The mass of a planet can be determined by observing the time period of its satellite.
Let M be the mass of the planet and m be the mass of its satellite. For the satellite to be in the circular orbit, gravitational force is equal to centripetal force.
If r be the radius of the orbit of the satellite,
If T is the period of revolution of the satellite,
So, knowing the distance of the satellite from the planet and time period of revolution of the satellite, the mass of the planet can be determined.