# Does the Earth move around the Sun?

1. Jul 24, 2010

### diegocas

I always hear people saying "Ptolemy thought that the Sun moved around the Earth, but it is the other way around: the Earth moves around the Sun".
I think that's wrong. I think that Copernicus's theory is not "truer" than Ptolemy's. It is just that Copernicus's theory is simpler! But both theories are correct.
It is just a matter of defining your reference frame!
Am I right? If that's so, why is it that even science teachers, science documentaries, etc. say that Ptolemy was wrong and that Copernicus was right.
Thanks!

2. Jul 24, 2010

### K^2

Both frames are valid, of course, but it's not just a matter of simplicity. If you choose Earth as your frame of reference, and have Sun rotate around it, then the Sun is undergoing extremely high centripetal acceleration with no corresponding force to account for it. You can, of course, make up a fictitious force to hold the Sun in "orbit" around Earth, and then make up even more complicated forces to keep all the planets moving the way they do. But by that point, Ptolemy's system is not just more complex, it also seems very arbitrary and forced. Which is not a good thing for any model trying to explain things.

But yes, it is possible to describe everything with Earth as the center of the universe and unmoving, and everything else moving around it.

3. Jul 24, 2010

### diegocas

Again, I think that, in the end, it really is about simplicity. We like simplicty and we accept that the simplest explanation is the correct one (Ockham's razor principle). Putting the Sun in the center together with Newton's equations of motion and Universal Law of Gravitation makes a nice and quite acurate description of the solar system. But that does not make the sentence "The Sun moves around the Earth" less true.

Last edited: Jul 24, 2010
4. Jul 24, 2010

### Dickfore

From the standpoint of Kinematics, both reference frames (one where the Sun is stationary - heliocentric and the other where the Earth is fixed - geocentric) are perfectly acceptable for describing observational facts. In fact, reference frames where the Earth is fixed are used quite often in Astronomy even today (horizontal and equatorial coordinate system) since they are very convenient to describe the everyday position of the celestial objects in the Sky from different points on the Earth's surface at different times.

However, science is not satisfied with merely describing phenomena. Science aims to find causal connections between the observed phenomena and to predict the outcome of future events.

So, the most common observation is that all stars on the Sky make one turn in a day. Is this because the "celestial sphere" is turning with such a period "above our heads" or is it simply because that the ground below our feet is rotating. Since different celestial objects are very far away from the Earth and it seems highly improbable that some interaction can be communicated between all of them to subdue them to rotate around the Earth with a common period, even the Ancient people had recognized that the latter option is much more viable and accepted the notion of a spinning Earth.

Now comes the question of the motion of the Sun, Moon and planets (literally meaning "wandering" stars) relative to the background of "immobile stars" (i.e. canceling the effects of the Earth's rotation). The (visually) largest among them, namely the Sun and the Moon seem to move around the Earth. And, this is indeed true. If you are only concerned about these two objects, saying that they revolve around the Earth is a very good approximation of reality.

The problem comes, however, when explaining the motion of the other planets (Mercury, Venus, Mars, Jupiter and Saturn are the only ones visible with the naked eye). Ptolemy had assembled tables for the predicted positions of the planets assuming they perform complicated revolutions around a moving point (epicycle), which in itself revolves around the Earth. Over the course of the centuries, the differences between the predictions and the observations were so drastic, that these tables were rendered useless.

Enter Copernicus. What if the planets do not revolve around the Earth, but around the Sun and the Earth is just one among them? Copernicus assumed the trajectories to be circles, so his predictions were of little practical value, but, nevertheless, his model made much better predictions and was much simpler. It was up to Kepler, using the data from many years of observations made by Tycho Brahe, to find that the true trajectories were ellipses, that the planets moved with a constant sectoral speed and that the cubes of the major semiaxes of the orbits were in proportion to the squares of the periods.

But, the model is still based on observations and there is still no causal connection between these curious results. If one applies the Newton's Laws of Dynamics to this motion, one can arrive at the Law of Universal Acceleration. This was, of course, done by Isaac Newton.

