# Motion of one body with reference to another

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.

• Are you, in effect, asking does the Sun orbit the Earth? Surely not. What absolute motion do you refer to. Sorry, but your question is unclear to me.
– user108787
Oct 6 '16 at 15:29
• no @countTo i m just asking that aren't these two situations equivalent. Oct 6 '16 at 15:31
• Possible duplicates: physics.stackexchange.com/q/10933/2451 , physics.stackexchange.com/q/25834/2451 and links therein. Oct 6 '16 at 18:37
• Actually he was really punished for telling the church how to interpret scripture. His first volume was endorsed by the church. Oct 15 '16 at 13:45

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.

• By saying that absolute motion has no meaning i tried to say that nothing is in state of absolute rest or in state of absolute motion. Oct 6 '16 at 15:49

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.

• Sorry for the d/v Yogi, I honestly don't think inertia is involved in this question.
– user108787
Oct 6 '16 at 16:34
• Care to elaborate? Oct 6 '16 at 17:06
• Sure, the OP asked The question i want to ask is if the absolute motion has no meaning,are the two viewpoints not equally correct or equally wrong. I would be more than happy to upvote, ( I really would), if you could expand your answer to explain how inertia helps answer the question asked.
– user108787
Oct 6 '16 at 17:13
• I think in context he was asking how we know the earth rotates around the sun not the other way around. 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 have 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. Oct 6 '16 at 17:34
• I reversed the vote and will be more careful in comments in future :) regards
– user108787
Oct 6 '16 at 18:40
1. Here the important thing is the frame of reference. When we look from the earth frame, the sun is rotating around the earth.

2. When we look from sun frame, the earth is rotating around the sun.

3. 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.