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There is no special machine that measures that directly. Astronomers have to observe objects known to be close to the black hole (most black holes observed are part of a binary or multiple system, simply because those are easier to detect), and use one of the usual methods used in astronomy to calculate distances.
infrared
Astronomers can use their eyes to study the stars. They can also use various telescopes that either refract, reflect, and detect exotic formations.
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Space Telescopes Planets that are orbiting stars that are far away creating fluctuations in the light that we see coming from the star. Astronomers can observe those planets by measuring the fluctuations of that light.
i think because of pollution and lots of light
By using the habo space telescle to detect the object's velocity
Their presence indicates the existence of molecular hydrogen, which is abundant but hard to detect.
They detect the absorption lines consistent with hydrogen.
Because the astronomers can detect that a star is being whirled around in space, or space is being distorted.
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