For example, how do they know that the Eistein Ring is “12 billion light-years” away? Why not 10 or 20? How do they arrive at that number?
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1) Parallax. Put your thumb in front of you and look at the screen. Close one eye and see where your thumb is compared to a point on your screen. Then do the same thing with the other eyes. You will see that your thumb move right and left as you switch eye. That’s because the angle between you eye, thumb and the screen change depending on which eye you use. You could calculate the distance to your thumb with some trigonometry by measuring the difference in angle and the distance between your two eyes. Well we can do the same thing with stars, but instead of your two eyes we use the position of the Earth on it’s orbit 6 month apart. Since we know this distance we just need to measure the difference of angle of a particular star at those two moment in time. This method only work for stats within 400 light years of Earth, because after that the difference in angle is so small that we can’t measure it with enough precision.
2) Brightness. When light propagate according to the inverse square law, which is just a fancy way to say that if the light travel twice as far, it will be 4 times less bright. So if we know the real brightness (called absolute magnitude) and we measure the brightness we see (called apparent magnitude) we can calculate the distance that light had to travel to look that way. The question is now, how do we know what is the real brightness of something. The answer is we don’t always know, but we do know for specific things and we call those standard candle. There is a lot of different Standard Candle and some are complicated, so I won’t talk about all of them.
Cepheid Variables are star that change in luminosity over some period of time (days to months) and some people really smarter than me in the early 20th century discovered that there is a link between that period and the real brightness of a star. So by identifying the right type of variable abd measuring their period, we would be able to calculate their real brightness and compared that to what we actually see to calculate the distance.
Type 1a Supernovae are created when two stars are orbiting each other. If one of them is a white dwarf and they orbit close enough to each other, the gravity of the white dwarf might start to attract the hydrogen off the other star. The mass of the white dwarf will start to go up until it reach 1.44 Solar Mass. At this exact moment, the mass of the white dwarf will reach a critical mass for fusion and create a supernovae. These supernovae all have the same energy and the same brightness. So as long as you can identify that type of supernovae, we can calculate the distance.
Like I said, there is others type of Standard Candle that exist.
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