Does the Earth actually revolve around the Sun

 Quote by Manula While we are walking its the earth sliding down our feet.Not we are moving.
Yes, you can describe the world from your rest frame, where the Earth is moving under your feet.

 Quote by Manula like earth is made of small pieces which can move independtly
No, in any frame there will be constraints how the earth's pieces can move, based on how the rest moves. Note that in your rest frame the other people also move differently than in the Earth’s frame.
 This thread smells of apologetics for false ideas that were eradicated 350 years ago and I won't have it. The reason why people could get the idea that the planets and the sun move around the earth is due to poor measurements. A periodic linear motion in the sky can usually be approximated by some kind of circular function. People could have realized that something is wrong when they noticed that planets sometimes move backwards through the heavens. Once you measure in three dimensions it is irrevocable that the planets move around the sun. This has nothing to do with physics, but simply with the laws of geometry, and we have measured the planets positions with incredible precision. As you might have noticed sometimes we get a better understanding of the laws of physics. For example the earth's orbit is not perfectly round, but an ellipsis with one focal point in the sun, and the other one close to it. Newtonian mechanics is almost perfect and can explain all of this. The only noticeable error that was left is the fact that mercury's ellipsis rotates with a speed of one revolution per 225000 years. This is a shift of 29 kilometers per year -- barely noticeable on planetary scales, ten percent of this could not be accounted for. This hole was fixed when GRT was found by Einstein, and of the ten percent error is an error of 0.02% left. So this is about 4 meters per year -- this is the maximum margin of error. Probably less these days. It is inconceivable that any physicist in the future will find that a rotation of the sun around the earth will be a better description of the system.

 Quote by 0xDEADBEEF People could have realized that something is wrong when they noticed that planets sometimes move backwards through the heavens.
They did. And they developed complicated kinematic models to fit this observation.

 Quote by 0xDEADBEEF Once you measure in three dimensions it is irrevocable that the planets move around the sun.
In don't see how 2D vs 3D is relevant here.

 Quote by 0xDEADBEEF This has nothing to do with physics, but simply with the laws of geometry,
I don't see why pure geometry should care what circles around what.

 Quote by 0xDEADBEEF and we have measured the planets positions with incredible precision.
A position always needs a reference coordinate system. Pure geometry doesn’t tell you where to put it.

 Quote by 0xDEADBEEF Newtonian mechanics is almost perfect and can explain all of this.
But that is physics, not just geometry. Newtonian mechanics is simpler than the old models and can explain much more. Therefore we use it.

 Quote by Manula Has our experiments proved the existence of aether? No they haven't. Then can we simply arrive at a conclusion that aether is just theory but nothing in existence? No we can't. We haven't dissaproved the theory of aether yet. It may or may be not there.But we don't know for sure. Because our laws of physics doesn't permit us to find out.
i understand your thought process but its about the variables its not that we completely discard the idea of an aether its that there are more longstanding thoughts as to the counter if you could in practice or in mathematical equation prove that there is an aether then it would be accepted as is there are too many variables to prove that one exists if you want to prove something already beat down and "disproved" then you must have a fill to what all else see as variables

 Quote by pureinterest i understand your thought process but its about the variables its not that we completely discard the idea of an aether its that there are more longstanding thoughts as to the counter if you could in practice or in mathematical equation prove that there is an aether then it would be accepted as is there are too many variables to prove that one exists if you want to prove something already beat down and "disproved" then you must have a fill to what all else see as variables
Some periods and capitalization would be nice. From the forum rules:
 Pay reasonable attention to written English communication standards. This includes the use of proper grammatical structure, punctuation, capitalization, and spelling.
The common consensus was that there was an aether until the Michelson-Morley experiment disproved the that notion. The mathematics held that if there was an aether, and the aether was the medium of lights' motion, the Michelson-Morley experiment would produce certain results. It didn't and so all aether-based models of light propagation had to be discarded.

 Quote by A.T. In don't see how 2D vs 3D is relevant here.
People observed planets moving on more or less straight lines through the background of the stars. The distance wasn't known, so people could get the idea of planets rotating around the earth on their heavenly spheres. Today we know the whole trajectory and even relative distances to satellites so there is no doubt that we know the orbits.

 I don't see why pure geometry should care what circles around what.
I guess we agree on the orbits of the planets and how to express them in different coordinate systems. I would say that this is due to the geometric relationships they fulfil especially of the angles under which they can be observed from different parts of the earth or the solar system. Now we get into the definition of one thing rotating around another one.

 A position always needs a reference coordinate system. Pure geometry doesn’t tell you where to put it.
Of course we could look at Mars in a non inertial frame that is centred in the centre of the earth. Then it looks as if Mars is doing a funky dance like this: http://upload.wikimedia.org/wikipedi..._2003-2018.png We can also draw two circles on the ceiling of our room, spin around and -- while looking up -- claim that the two circles are spinning around each other. I would say that the common understanding of things spinning around one another is about what happens in inertial frames, an in those the sun hardly accelerates as compared to the planets.

 But that is physics, not just geometry. Newtonian mechanics is simpler than the old models and can explain much more. Therefore we use it.
I guess we agree there, and you were not really the target of my rant. While you wanted to encourage Manula to lose the idea of fixed coordinates and reference frames, I was afraid that by fueling the overly broad claim that in the future people might consider the sun to be moving around the earth, we'd encourage another apologist who'd go out and proclaim that holy book of choice$^\text{TM}$ is right and even physicists doubt that heliocentrism was a good idea. I have met too many of this type.
 to put it in the simplest possible terms then: no, the earth revolves around the sun and there is absolutely no way that the sun will revolve around the earth, given Newton's laws applying in their standard forms. That is because the earth is NOT an inertial frame while the Sun, for basically all applications and purposes, is.