While looking through the Mt$.$ Palomar telescope, you discover a large planetary object orbited by a single moon. The moon orbits the planet every $9\mathrm{.}10$ hr with the centers of the two objects separated by a distance roughly $2\mathrm{.}25$ times the radius of the planet.

Fellow scientists speculate that the planet is made of mostly iron. In fact, the media has dubbed it the "Iron Planet" and NASA has even named it Planet Hephaestus after the Greek god of iron. But you have your doubts.

Assuming that the planet is spherical and the moon's orbit is circular, calculate the density $$ of planet Hephaestus.