What evidance is there to prove that the earth moves around the sun?

Answer 1

Let's put it this way... You can observe the apparent movement of the Sun, planets, moons, etc., and as a result consider the Earth to be fixed in space, and everything moving around the Earth; or use the approach that is more common nowadays, to claim that Earth rotates around its axis once every 23h 56m, that Earth revolves around the Sun once a year, etc.The second approach is simpler, mathematically, and is consistent with what are considered valid laws of physics, such as Newton's laws of motion, different conservation laws, and the fact that nothing can move faster than the speed of light. However, you may just as well have a "world view" in which Earth remains static. Such a world view might even be valid, in a sense - but it would be more complicated, mathematically.

Answer 2

Well, first of all, in real science, evidence is not used to prove theories.
Theories are offered to explain the evidence.

We see the planets in our sky. Their positions and motions have been precisely
observed, measured, tracked, and recorded, for more than 500 years now. We
KNOW how the planets move. We just have to explain what makes them move
that way. Many different explanations have been offered, most of them with
the Earth at the center and everything else revolving around the Earth. In order
to make those match what we see, they had to be ridiculously complicated.
Then Kepler came along, and after working with it for most of his life, came up with
a new, different explanation, which was really really simple: Planets revolve around
the sun, in elliptical orbits, and the line between the sun and each planet sweeps
over equal areas in equal times. That's IT, and it explains everything we see the
real planets doing in the sky. So although it can never be proved, there was a
great temptation to accept it as true, because it explains the evidence so beautifully.

Then, roughly 100 years after Kepler, Newton came along. One of the many many
many contributions to physics that Newton made was his law of universal gravity.
Again, gravity can never be proved, but it does a spectacular job of explaining the
evidence. And guess what ! When you take Newton's law of gravity, and massage
it with geometry and calculus, it predicts that the planets MUST move exactly as we
see them move, and exactly as Kepler described their motions. So we gain more and
more confidence that there must be something to these explanations, because they
all fit together so beautifully.

But hey ! They're "only theories". They can never be proved, and if a better theory
comes along tomorrow ... one that more accurately explains what we see ... then
Newton's and Kepler's theories will be dumped, and the new one adopted. That's
how real science works.