Question: How do scientists calculate the distance of stars from the earth?

Susan Cartwright answered on 16 Jun 2015:

The basic method is called parallax, and relies on the fact that the Earth orbits the Sun.

Hold your hand out in front of your face, and make a “thumbs up” sign. Close your left eye, and look at your thumb. Now open your left eye and close your right eye. You should find that the position of your thumb seems to shift relative to the background. That’s parallax, and it’s caused by the fact that your eyes are not in the same place.

Look at a star, and then look at it again six months later. If it’s a nearby star, it will shift relative to the background, and the shift lets you calculate the distance. The shift is VERY SMALL – the nearest star, alpha Centauri, moves about 1/2000 of a degree. This is why it took till 1838 for the first measurement to be made, even though people had been looking for it since about 200 BC.

This only works for quite nearby stars, but then you have a comparison sample that you can use for more distant stars – for example, suppose you find from the nearby stars that a star with such-and-such a spectrum emits X amount of energy per second, then you can look at any star with that spectrum, see how bright it appears to be, and use that to calculate its distance (the further away it is, the fainter it will appear).