Great question! The hardest thing about space science is convincing people because it is so hard to prove stuff ‘out there’ when we are stuck here.
I’d say, the cosmic microwave background.
Cosmic background radiation is explained as radiation left over from an early stage of the universe, just after the Big Bang. When the universe was young, before the formation of stars and planets, it was smaller, much hotter, and filled with a uniform glow from white-hot hydrogen. As the universe expanded, it grew cooler. When the universe cooled enough, stable atoms could form but the ‘glow’ remained as the CMB.
The largest observed redshift, corresponding to the greatest distance and furthest back in time, is that of the cosmic microwave background radiation; redshift is about z = 1089, and that tells us the Universe about 13.7 billion years ago, and that the CMB formed about 379,000 years after the Big Bang.
We can measure the light of the galaxies that we observe and the redshift (the lengthening of the waves of light) tells us how quickly the galaxies are moving away from us. We can also tell from standard types of stars how far away the galaxy is to start with. If you trace all the galaxies that we can see back to the beginning, it takes 14 billions years!
That is, really, only the start of the argument though, but it’s a good start.
A hard question Freddie. My defense would go like this – Edwin Hubble worked out that other Galaxies are moving away from us at an increasing rate. He found the further the galaxies were away from us, the faster they were moving. He then worked this relationship backwards, to ind out how long ago everything must have been at the same place – when all matter was at a certain spot (the big bang). I think that’s a pretty clever way of working it out! There are lots of assumptions though, and if we get one of them wrong, this number might be wrong too!
Hmmm. Are you having trouble convincing someone else, or yourself?
We can measure the stretching of the Universe through something called red shift (http://www.esa.int/esaSC/SEM8AAR1VED_index_0.html). We use the red shift to determine how long ago the light left an object. The most distant light that we can see is the Cosmic Microwave Background (CMB) and this has a red shift of over 1000, which corresponds to an age of 13.7 billion years. The CMB was create just a few hundred thousand years after the Big Bang.
I realise that this is not perhaps the answer you’re hoping for. It difficult to ‘prove’ some things without having to really learn about them. Can you prove that the Earth is round or that it orbits the Sun and not the other way around? It can be done, but its not as straightforward as it feels like it should be.