How are the masses of celestial bodies determined?
Newton's analysis of Kepler's laws lets you determine the ratios of the masses of everything in the solar system with quite high precision, but it doesn't let you determine the actual mass.  The actual masses were one of the large unsolved problems of physics for almost a century, until 1798 when Cavendish's work with a torsion balance (described by him as "weighing the world") determined the density of Earth, from which the masses of everything could be computed.