How do we measure distance of a galaxy?

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We hear now and then that a new galaxy or star is discovered some “x” light years away. How do we measure this value?

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The red shift is measured. There’s a formula for distance derived from the amount that the light from the star has shifted to the red end of the visible light spectrum. This is known as the Hubble Constant. It is based on the assumption that the universe is constantly expanding and that the farther away an object is from earth the faster it’s moving away from us.

In astronomy we have many ways of measuring distances. Unfortunately, non of these methods are perfect. Each of them typically has a range of distances that they are ideally suited for measuring.

Parallax is one of the most important measurements, because it’s what’s called a direct measurement. When Earth moves around the Sun, it changes the apparent position of stars in the sky (hold out your thumb and close one eye, then switch to the other eye. Your thumb moves relative to the background). We can use this along with some basic trigonometry to measure the distance, but it only works with relatively close objects, otherwise the movement becomes too small. We can use this to measure distances in our galaxy, and to some nearby dwarf galaxies.

Another method of measuring distances is called “standard candles”. These are objects or events where it is possible to know exactly how bright the event is, not how bright it appears to us but how bright it would be if we were next to it. Once you know how bright these objects should be, and you measure how bright they appear to us, you can figure out how distant they must be. The problem is figuring out how bright they should be.

An example of a standard candle is a type of star called Cepheid variable. This star fluctuates in brightness on a regular period. The period of fluctuation is directly related to the intrinsic brightness of the star. All you need to do is calibrate this relation using empirical observations. To do this you need to find Cepheid variables close enough to measure their parallax, and then you can use this method with ones too far away for parallax.

Eventually these stars become too dim to measure, and so we use them to calibrate another type of standard candle called Type 1a supernovae. This is what happens when a white dwarf steals mass from another star until it explodes.

After all this, we can use the fact that the universe is expanding in a way such that the distance to a far object is equal to it’s recessional velocity times a constant (the Hubble constant). This can only be used for distant galaxies because otherwise the velocity is too small to be measured and the random velocity distribution causes too much noise. To do this though we need to first measure the Hubble constant, and so we do this using the Type 1a supernovae.

(Bonus information: there are other ways to measure the Hubble constant, one is using the cosmic microwave background. Unfortunately when we compare these two methods, they do not quite agree. This is known as the Hubble tension and is one of the major problems in modern astronomy).