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# What is the Smallest Exoplanet?

If you would like to be able to find out yourself what is the smallest exoplanet found so far, here is how you do it. Go to the Extrasolar Planets Encylopedia catalog page and click on the button in the header of the table that says “All fields” and then click on the column called Radius. When you click on it, the data in the table should be sorted in order of numerical value in that column (i.e., the radius of the planets). An arrow just to the right of the word Radius tells you whether the numerical order is ascending or descending (the arrow will point upwards for an ascending order). If you click the column header again, the numerical ordering will flip from ascending to descending or vice versa.

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To find the smallest exoplanet you want the radii measurements to be ascending, with the smallest values appearing first. (Note that at the end of the sorted table the rows that appear first will have no entries in the radius column and these correspond to exoplanets for which the radius has not been measured.) The first non-blank entry in the sorted radius column corresponds to the smallest confirmed exoplanet. The number in the cell in the radius column is the radius in units of Jupiter's radius. You can convert to Earth radii by multiplying the number by 10.9733 (which is the radius of Jupiter in Earth radii). If you need the answer in kilometers (km), then multiply the number in the cell by 69911 (which is Jupiter's radius in km). From here you can convert to any other units by typing an appropriate statement in a Google search box. See also http://astrophysicsformulas.com for sources for solar system data.

For example, in August 2012, the smallest exoplanet was Kepler 42d. This planet has a radius of $0.56 \pm 0.16$ Earth radii, a minimum mass estimate of about 95% of Earth's mass, and an orbital period of about 1.86 days. What is rather disturbing is that the implied average minimum density is more than 5 times that of Earth's density. To physically achieve such a high density is not easy without invoking extreme physical conditions.

A word of caution: you should always try to find out what measurement uncertainties are associated with any quoted number (not just for exoplanet radii, but any measurement in general). In particular, exoplanet radii can be uncertain by substantial amounts, a factor of 2 not being uncommon. Since density is proportional to radius cubed, any error in the radius becomes cubed for the uncertainty in minimum density.

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