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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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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