> From Earth, solar radius = 0.25 degrees. 233 solar radii in 1 radian.
I don't understand this. I think I understand that the sun would take up 0.5 degrees of the "view" (I don't have a good word for this) when looked at from Earth, so radius is 0.25 degrees. But how does the second statement follow? I get that a radian is about 57.3 degrees, so 57.3 / 0.25 = 230, but why why does 1 radian make sense to use here?
An arc that spans one radian of a circle's circumference has the same length as the radius.
So if you imagine a connected line of 233 suns across the sky, spanning 57.3 degrees, the actual length of that line would be the same as the distance from your eyes to the sun.
Solar radius = 700000km Mean distance of Earth from sun = 1AU = 1.5e8 km = 214.3 solar radii.
From Earth, solar radius = 0.25 degrees. 233 solar radii in 1 radian.