Does the Earth move around the Sun?

[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!

 

[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.

 

[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.

 

[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.

 

[russ_watters]

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.

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.

 

[K^2]

But that does not make the sentence "The Sun moves around the Earth" less true.

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

 

[diegocas]

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...

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.

 

[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.

 

[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!

 

[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.

 

[K^2]

I wonder: What is the fundamental evidence for F = ma?

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.

 

[Dickfore]

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.

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.

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.
[/QOUTE]

It is a common misconception to state 2nd Newton's Law as a definition of force. This is not true. What this law says is that if such and such forces act on a particle it will have such and such acceleration, or, conversely, if the particle has acceleration, then the net force is so and so. It does not care what acts on the particle. Hence, the use of "free body diagrams".

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.

This is a postulate about the forces and cannot be derived. It stems from previous studies in statics.

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.

In Newton's Dynamics, the conservation of momentum pf an isolated system of partricles is a consequence of the 3 Newton's laws.

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

This only holds in Inertial reference frames. This is why First Newton's Law has content different than the other two and is not a simple consequence of them.

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.

Actually, Classical Physics covered these concepts fairly nicely.

 

[nonequilibrium]

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.

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.

 

[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.

 

[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?)

 

[K^2]

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

 

[nonequilibrium]

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

 

[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)

 

[K^2]

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

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

Say you have a particle field. Let's diagonalize it with respect to momentum and energy.

k_i |\psi_i&gt;= \frac{1}{i}\frac{\partial}{\partial x}|\psi_i&gt;
\omega_i |\psi_i&gt;= i\frac{\partial}{\partial t}|\psi_i&gt;

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.

 

[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?

 

[K^2]

They were, but things were defined differently. 1kg was defined as the mass of 1 liter of water. Mass just being defined as the intrinsic property that relates momentum to velocity.

 

[nonequilibrium]

How was momentum defined?

 

[brainstorm]

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.

I don't want to derail this thread, but this is a false view of science. Scientific method has to have some explicit recognition of empiricism and critical rigor. You can't just follow rules and procedures and come out with science. You have to take a critical position on some previously asserted knowledge-claim and come up with a research-design that links your critique to empirical observations and/or testing. This doesn't necessarily verify a knowledge-claim, but it may support it - and it can certainly render a false claim empirically untenable. If you break existing rules and procedures and still achieve these basic goals of critical theorizing and empirical testing, why wouldn't that constitute science?

 

[brainstorm]

While you're playing with the relativism of what revolves around what, consider the following:

If particles themselves are taken as the basis for measuring distance instead of space, then you could say that there is the same distance between the sun and the Earth as between a corresponding number of particles in Earth's atmosphere. You would just count the apparent distance between the particles in deep space as a side-effect of an increased ration between the speed of light and gravitation. I.e. you could say that light takes longer to go between particles in lower gravity, but that the particles are actually the same distance apart if gravity-level is controlled for.

If you looked at it in this way, the Earth and sun would actually be much closer and only appear more distant because of the relative constancy of the speed of light relative to changes in gravitation. If you looked at it in this way, neither Earth nor sun would really revolve around the other. They would just be layers/strata that drift in regular patterns relative to each other. The apparent rotation of the Earth could be chalked off to points of low gravitation between the two planes, sun and Earth, which cause the sunlight to bend inward before reaching the parts of the Earth-plane that have drifted out of gravitational alignment.

I like this perspective because it gives you Earth and sun as flat planes without anything revolving around anything else. However, given the standardization and pervasive elaboration of the heliocentric model of spherical heavenly bodies, it is very hard to think in terms of planar layers, even just as a thought experiment to see if it is even possible.

 

[K^2]

How was momentum defined?

"Quantity of motion" that is proportional to velocity.

 

[nonequilibrium]

That seems a kind of fishy definition? If I define the Ziblach with "It is a quantity that is proportional to the third derivative of distance", I haven't given an exact definition, have I (as it could be many a thing).

 

[K^2]

You only need to know two facts, both of which are experimental.

1) "Quantity of motion" is proportional to velocity.
2) Total "Quantity of motion" is conserved.

That's really all Newton had to go with. Defined slightly differently, but this is more compact.

Edit: So say you have an object A and you want to find it's mass. You know that mass is the proportionality constant between A's velocity and its momentum. You also know that proportionality constant for 1L of water is 1. So have a light container with 1L of water travel at some velocity, collide into A, and stick to it. You can now find A's mass by measuring final velocity.

 

[nonequilibrium]

Oh that's a nice summary, I like that, thank you very much.

 

[russ_watters]

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?

It is true and we accept it because it works, is very simple and explainsn a lot of phenomena. That's all that can be asked of a scientific theory.

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.

Whether "more useful" and "more true" are synonomous is something I think is true but it isn't something I'm interested in arguing about.

 

[brainstorm]

Whether "more useful" and "more true" are synonomous is something I think is true but it isn't something I'm interested in arguing about.

That's not really a useful statement then, is it? So does that make it false? . . . sorry, I couldn't resist pointing that out.