How do astronomers work out how far away a star is? They use the star’s parallax and the brightness of the star.
The easiest way to work out the distance to a star is to use parallax, but this only works for stars that are less than 3000 light years away. Parallax is a way of working out the distance to something by viewing it from two viewpoints a known distance apart. You can witness parallax for yourself. Hold your hand out in front of you with one finger up. Close one eye and then the other. The background behind the finger will jump from side to side. This is parallax and it happens because your eyes are set apart and you are viewing the finger from a different angle. This can be used to work out the distance to a star.
To use parallax to work out the distance to a star you need to know the distance between the two viewing angles and you need a background to view the star against. Astronomers manage the first step by viewing the star they are trying to measure six months apart. The Earth orbits the sun once a year so if the star is viewed six months apart, the distance between the two angles is the distance from Earth to the sun multiplied by two. The second step is managed by using the background of far distant stars that don’t move as much when the viewing angle changes.
It works like this. You can work out the length of any side of a triangle if you already know the length of one side and if you know the angles. The astronomer takes a picture of star A in July and another picture of star A in December. We know the length of the bottom of the triangle because it is 2 AU. (An AU is an Astronomical Unit and is roughly the distance from the Earth to the sun – 150 million kilometers.) If we draw a line from the two viewing points to the place where the star appeared against the background, we can work out the angles of the triangles, which makes it possible to calculate the length of the sides of the triangles. Once you have that, you can work out the distance to the highest point of the triangle from the center of the base. It’s the square root of one long side squared, minus the short side squared and divided by four.
The distances are too far to work out the distance in km, so astronomers use parsecs. A parsec is a parallax second. When using parallax, the angle between the two viewing points is calculated in arcseconds. 1 degree of angle is 60 arcminutes. The distance to the stars astronomers are measuring is so great, that the angle becomes tiny and it is measured in arcseconds. 1 arcsecond is a 60th of an arcminute, so it is 0.000277778 degrees. Tiny. A star with an angle of 1arcsecond is 3.26 light years away, so 1 parsec is 3.6 light years. The further away a star is, the smaller the angle is. It is only possible to make out a difference of 0.01 arcseconds from Earth because of our atmosphere. Space telescopes can measure angles of 0.001 arcseconds, which is 1000 parsecs. That means the distance to stars up to 3261.563 can be calculated. The problem is, the Milky Way is 105,700 light years, or 32,408 parsecs across, which means there are trillions of stars we can’t work out the distance of. What happens in this case?
For stars too far away to use parallax, astronomers use the brightness of the star to calculate its distance. Astronomers have created a library of stars whose distance, size, and brightness are known. These stars are known as standard candles. There are two types of stars which are used as standard candles: cepheids, which are stars that brighten and dim periodically and predictably, and supernova. Because the distance and brightness of these standard candles is known, it can be used to calculate the distance to far distant stars. Astronomers can measure the brightness of a star, and by knowing how much dimmer it is than a standard candle, they know how far it is because stars dim predictably with distance. The apparent brightness of a light source is proportional to the square of its distance.
All of these calculations are obviously only approximations and there is no way of knowing exactly how far away a star is. There are too many variables that could affect it. However, having a rough idea helps. And, of course, because of the possibly infinite size of the universe, we can only measure the distance to the stars that we can see. There are probably infinitely more stars that are outside of our bubble of the universe and that are invisible to us. And this is what I learned today.
Sources
https://www.space.com/30417-parallax.html
http://www.astro.ex.ac.uk/people/hatchell/rinr/candles.pdf
https://www.gigacalculator.com/converters/convert-parsec-to-light-year.php
https://physics.stackexchange.com/questions/286309/how-is-the-parallax-angle-actually-measured
https://science.howstuffworks.com/question224.htm
https://lco.global/spacebook/distance/what-is-distance-modulus/
https://lco.global/spacebook/distance/cepheid-variable-stars-supernovae-and-distance-measurement/
https://lco.global/spacebook/distance/parallax-and-distance-measurement/
https://en.wikipedia.org/wiki/Minute_and_second_of_arc
https://en.wikipedia.org/wiki/Parallax
https://www.schoolsobservatory.org/learn/maths/distance/parallax