Have a telescope that you don’t know what to do with? If you are able to observe Jupiter you can also observe the largest four moons, known as the Galilean moons. By making a note of the relative position of each moon (Io, Europa, Ganymede and Callisto) you can very easily calculate the mass of Jupiter using Kepler’s 3rd law. The moons closest to Jupiter will have shorter orbital periods than those further away.
This short video shows you that by creating a plot of the moons movement over a number of weeks you can get enough information to measure the mass of the Solar System’s largest planet.