Stellar Parallax: An Astronomical Ruler

Stellar Parallax: An Astronomical Ruler

Image Credit: Gaia UK - https://gaia.ac.uk/science/parallax

Stellar parallax is an idea that has been around for thousands of years. To understand what it actually describes, we must first understand the word parallax. Parallax is the idea of an apparent shift in position of an object relative to surrounding objects based on the location of the moving observer. An example of this is a close road sign seen while driving as compared to the trees in the distance. The sign appears to move across the trees, despite the fact that its position remains constant. 

Now how can we use this phenomenon to our advantage? Clearly the intrinsic property that drives parallax is distance. Thus, when we see an object "shift" relative to another, we can conclude that the object that shifted is the closer one. This is the idea that the Greeks had when they considered stellar parallax. Stellar parallax is just what is sounds like, parallax of the stars. These Ancient Greek astronomers were considering the question of the center of the universe, and thought that if there Earth were moving around the Sun, they should observe some amount of stellar parallax. Of course, they were right about this theory, but ultimately were unable to make any observations of stellar parallax and ended up throwing away the heliocentric model and settled on the geocentric model.

Since then, our ability to observe far-away objects has obviously seen massive improvements. Thus, we have actually been able to record instances of stellar parallax, however small. The first measurement of such was taken in 1838 by Friedrich Bessel [1]. Clearly, it took quite awhile for stellar parallax to actually be proven through observation, but we knew that it should exist once we accepted Copernicus' heliocentric model. 

Stellar parallax made a large contribution to understanding the relative positions of stars in our galaxy. Modern technology has also made taking parallax measurements far easier and more accurate. The Hipparcos satellite (meant to represent "high precision parallax collecting satellite", also an homage to the Greek astronomer Hipparchus) has been the primary source of parallax measurements in recent decades. Since its launch in 1989, it has published position data on close to four million stars. This has given us a much greater model of what our galaxy looks like. [2] Pictured below is the Hipparcos satellite. 

Image credit - Hipparcos Wikipedia - https://en.wikipedia.org/wiki/File:Hipparcos-testing-estec.jpg

To use parallax to calculate distance, we have a simple equation: d = 1/p where d is the distance to the star measured in parsecs, and p is the parallax angle measured in arcseconds. The quantity 'p' can be visualized better in the schematic below. 

Image Credit - Las Cumbras Observatory - https://lco.global/spacebook/parallax-and-distance-measurement/

To use this equation, there are a few things we must know beforehand; the distance from the earth to the sun (1 AU, known with high accuracy), and the distance to the 'fixed' stars that we measure parallax against. We approximate this distance to be infinite, since we observe no parallax shift from them. In reality, there is a parallax shift in these stars, just not one that we can observe with our technology. An important thing to note about this equation is that it makes use of the small angle approximation. This approximation says that sin(θ) ≈ θ. In this case, the small angle is the parallax angle. One can imagine that the angle made by something multiple lightyears away from us would be quite small. Thus, the approximation is valid and our equation works. 

Another example of parallax (unfortunately not stellar) that I personally identify with is found in sailing. An adage that many sailors are familiar with is the one of "making trees" on another boat. This phrase comes from the idea that, when you are sailing faster than another boat during a race, it often appears as through trees are emerging from the front of their sail. This is due to parallax - since the opposing boat is closer to you than the trees in the distance, it appears as though the boat is actually moving backwards, when in reality you are just moving faster than them. So, parallax proves to be a useful tool in other parts of life outside of astronomy. 

I found a video that showcased this idea starting at 14:50 and ending around 15:05. In this case, the observer boat was "making trees" (well, making buildings, really) on the boats it was filming. This is a short instance of making trees, so it does not quite do justice to how useful it really is. However, I can say with confidence that parallax has helped me determine important details about wind strength and positioning on various courses that I've sailed on. 

https://youtu.be/mXOPvQz-JtY?t=14m50s

References

[1] Zeilik, Michael A.; Gregory, Stephan A. (1998). Introductory Astronomy & Astrophysics (4th ed.). Saunders College Publishing. ISBN 0-03-006228-4..

[2] https://en.wikipedia.org/wiki/Hipparcos

[3] https://lco.global/spacebook/parallax-and-distance-measurement/