# Calculating distance to galaxies seen through a telescope

When we see a galaxy through a telescope, say the James Webb telescope, it is said we see a galaxy as much as about 10 billion light years away. But 10 billion years ago we were much closer (because the universe was less than 4 billion years old) and now we are much further apart because of the expansion of the universe.

How do we know what distance the light had to travel to get here? Ten billion years ago the Earth did not even exist. If we use the Hubble relationship to calculate distance, that would be based on the red shift 10 billion years ago. The Earth formed 5.3 billion years later because the Earth is about 4.7 billion years old.

• Space expansion can be modelled with the Friedmann equations. If we see a galaxy 10 billion light years away, then we can evolve the Friedmann equations backwards in time to deduce where it was 10 billion years ago (assuming peculiar velocity is negligible). Commented Dec 11, 2022 at 7:58
• @Allure - This looks like an answer to me? Commented Dec 11, 2022 at 8:22
• @Farcher I don't know the math well and am not confident in writing an answer, unfortunately. Commented Dec 11, 2022 at 8:31