There is one caveat, however. The Laws of Dynamics are valid only in so called Inertial reference frames. The First Law is an experimental test whether the reference frame we are using is inertial to a good degree of approximation. In the XIX century, the French scientist Leon Foucault constructed a pendulum that did not preserve its plane of oscillation relative to the Earth's surface, which was a direct demonstration that the Earth actually rotates.

After Newton's Law of Universal Gravitation was developed and Calculus was refined in a practical form, scientists could perform extensive calculations regarding the characteristics of the planet's (and Moon's) orbits. Particularly, they discovered anomalies in the trajectory of a newly discovered planet, Uranus and the French astronomer Le Verrier conjectured that these anomalies would be due to some unknown until that time celestial body and predicted its mass and trajectory. That body - Neptune was soon observed by the Berlin observatory. This was an unprecedented triumph of celestial mechanics, whereby a scientists had discovered a whole planet at the point of his pen.

5. Jul 24, 2010

### Staff: Mentor

You're not quite getting the purpose of Occam's Razor and why a simpler theory really is better. The goal of science is to explain how things work and if you add assumptions for which there is no evidence, you create more questions than you answer and as a result have subtracted more from our understanding of the universe than you've added.

"The Sun moves around the Earth" is less true than "the Earth moves around the Sun" because the extra assumptions make it less consistent with reality.

6. Jul 24, 2010

### K^2

No, it doesn't. It only makes it a far less useful one.

7. Jul 24, 2010

### diegocas

I wonder: What is the fundamental evidence for F = ma? I know, of course, that almost every experiment confirms this equation. However, does that make it true or do we just accept it because it works, it is very simple and it explains lots and lots of phenomena?

I think the simplicity issue is not minor. I also think that the ultimate goal is to find some basic, very simple, principles that describe everything. However, that does not make them any more true than any other complicated system. They're just simpler, more general, useful principles.

8. Jul 24, 2010

### Pythagorean

If you take ptolemy's view, you also have to account for the strange little loop-de-loops stars do if we're not rotating around the Sun.

9. Jul 24, 2010

### nonequilibrium

What exactly is the scientific method, explicitly?

I tried to write it down, but it seems to be too hard... First I tried to make the first point that "What we see we accept as true", but then would take hallucinations into account. Then to exclude those I tried to formulate "We postulate there are observations independent of the observer and those are true", but then we'd come into conflict with special relativity (speed determines your perception/reality). Maybe the first axiom is something like... "We postulate the existence of an exterior world that we can observe independently of the observer -- if the observation is dependent of the observer, it has to be explained from outside the observer" (the latter would be talking about the fact that the velocity used to explain different observations in SR is a characteristic outside the mind of the observer). But jezus, even that axiom is not good enough for some interpretations of QM.

Okay I'm making a mess, feel free to ignore it, but I implore someone to try and write down the scientific method, I'm very curious!

10. Jul 24, 2010

### Dickfore

The scientific method is a series of procedures and rules used for obtaining scientific knowledge, i.e. factual, objectively verifiable statements about the phenomena occurring in our environment.

11. Jul 24, 2010

### K^2

It's not exactly F=ma. It's dp/dt=F. Force is equal to rate of change of momentum. That's actually the way Newton stated it orginally. Since p is roughly mv, dp/dt is roughly d(mv)/dt = (dm/dt)v + m(dv/dt) = ma, but only for v<<c. Near the speed of light, it becomes more complicated.

Net force is defined as dp/dt. I mean, how do you measure a force? You try to accelerate something with it.(You can use springs, but that's just a simpler way of measuring the force, not the definition of it. A spring scale must first be calibrated, which is usually done with a known weight, and gravitational weight is due to gravitational acceleration. So you still fall back on acceleration in the end.

So the only real question is why forces are additive. That is, we define F1 and F2 based on the amount of acceleration they cause. How do we know that if you apply both you get effect of F1+F2? Well, you know that action is equal to reaction. Say these two forces are caused by two separate objects. Each one experiences -F1 and -F2 respectively, and of course, experience corresponding change in momentum. To conserve momentum, the change in momentum of the object to which these two forces are applied must correspond to application of F1+F2.

