You need the same corrections in a true heliocentric model as well, they are just smaller. The true leap in understanding comes when you realize that none of th

You need the same corrections in a true heliocentric model as well, they are just smaller. The true leap in understanding comes when you realize that none of the objects is special, none of them is the true center, they all follow the same rules. That's where the simplification of the theory happens.