Why is the Sun so round?

[NOTE: When I originally wrote this, I made a mistake - I said the Sun was 30 arcseconds across, when it's actually 30 arcminutes. For some reason, that number got stuck in my brain, and the math I did was based on the incorrect number! I have corrected the math in the text below. Usually I keep the original mistake in an article (striking through the text) along with the correction - that's my way of admitting mistakes. But given that this is math, I was afraid that might look a bit confusing, so instead I'll note my brain hiccup here, and keep the math clean by simply fixing it. However, this does change the analogy I used in the text comparing the Sun to a basketball, so in that case I struck through the text and added the correct analogy. I know, it sounds confusing, but it'll be clear when you read the article. My apologies for this!]