I need some clarification here. We know that the Earth rotates about it's own axis and also around the Sun. Now my questions are:

1. In the geocentric model of Ptolemy the Earth was at the center of a circle while the planets (and sun) moved along epicycles and the centers of those epicycles moved along the circle which had Earth at the center.
Copernicus viewed the motion of planets as though we were standing on the Sun; which made the planetary orbits much simple.
Now my question is, when we say that the Earth moves round the sun (and reject the Ptolemy model) do we do that for mare simplicity and convenience?

2. The Earth rotates on its own axis. This rotation is measured relative to some reference frame, right? Now which reference frame did we use to measure Earth's rotation speed?

3. Form a certain reference frame (for example one attached to earth) Earth is not rotating. But forces like Coriolis force as detected by a Foucault pendulum suggests that Earth must be rotating. Is Earth's rotation an absolute motion? I thought it is not. But please explain.

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1) At the time of Copernicus, actually Ptolemy's model more closely matched experimental data than Copernicus's model (due in large part to the idea that the planets were still in circular orbits). But through the careful observation of Tycho Brahe and the subsequent analysis by his apprentice Kepler, a more accurate model was derived, the Keplarian model of the solar system wherein the planets orbit the Sun in elliptical orbits with the Sun at one focus. In addition, Galileo found aspects of the solar system in contradiction with Ptolemy's model. Namely, he found the phases of Venus, and the Galilean moons of Jupiter Io, Europa, Ganymede, and Callisto which orbited Jupiter and not the Earth.

So, we can reject the Ptolemaic model on grounds of experimental accuracy.

2) Rotation is an absolute measure. Practically speaking, we can measure the Earth's rotation with respect to the distance stars. Stars very far away are roughly fixed in the sky, because any proper motion becomes a tiny angular motion due to the distance. We can use these fixed stars to figure out Earth's rotation as well as the Precession and Nutation of the Earth's axis.

3) As above, Earth's rotation is an absolute motion. Why do you think it's not?

Rotation is an absolute measure... Earth's rotation is an absolute motion. Why do you think it's not?

Well I thought we measure rotation with respect to a reference frame. So rotation of an object should seem different from different frames.
Would you please explain why we consider rotation to be absolute? Doesn't it depend on reference frame of the observer?

Rotation is an absolute measure. Practically speaking, we can measure the Earth's rotation with respect to the distance stars.

So should we assume that anything moving with respect to distant stars is in absolute motion?

As you mentioned in your first post, a rotating frame has fictitious forces present, the Coriolis force, the centrifugal force, and for non-uniform rotation, the Euler force. The presence of these forces tell us that we are in a rotating frame rather than a freely floating frame. Therefore, we can always tell if we are rotating or not without reference to external objects, and rotation is said to be absolute.

2. The Earth rotates on its own axis. This rotation is measured relative to some reference frame, right? Now which reference frame did we use to measure Earth's rotation speed?

2. The Earth rotates on its own axis. This rotation is measured relative to some reference frame, right? Now which reference frame did we use to measure Earth's rotation speed?

One can use the sun as a measure of rotation and obtain solar time. This would be in keeping with measuring the shadow of a stick coming to the same location each day.
One can use the distant stars and obtain sidereal time. One measure the angle between a star and some reference, say the Earth's horizon, to be the same from one day to the next.
http://en.wikipedia.org/wiki/Sidereal_time

Therefore, we can always tell if we are rotating or not without reference to external objects, and rotation is said to be absolute.

Thank you.
So if I am in an empty space with nothing to compare with then just by proper experimentation I can tell if I am rotating or not.
But then as I am rotating, I can imagine a reference frame which is not rotating, right? I can call this reference frame the absolute frame which never rotates at all. (?)
So is there a frame of reference throughout the universe which is absolutely non-rotating?

If you are just freely floating out in space, and you detect no centrifugal, Coriolis, or Euler forces, then your frame is non-rotating.

For such purposes, a gyroscope is perhaps the most practical: http://en.wikipedia.org/wiki/Gyroscope

I can imagine a reference frame which is not rotating, right? I can call this reference frame the absolute frame which never rotates at all. (?) So is there a frame of reference throughout the universe which is absolutely non-rotating?
There is not just one, but an infinite number of frames of reference which are absolutely non-rotating.

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Well I thought we measure rotation with respect to a reference frame. So rotation of an object should seem different from different frames.
Would you please explain why we consider rotation to be absolute? Doesn't it depend on reference frame of the observer?
Although velocity is always relative, acceleration is absolute ("frame-invariant" might be a better term than "absolute"). Some of the confusion in this thread comes from people not clearly distinguishing the two when they say "motion".

Yes, velocity is relative because it depends on the frame of the observer. When I say that I'm at rest while you're moving north, and you say that you're at rest while I'm moving south, your description is just as good as mine; no experiment will give different results either way.

Acceleration, which is change in velocity, is not relative. I can take a small box, suspend a weight inside it with six springs (one to each face of the box), and then measure acceleration by observing the motion of the weight relative to the box and the stretching of the springs. All observers, no matter what frame they choose to use, will agree about whether the springs are stretching or not and hence whether the box is being accelerated or not. (A device like this that measures acceleration is called an "accelerometer").

Every point on a rotating body is undergoing acceleration - its direction of motion and hence its velocity is constantly changing, and an accelerometer will detect that acceleration.

So should we assume that anything moving with respect to distant stars is in absolute motion?
No. Its motion is relative to the distant stars, not absolute. If it were accelerating that would be absolute, but we wouldn't need to look at the distant stars or measure acceleration relative to them to know we we were accelerating; a local accelerometer would tell us that.

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Just to add an extra morsel of interest: This recent IOP web page suggests that the Universe is (and has always been, since the big bang) spinning. This conclusion was reached as a result of observing many distant galaxies, apparently.

The Earth's rotation is definitely not absolute. Consider, in a simpler case, a rotating hoop. The hoop's "rotation" is really just a macroscopic emergent phenomenon perceived by our human brains. The "rotation" doesn't really exist in the strictest sense. From a finer perspective the "rotation" is just an illusion caused by a bunch of particles all moving around in a circle. A given particle at angular location $x$ on the hoop as a partner particle at angular location $x + \pi$, and that partner particle has a velocity which is exactly the opposite of the velocity of the original.

And so, the rotating hoop is just a collection of particles moving relative to each other. No strictly absolute motion is involved. The same goes for the Earth.

The Earth's rotation only feels "absolute" to us humans when we conceptualize the Earth as an indecomposable body, which is really isn't.