To calculate the density of a planet based on the period of a satellite in circular orbit, Kepler's Third Law is used, relating the orbital period with the planet's mass and radius, allowing us to solve for the planet's density.
The subject of this question is Physics, more specifically, it deals with orbital mechanics and gravitation. To find the density of a planet based on the orbital period of a satellite in a circular orbit, one can use Kepler's Third Law which relates the period of an orbit (T) to the mass and radius of the planet. Assuming uniform density and that the satellite orbits close to the planet's surface, we can use the formula T² = (4π²r³) / (G⋅M), where G is the gravitational constant, r is the radius of the orbit (which equals the radius of the planet), and M is the mass of the planet. With the satellite's orbital period known (T = 1.82 hours), we can solve for the radius of the orbit and consequently the planet's volume. We can then determine the planet's mass and calculate the density as mass divided by volume.