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,

\dfrac{GMm}{r^2} = \dfrac{mv^2}{r}

M = \dfrac{v^2 r}{G}

If T is the period of revolution of the satellite,

v = \omega r = \dfrac{2 \pi r}{T}

Then,

M = \dfrac{4 \pi^2 r^2 r}{T^2 G} = \dfrac{4 \pi^2 r^3}{GT^2}

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.