Chapter 2 — Distances
Introduction
I suppose this is kind of an Astrophysics topic? Well, I would say it is. Now distances seem kind of bland and boring but let me tell you they are absolutely crucial when it comes to understanding the cosmos.
“Being apart teaches us how to be together”
No, I’m not talking about that kind of distance, or wait maybe I am. Either way, when it comes to distances in space, it’s a bit weird. We don’t stick with the SI unit for length anymore. We don’t use meters, and probably for good reason as well.
Now things in space are far apart, the Moon is 384,400 km from Earth, the Sun is 149,000,000,000 m from Earth and the nearest star apart from the Sun — Proxima Centauri — is 40,208,000,000,000,000 m from Earth.
We ourselves cannot comprehend this number and this might make sense to you in our next post but for now let’s just roll with it. We use different units because frankly SI units result in really large numbers.
The distance from the Earth to the Sun is 1.49 x 10¹¹ m and the distance from the Earth to Proxima Centauri is 4.0208 x 10¹⁶ m. Notice how we often have a lot of zeroes at the end, to prevent this, we have created three new units.
The Astronomical Unit
The Astronomical Unit is a measure of distance that is mainly used when we talk about the solar system.
It is defined as the average distance between the Earth and the Sun. Why can’t we take the actual distance? The reason is because the Earth has an elliptical orbit around the Sun.
That means at certain points of the year, the Earth is closer to the Sun and at certain points it is further. So we have to take the average.
1 AU = 1.496 x 10⁸ m.
The Light Year
If there was an Olympics for the most confusing unit, this would win the gold medal.
“To Infinity and Beyond”
Buzz Lightyear
Now the light year is confusing solely because of its name. It sounds like a unit of time, however it is a unit of length.
The light year is defined as the distance light travels in one year. Now with the speed of light being 3.0 x 10⁸ m/s. You could use dimensional analysis (Check out the previous post), to calculate how many meters there are in one light year. Don’t worry I’ll calculate it for you
1 ly = 9.461 x 10¹⁵ m. This means that there are 9461000000000000 m in 1 lightyear, or 9461000000000 km. This number is super large. Remember the distance from the Earth to Proxima Centauri? Instead of writing that huge number, we can round it to about 4 lightyears. Way more convenient!
The Parsec
This is probably the most commonly used unit of distance in space. To get the definition of a parsec we have to use a bit of trigonometry. You could also define a parsec as:
1 pc = 3.27 ly
Remember this quote? It’s well… wrong. They used the parsec here as a measure of time when in fact it is a measure of distance. I can understand why they would mix it up though, astronomical distances and names do not go together.
Now how do we derive the parsec with trigonometry.
For sake of simplicity we are going to assume that the orbit between the Earth and the Sun is circular.
Forgive my horrible drawing please. This picture represents the Earth at six month intervals. d = 1 AU
Now we take another star like so
Let’s say the distance from the Sun to that star is D. Notice how we can create a triangle?
Now if we simplify this diagram we get the following triangle
A parsec is defined as the value of D when θ = 1". Hold on what does 1" even mean? This refers to one arcsecond. Is it a unit of time? Nope, it’s a unit for angles. Confusing right?
Now we can use a bit of trigonometry and solve for the value of D. You can check out my post on trigonometry if what I’m about to do looks like Greek and Latin. Well it might look like Greek… we’re using Greek letters after all.
Now if we solve for D we get
This is perfect as we know what the values on the right side of the equation are. Therefore by substitution we get
If we just take the numerator as 1, we get our answer in terms of AU. We get 206265 AU. Now to find the number of light years this is, we have to find the number of astronomical units in 1 light year. There are 63115 AU in 1 ly. So we get
We can cancel out the AUs and divide to get
Plugging this into a calculator and rounding to two decimal places we get 3.27. Thus there are 3.27 lightyears in 1 parsec.
Conclusion
I hope you enjoyed our official introduction into Astrophysics. Next we are going to be looking at the scale of the cosmos and how its size is actually incomprehensible. I hope you enjoyed!
Images can be found at:
- “Proxima Centauri.” Wikipedia, Wikimedia Foundation, 7 July 2021, en.wikipedia.org/wiki/Proxima_Centauri.
- “Earth’s Orbit.” Wikipedia, Wikimedia Foundation, 28 June 2021, en.wikipedia.org/wiki/Earth%27s_orbit.
- Starwars. “Episode 4 Its The Ship That Made The Kessel Run In Less Than 12 Parsecs GIF by Star Wars — Find & Share on GIPHY.” GIPHY, GIPHY, 17 Sept. 2019, giphy.com/gifs/starwars-movie-star-wars-xTiIzxt2LbvM1mi2nS.
