I studied that Galileo was punished by the church for teaching that the sun is stationary and the earth moves around it. His opponents held the view that earth is stationary and sun moves around it. The question i want to ask is if the absolute motion has no meaning,are the two viewpoints not equally correct or equally wrong? Thanks in advance for any help.
This is an interesting question. You say that "absolute motion has no meaning." Can you explain that a little more? Suppose that I am in a spacecraft. For simplicity imagine that I am far from any other object, so I can neglect gravity (I don't think this restriction is necessary, but it simplifies things.) I can certainly tell if I'm accelerating or not without looking outside of my spacecraft.
The two frames that you imagine are fixed to bodies in space. One is fixed to the earth, and the other is fixed to the sun. But measurements would show that both are accelerating, and one at a greater rate than the other. The observed motion of the other solar system bodies is certainly simpler in the frame fixed to the Sun, and by Occam's razor we might conclude that earth-orbiting-sun is the better explanation of the observed motion.
But there's another problem. The body-fixed frames are accelerating, so we can't apply Newton's laws. We have no theory that explains the motion, only observations.
The way out of the dilemma is to make all observations from an inertial frame. Now Newton's laws are valid, and we have a potential theory. And this theory tells us unequivocally that both the earth and the sun revolve around their center of mass (which is inside the sun). Neither is "stationary".
All this is a long way of saying that there is a sense in which absolute motion does have meaning, and that the two points of view are not on equal footing. And in fact, they are both incorrect.
Because the sun has more mass and a higher inertia, so the gravitational attraction between the two will impact the Earth's momentum more than the Sun's.
If we look at the two bodies in isolation and have no prior knowledge of the system the only thing that breaks the symmetry is mass. If gravity exerts an equal force of attraction between the two objects, the earth will experience a greater change in momentum because it has less mass and less inertia, in other words the earth changes it's movement to accommodate the sun more so than the other way around.
That being said, when the two bodies move by each other (motion can be relative in this case) if they're at that right distance/speed/trajectory, where gravity overcomes escape velocity and the orbital momentum between the objects is enough to keep them from falling into each other, it will always be the earth that changes it's momentum and orbits the sun, and since the sun is so much more massive we see the extreme that we do in that earth does nearly all the orbiting.
Here the important thing is the frame of reference. When we look from the earth frame, the sun is rotating around the earth.
When we look from sun frame, the earth is rotating around the sun.
When we look at them from outside of both frames, like when we are looking from the galaxy of sun system, then we come to know that the earth is rotating around the sun.
So both points of view are different. Galileo looked at it from outside of the two frames. The church looked at it in the earth frame.
That is a nice question.