How do you know that Newton's 3rd holds? Well, you apply the same idea of conservation of momentum to interaction of two bodies. Since momentum changes must be equal and opposite, so are the forces.

Just for completeness, if you have just one object, its momentum is going to be conserved. Hence, object in motion remains in motion.

Finally, how do we know that momentum is conserved? That's a more complicated question. It ultimately has to do with the fact that laws of physics are invariant under translation. But we are talking about Quantum Physics by this point. Unless there is a similar theorem in Classical Physics that I missed.

So that's all 3 Newton's Laws covered.

12. Jul 24, 2010

### Dickfore

Both statements are equivalent. Newton's second Law holds strictly for motion of "particles". This means, if a particle looses mass, then it ejects other particles by pushing on them. The ejected particles, by 3rd Newton's Law push back and this causes the particle to accelerate. But, a body with variable mass is not a single particle. It is a system of particles. Relativity has nothing to do with Newton's Laws as those hold only at speeds much lower than the speed of light.

13. Jul 24, 2010

### nonequilibrium

You don't understand my point, you just used terms you assumed to be predefined, but in those definitions is exactly the hard part!

What is "factual"? "objectively"? "environment"?

And the use of the term "a series of procedures" isn't really clarifying on what those allowed ways of acting are.

14. Jul 24, 2010

### K^2

Dickfore.

1) Fact that F=ma fails at v~c has nothing to do with dm/dt term. I took it to be zero in my derivation. See that equal sign? Meaning exactly equal? That's not where approximations took place. They took place when I took p to be roughly mv. That's an approximation.

2) Why don't you go ahead and define force, then?

3) Conservation of momentum does imply that forces are additive. I can show that as a general result.

4) Conservation of momentum is far more general than Newton's 3rd Law and follows from more fundamental principles. While Newtonian Physics takes it as a postulate, question I was answering is how these laws are confirmed. And while statistical argument might be compelling, an argument from a more general model will always win, because it will always be based on a greater sample.

5) In non-inertial frames there is such a thing as fictitious force. With fictitious forces in places, Newton's 1st holds.

6) Classical physics takes them as postulates. Not the same thing.

15. Jul 24, 2010

### nonequilibrium

Something that always struck me as odd: if force is defined as F = ma, how is m defined? (or if m is defined by F = ma, how is F defined?)

16. Jul 24, 2010

### K^2

How deep down that rabbit hole do you really want to go?

17. Jul 24, 2010

### nonequilibrium

All the way down and then start digging some more -- we're physicists after all, aren't we?

18. Jul 24, 2010

### pallidin

The earth's moon moves around the earth, the earth moves around the Sun, and that total system moves around the galaxy.
To my knowledge, our galaxy does not revolve around something(could be wrong)

19. Jul 24, 2010

### K^2

Alright. In that case, I would go all the way back to quantum mechanics.

Say you have a particle field. Lets diagonalize it with respect to momentum and energy.

$$k_i |\psi_i>= \frac{1}{i}\frac{\partial}{\partial x}|\psi_i>$$
$$\omega_i |\psi_i>= i\frac{\partial}{\partial t}|\psi_i>$$

That should give us continuum of states, so that we can define.

$$p = \hbar k$$
$$v_g = \frac{\partial k}{\partial \omega}$$
$$m_{rel} = p/v_g$$

Finally, we can define rest mass.

$$m = \lim_{v_g\to 0}m_{rel}$$

I think that should do it.

20. Jul 24, 2010

### nonequilibrium

Oh jeez louise :) Thank you very much for the great reply, but sadly I haven't had any quantum yet. But I promise I'm bookmarking this to visit it once I did. I once was talking about it with another student and he suggested we could define mass by E = mc²; I found that an intelligent remark, but it seemed like you were "giving up" something which you could normally deduce.

Anyway, the fact you had to use QM brings up the following horrible question: before QM the laws of Newton were actually not even well-defined?