Astronomers have recently discovered a new planet in a faraway solar system, with a radius of roughly 380 km. Spectroscopic results indicate that the atmosphere (whose height is much smaller than the planet's radius) is largely argon, making the discovery truly controversial. Experts have deduced that argon is unlikely to be generated from the planet itself, therefore it is assumed that the argon in the atmosphere was created at the inception of the planet and is completely contained by its gravitational attraction. However wide disagreement abounds about the composition of the planet. The surface of the planet is clearly composed of aluminum oxide but some astronomers claim that this aluminum oxide is only a thin crust and that the planet is mostly iron. Given that the atmospheric temperature is 512 C calculate the minimum density of the planet so that its atmosphere could contain argon atoms.