Eli5: how do we know how old is a light source?

Question

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

Answer 1

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.