Using the Parallax measurement to calculate the distance to a star.
For thousands of years people have looked up at the night sky in awe, presented before the countless little shining stars.
Even before we were able to understand the true stellar nature, we started cataloguing the stars and measuring their apparent characteristics like position, colour and apparent brightness.
The Greek astronomer Hipparchus was the first to create a consistent catalog of about 850 stars carefully measuring their position and brightness.
But how far away were those stars? Ftom the ancient Greeks, all the way until Kepler in the 16th century, it was an established belief that all the stars are fixed points in a sphere surrounding our solar system.
If this were true, then all the stars would be at the same distance from earth. However, careful observations in the 18th century showed that some stars can actually be seen moving compared to some others. The progressive improvement of the observing devices enabled the application of an old and well-known distance measurement method called the "parallax" measurement.
To make things simpler, let's try to understand why having two eyes makes it possible to estimate the distances of the objects that we see! Take any object in front of you and try to observe it two times, each time closing one of your eyes. You might also use your finger as the object to measure. You will find out that your object seems to move against the "static" background.
If you repeat the same experiment with an object that is farther away, you will see it moving slower and if you look at a mountain that is 10 kilometers away, it should appear almost static.
We can generalise this experiment by replacing each eye by a more generic "Viewpoint" as in the following image.
If we find a way to measure this "apparent" movement of the object against the background then we would be able to calculate the distance to the object itself using some basic trigonometry that will be described later.
We can also understand that the farther away the object, the smaller the parallax angle p.
If we can do this for every object, then why not do this for the stars as well ?
There is a slight problem though! Even the "near" stars that we are trying to track against the more distant stars (that will act as the fixed background in our measurement), are so far away,
that the parallax angles are tiny for our eyes to detect. What we need is a larger distance between the two viewpoints, so that the parallax angle will be easier to measure.
Then we thought about photographing the same "near" star from 2 anti-diametric points on earth. In this case we can simulate a human with a distance between his eyes the same as the diameter of the earth! This was also not enough however. The solution would be to photograph the star at two anti-diametric points of the earth's orbit around the sun. Indeed this is the largest distance between the viewpoints that we can achieve.
By measuring the parallax angle p and knowing the radius of the earth's orbit around the sun, one can easily calculate the distance to the star:
d = r / tan(p)
Using this technique Friedrich Bessel in 1838 was able to calculate the distance for the star 61 Cygni quite accurately. The technique is still used until today.