When we say a body in space is X light years away from us(say 5000), how do we know that it took 5000 years for this light to reach us?
And, how accurately can we measure this figure?
In: 5
So I’m going to assume that by “How old a light source is” you mean to ask “How old the *light that left the source is* because then the rest of your question makes sense.
I am nowhere close to an expert in astrophysics, but: To answer your first question I’ll consider the thing you said first.
>When we say a body in space is X light years away from us(say 5000)
So establishing this itself is the difficult part. The better we do this, the more accurately we can say how much time it took light to reach us. Basically our car goes at a fixed speed. If we want to know how long it takes to get from home to school we only need to measure the distance as well as we can.
In the case of heavenly bodies, astronomers use triangulation methods using data from multiple observation locations on Earth with the help of a cool trick called **parallax**.
I should also say, there are also relationships between how bright an object shines and how far away it must be – **apparent brightness** I think it is. Essentially if candle very light, very close if not, very far.
Once they’ve done the best they can with their fancy telescopes, they know the speed of light is just one number so they multiply that speed with the distance and boom, they get the amount of time the light has to have been traveling before it entered our eyes or telescopes here on Earth.
>And, how accurately can we measure this figure?
Well I’ll really have to defer to someone more informed on this one but my opinion is that at this point we are able to measure distances to far away objects very very well and of course the further away an object is, our abilities decrease. Someone better informed can probably comment further on the specifics.
With nearby stars we can measure their distance using parallax. Think of this as being like holding your thumb out and looking at it with one eye and then the other. Your thumb appears to move relative to a more distant background, and how much it moves depends on how close it is to you. With stars we can do this by using the different positions of earth as it orbits the sun. If doing this gives you a distance measure of 24 light years, then that means the light we see must be from 24 years ago, as that’s how long it takes light to travel that far.
Galaxies tend to be too far away for us to use parallax, as the apparent motion becomes too small to measure. So instead we look at “standard candles”. These are things that we can figure out how much light they are emitting and compare this to how much light we are receiving to work out how far away they must be.
When we start looking at things very far away, it gets more complicated. Because space between us and the object is expanding there are different things that we may refer to as the “distance”. If we naively used the same equation as previously to calculate distance based on the luminosity difference, we could end up very off. For example, an object with a “proper distance” of 30 Gly has a “luminosity distance” of about 335 Gly. We can measure the expansion of the universe though, so we can account for this and have a knowledge of how these different measurements relate to each other (see David Hogg’s notes on cosmological distance measures for a very brief overview). With this knowledge of how these things relate to each other, we can also figure out how long the light has been travelling. For our previous example of a proper distance of 30 Gly, the light has been travelling for about 13 billion years, and was emitted when the galaxy had a proper distance of about 3 Gly.
As for how accurately we can measure this, well that depends on what is being observed, what method is being used, what telescope is doing the observation, etc. In scientific literature, these numbers are normally presented with an associated error range, eg 24.72±0.03 light years.
There’s a thing called the “cosmic distance ladder”, which states the different ways you can measure the distance of astronomical objects depending on how far away they are.
For nearby stars, you use parallax. This is the change in the apparent location of an object depending on the angle you view it from. If you hold your finger up in front of your nose, and you close one eye and then the other, your finger will look like it’s moving left and right. Measure the angle between those two positions, do a bit of fairly simple trigonometry, and you can work out how far away your finger is.
You can do the same thing with stars. Measure the change in angle due to th Earth’s movement around the Sun, do some trigonometry, you get the distance. The angle is very small so it requires precise measurement, but it’s doable.
For objects further away than that, there’s something called a standard candle. This is an object where we know fairly well how bright it should be based on various properties. By comparing that known brightness to how bright it appears, we can work out how far away it is.
And one more method is redshift. Redshift is the doppler effect applied to light. For the sake of keeping this comment short I’ll assume you know what the Doppler effect is, you can look it up on this sub if you don’t. Point is, objects that are moving away from us look more red than they normally would, and the size of this shift depends on how fast they’re moving away from us.
But, thanks to the expansion of the universe, the velocity with which a distant object is moving away from us is directly proportional to its distance. The further away it is, the faster it is. So if you can measure the redshift you can work out the distance.
There are other methods, but these are the basics, and the easiest methods to understand.
Scientists use [Redshifting](https://en.wikipedia.org/wiki/Redshift) / [Blueshifting](https://en.wikipedia.org/wiki/Redshift#Blueshift) – It’s basically [“The Doppler Effect”](https://en.wikipedia.org/wiki/Doppler_effect) but for light.
When an ambulance drives past you, you hear the pitch of the sirens get higher as it gets closer, and they get lower pitched as they get farther away from you.
Light does the same thing, but it shifts in color – redshifting or blueshifting.
Scientists can tell how old light is based on what color it is – the longer it’s been travelling, the more it will be shifted in color.
When we look at the light from the big bang, the beginning of the universe, we can see that it is massively red-shifted, so much so that it is actually no longer in the visible spectrum, and is far into the infrared.
It’s like how you can tell how far away an ambulance is based on the sound of the siren. We can tell how far away the light is based on the shift. We know how far the light went, now we just have to figure out how long that would take – light moves at light speed so we can easily calculate a ballpark figure – which gets us the “Universe is ~14 billion years old” we’ve all gotten to know. [Which is still up for debate today.](https://www.usatoday.com/story/news/nation/2023/07/14/universe-may-older-than-thought-study-shows/70411343007/)
I suspect you might be slightly confused by light year being a unit of distance. You are basically asking how they know how far the light source is (same thing as how long it took the light to come but less clumsy).
There are many methods for things at different distances. These are collectively known as the [“cosmic distance ladder”](https://en.wikipedia.org/wiki/Cosmic_distance_ladder). For nearer objects we can use parallax caused by the movement of the Earth orbiting around the Sun. However, for further distances, we may use “standard candles”, one example being Cepheid variables which are stars whose brightness changes regularly and for which there is a known relationship between their luminosity and their period. By seeing how bright they are and checking that against how quickly their brightness changes, we can estimate the true distance of the galaxy they are in.
However, none of these methods are very precise and reliable.
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