Check out this great post on Slate from Phil Plait to learn how scientists measure black holes.
But how do you measure the mass of a black hole?
Isaac Newton helps us here. Objects near the black hole orbit it, and the speed at which they move (together with their distance from it) reveals the strength of the gravity of the black hole. That in turn—as Newton pointed out 400 years ago—depends on the mass doing the pulling.
It’s not that simple, of course! But it can be done, and has been done. A camera I worked on for Hubble, called STIS, was designed in part to be able to make these kinds of measurements.
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