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Measuring Galaxies and Black Holes

If you know how far away it is, and the angle that it subtends, you can tell its size. For example, if something is 100 meters away and it fills 10 milliradians, it's 100 * 0.01 = 1 meter across. (A milliradian is 1/1000 of a radian, and a radian is about 57 degrees.)

The size in your telescope is easy, and it's a simple optical calculation to figure out how large an angle it actually takes up. That is, so long as it's something that appears as an object, not just a point. So the method will work with a galaxy, but not a black hole.

The only part with uncertainty is how far away it is. The red shift of the light can tell you that. Everything in the universe is moving apart, and the farther away something is the faster it is moving, so the greater the red shift. This method has been calibrated in a number of ways, in particular by observing certain types of variable stars. So that part of the method is pretty solid, too.

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