Nice question, Loki! In space, one of the hardest things to measure is size. We evolved with two eyes in the front of our head so that we could see distance and size. Having the two eyes slightly offset gives a different picture to each. Your brain puts the two pictures together to work out distance and size.
This doesn’t work so well for objects that are really far away, in space, because they are so far out that the image from both eyes is the same. So how do we measure the size of the sun or the moon?
One thing that we can do with objects in space is measure what we call their “angular distance”. That’s how far across they go in the sky. By coincidence, both the sun and the moon have about the same angular distance — about half of a degree. But they aren’t the same size — the sun is much much bigger! So angular distance is only part of the story.
If you know the angular distance across the sky AND how far away something is, then you can use it to measure the size of the sun. But how do you measure the distance to the sun?? Sounds hard, doesn’t it? Actually, it isn’t too difficult — you use relative measurements of the Earth, the sun, and other planets (like Venus) to work it out. The first guy who we know managed to do this was a chap called Aristarchus. He lived from 310 to 230 BC. So no really high tech was needed!
This is a short(ish) answer, but if you want to learn more, here are two good web pages that you could look at:
Hmm good question. We can easily measure the angle of the sun – that is if I point straight at the top of the sun, then point straight at the bottom, my finger has moved through an angle of about 1 degree. If we know the distance to the sun, we can then work out it’s size using Maths called trigonometry (which you might have heard of?)
To work out the distance is tricky. First, we know the how long it takes to go all the way round – one year. With some more clever working out we can use this to get the distance to the sun.
So for most things in the Solar system the strategy is the same – what angle is it from top to bottom? how far away is it? Answer these two questions and you have the size.