I just can’t comprehend how we can tell that something is 500 light years away. Or how we know that a galaxy is 100 light years wide.
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We see an object by observing the light that it emits. Distant stars emit visible light, which is why we can see them with telescopes.
Everything in the universe is moving. Have you ever noticed how if an ambulance is driving towards you and playing its siren, the pitch of the siren gets higher as it gets closer to you, and then lower as it drives away? That’s because of the Doppler Effect, because the ambulance is moving fast enough relative to the sound it’s emitting, that it is “catching up” to its sound waves, causing them to be closer together, which makes them sound like a higher pitch.
Moving celestial bodies experience the same thing. The light coming off of a distant star is a lower frequency than the light coming off of a close star, like the Sun. That means its spectrum has less blue light, and more red light – which is referred to as “Redshift.” Hubble’s Law tells us that the further away something is, the more redshift we’ll see. So we figure out something is 500 light years away by measuring the amount of redshift and then doing the math for what distance it must be away from the Earth.
Hold out your thumb against some distant background. Close one eye and note your thumb’s position, then repeat with the other eye closed. Note that your thumb’s position shifts. If you measured the angle it shifted, you could calculate the length of your arm.
Similarly with stars. Take a picture of a nearby-ish star, and six months later, take another. Measure the shift of the star relative to the background of much more distant stars. That’ll let you calculate the distance to the nearby star.
> The Hubble telescope WFC3 now has a precision of 20 to 40 microarcseconds, enabling reliable distance measurements up to 3,066 parsecs (10,000 ly) for a small number of stars.[10]
https://en.wikipedia.org/wiki/Stellar_parallax
> Or how we know that a galaxy is 100 light years wide.
That’s not much of a galaxy. The Milky Way is about 100,*000* light years wide, and a mere thousand thick.
There are various methods used in conjunction. This is called “[cosmic distance ladder](https://en.wikipedia.org/wiki/Cosmic_distance_ladder)”. As others have said, parallax is one of the methods, light redshift is another, but there are many more.
The main problem is to have a reliable method that is common enough to be widely used, but also for them to overlap, so we can count on others when the method becomes unreliable.
Geometry! As others have mentioned we can use stellar parallax to make measurements and use known distances to calculate unknown distances. Additionally we can also use other phenomenon such as Doppler effects to get information on the distance of stars.
Also worth keeping in mind, that when we measure anything there is some margin of error. As long as that margin of error is low enough not to effect the outcome of whatever we are using that measurement for, we generally don’t think about it. For example, when you use a ruler to measure something, that ruler isn’t going to give you an exact, down to the Planck length measure of your distance. But unless you are doing some very specific scientific work (that we probably can’t even do at this point if ever) then that margin of error doesn’t really matter. So when we say an object is 500 light years away, we probably aren’t getting that EXACTLY right, its probably not exactly 500 light years away. There is margin of error in there. How much depends on the measurement. But for most purposes its also not significant. Its doubtful you are trying to calculate the fuel necessary to travel there for example, so you probably don’t need to get the value right down to the last liter. But 500 vs 490 vs 510 is probably not a big deal for most purposes and unless you have some way of getting a more precise measure (and that will significantly affect the outcome of whatever you are doing) you build that margin of error into your calculations and live with it.
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