We all know Alpha Centauri is the closest star to Earth but how do we determine that? Read this article to find out how to measure the distance of the stars from the Earth.
Introduction
It is well-known that Alpha Centauri is the closest star to Earth outside our solar system.
However, what is less known is how this distance was measured. When one imagines
astronomers and physicists, they visualise blackboards full of complex symbols not for the
novice. With the right set of data though, calculating the distance of stars is a simple matter of
high school trigonometry.
So what is this seemingly ‘simple method’?
Stellar parallax is the method used for stars close by, within the radius of 100 parsecs (which in the grand scheme of the universe may not seem like much, but comprises over 60,000 stars!). Stellar refers to stars, while parallax is the apparent displacement of an object because of a change in the observer’s point of view.
Wait…Huh?
In more organic terms: place your thumb close to your face and look at it from only one eye and then the other. The change in position with respect to the background seems rather prominent. Now, place the thumb away from your face you would realise that with increasing distance this change in position becomes less noticeable or apparent.
Image credits: Alice Hopkinson, LCO
A similar phenomenon occurs while viewing stars: the ones close by seem to shift position relative to the distant ones as we orbit the sun.
Astronomers record the position of the star at an interval of 6 months when the Earth is on opposite ends of its orbit.
The intersection point of the two apparent positions is the actual location of the nearby star, and half the angular shift (in arcseconds, which is 1/3600 of a degree) is considered the parallax angle, effectively creating a right-angled triangle. It then becomes a matter of simple trigonometry to determine the star’s distance from the sun.
Assuming the parallax angle to be theta:
tan θ= distance between the sun and the Earth
distance between the sun and nearby star
Taking the distance between the sun and the Earth in Astronomical units (1AU)
The formulas make sense, but what’s up with the crazy units?
At a scale as large as the universe, it is rather impractical to utilise SI units to measure distance, speed or angles.
For stellar parallax, angles are measured in 1/3600 of a degree. Unlike the shift of your thumb, distances across the galaxy are so vast they cannot be recorded by the naked eye. Alpha Centauri itself only yields a 0.76-arcsecond parallax angle when measured.
On the other hand, distances are too big to measure in metres; thus the Astronomical Unit, roughly the distance between the sun and the Earth, is employed. It, of course, has the added advantage of making calculations easier, as the perpendicular (in the image above) becomes ‘1’.
The unit of the distance between the sun and the star however is now AU/arcsecond, which is essentially a parsec (or 3.26 lightyears). It displays why the parsec is such a widely used unit by astronomers.
Got it! But can I use the method for all the stars in the universe?
While this method is straightforward, it comes with its restrictions. It requires specialised equipment like filar micrometres and highly accurate telescopes, rendering it inaccessible to amateur astronomers. Stellar parallax is accurate upto a 100 parsecs, after which the parallax angle becomes too small to measure correctly.
Final thoughts
The method, overall, is a great way to begin the adventure of 3D mapping of stars across the galaxy before jumping into more complex techniques, provided you have the relevant data or the required equipment.
References:
“Parallax and Distance Measurement.” Lco.global, lco.global/spacebook/distance/parallax-and-distance-measurement/#:~:text=Astronomers%20use%20an%20effect%20called.
Rit.edu, 2013, spiff.rit.edu/classes/phys301/lectures/parallax/parallax.html.
“Lecture 6: How Far Is a Star?” Www.astronomy.ohio-State.edu, www.astronomy.ohio-state.edu/ryden.1/ast162_2/notes6.html#:~:text=p%20%3D%20parallax%2C%20measured%20in%20arcseconds. Accessed 10 May 2023.