  The requirement that a planet must orbit outside of its Roche limit gives a
lower limit on the planet's mean density. The minimum density depends almost
entirely on the orbital period and is immune to systematic errors in the
stellar properties. We consider the implications of this density constraint for
the newly-identified class of small planets with periods shorter than half a
day. When the planet's 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 planet's 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).
