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I was scrolling through the list of moons of Jupiter and I wondered how astronomers where able to determine the masses of those objects. When I tried to google it I meanly found results of people deriving the mass of Jupiter from the masses of its moons using Kepler's laws. So the mass of celestial bodies with satellite(s) can be estimated this way. But what about the rest? Or are they all derived from the trajectories of man-made satellites passing near them?

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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.

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Good answer. As for asteroids, they are estimated to be similar in composition to the one NEAR flew by. The course deviations in NEAR's path from Mathilde have yielded its mass. –  Jack May 19 at 14:11

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