^{-3}$, compared to Earth's $5.513 \ {\rm g \ cm}^{-3}$. You will have to consult the original data in the table to figure out a reasonable estimate for the margin of error on the density, given the uncertainties on the mass and radius estimates (also see the important caveat at the end of this article).

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For a sphere, density is proportional to mass times radius cubed. If you would like to be able to find out yourself what is the least dense exoplanet found so far, here is how you do it. Go to the Extrasolar Planets Encylopedia catalog page. You will then have to download the data table using one of the options given just above the table header. Read the columns of data into an application or program that you are familiar with (for example, EXCEL). Then follow the instructions on the exoplanets density distribution page of this website.

A word of caution: the mass estimates for the majority of exoplanets are lower limits (i.e., minimum values only). This means that most density estimates will be lower limits as well. The radius measurements also have uncertainties and margins of error, which can be as large as a factor of 2 or more in some cases. You should always try to find out what measurement uncertainties are associated with any quoted number (not just for exoplanet masses and radii, but any measurement in general).

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