That the sun goes round the earth is not more or less right than the converse. It's a construction of the same system in different coordinates and quite valid.
Not if you take "the sun goes round the earth" to be an explanation for the sun's apparent movement in the sky.
The sun does go round the earth, and it's a perfect explanation/prediction of its movement in our sky. If you plot the point on Earth's surface above which the Sun is located, it goes round and round the planet (with seasonal perturbations).
The only problem with this theory (things go round the Earth) is that it doesn't explain the movement of bodies other than Sun and Moon. Retrograde motion leads you to epicycles, which are hard - you never have quite enough of them. That's why "things go round the Sun" is much better, at lest until you discover extrasolar objects aren't immobile.
But as far as the Sun-Earth system is concerned, both theories are equally valid.
This is an excerpt from an article George Orwell wrote in 1946. I will let the text speak for itself.