The requirement that a planet must orbit outside of its Roche limit gives a lower limit on the planets mean density. The minimum density depends almost entirely on the orbital period and is immune to systematic errors in the stellar properties. We co
nsider the implications of this density constraint for the newly-identified class of small planets with periods shorter than half a day. When the planets radius is known accurately, this lower limit to the density can be used to restrict the possible combinations of iron and rock within the planet. Applied to KOI 1843.03, with a radius of 0.6 Earth radii and the shortest known orbital period of 4.245 hr, the planets mean density must be greater than approximately 7 g/cm^3. By modeling the planetary interior subject to this constraint, we find the composition of the planet must be mostly iron, with at most a modest fraction of silicates (less than approximately 30% by mass).
