Why was Galilei "right"?

Question

Considering that all frames are equivalent, isn't it up to the observer to say "The earth turns around the sun" or "The sun turns around the earth"? Isn't this more or less like arguing about which meridian should be considered the null-meridian, or whether time should be counted according to years before/after Jesus Christ or the conquest of Mecca?

Answer 1

All frames are not equivalent. All inertial frames of reference are equivalent.

Having said that, you don't really need to appeal to relativity to sort this one out. If you have two bodies revolving around each other due to gravity, usually one would say that both bodies are revolving around a common centre of mass. But in the case of the Earth-Sun system the Sun is so much more massive than the Earth, that the centre of mass of the combined system is inside the sun (you can verify this yourself using Newtonian gravity).

This means that effectively the Earth is revolving around the sun, and you can't really look at it any other way. But the centre of mass of the system is slightly off centre, and this causes the Sun to wobble just a tiny bit around it's axis.