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In college I took a great "Philosophy of Physics" class, where on the first day the professor asked everyone to write one page on whether the Earth revolves around the sun, and the final project was another paper on the same topic, so we could see how nuanced a question it was and how our views had evolved over the course.

With that said, I don't think there's any valid answer besides "you can define your terms and points of reference such that it does or doesn't; there's no particular physical reality to the matter".

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An interesting tangent: At the time of Gallielo, the church used the Tychonian model of the solar system.

In the Tychonian model, the earth is the center and the sun revolves around the earth. But the other planets revolve around the sun! You will notice this is practicallty the same model as the Copernican model except for the arbitrary definition of what is "the center".

The only observable difference was the relation to the firmament which in the Tychonian model revolved around the earth but in the Copernican revolves around the sun. If the Copernican model was correct, some parallax to the stars should be observable. Now we know this is not observable due to the distance to the stars, but this was not known at the time.

It's not arbitrary. The only two choices that work are the real center of gravity, and the observer's position with the real center of gravity orbiting the observer and everything else orbiting the real center of gravity. If Tycho chose Jupiter as the center of the orbits, the planetary orbits would have the same problem of epicycles as the older models.

What precisely do you mean by “the same problem with epicycles”? You can fix Jupiter at the origin. You use exactly the same equations, except that the sun is using the equation that used to describe Jupiter (with an extra negative sign) and the other planets add in the term describing the Sun’s motion.

Earth is no different than any other planet (or other celestial body in a stable orbit relative to the solar system) in this respect. Hell, you could make the Moon the center of the solar system - the math works just fine.

If observer is on the Earth then equations for Jupiter will not work for describing the apparent motion of the planets.

You can claim that any arbitrary point is "the center of the universe" if you acknowledge that the planets rotate around the sun, not around the designated "center". If you choose Jupiter as the "center", there would still be no observable difference and you wouldn't need additional epicycles.

An interesting read is On the Revolutions of Heavenly Bodies by Copernicus, even if you just read the introduction. It’s an appeal to the Pope regarding the scientific nature of his conclusions. Regardless, they still excommunicated him years later for going against what was thought the authority of scripture.

no, Copernicus was never excommunicated, although "On the Revolutions of Heavenly bodies" went through various stages of requiring errata pointing out it was only a hypothesis and even a ban

He was never excommunicated as far as I know, and the book was only published after his death. The church did suppress the book though.

Thanks - I was confusing the stories of Copernicus and Galileo. Galileo’s works, based on Copernicus’s ideas, were declared heretical. While not excommunicated he was persecuted by the church.

https://en.m.wikipedia.org/wiki/Galileo_affair

>An interesting read is On the Revolutions of Heavenly Bodies by Copernicus, even if you just read the introduction. It’s an appeal to the Pope regarding the scientific nature of his conclusions. Regardless, they still excommunicated him years later for going against what was thought the authority of scripture.

This... is completely false. Copernicus never faced adversity for his heliocentric model.

this isn't entirely true. At the time of Galileo, Tycho was presenting his model (and was a militant enemy of Galileo). Tycho's model was either used or not depending on more local scientific stances, but it wasn't entirely popular.

Claiming that "there's no particular physical reality to the matter" I don't understand at all. I can make sense of that to a limited degree as a variation on the saying "all models are wrong..", but you seem to have extended that to say that there is no 'right' possible (ie the 2nd part of that saying, that "...but some models are useful").

A naive reading of what you said suggests eg. no spaceflight is possible because no astronomical (or any...) calculation is reliable. Can you clarify?

What does it mean for the earth to orbit the sun or vice versa?

What they mean is that you may take whatever point in space to be your immobile frame of reference and describe all motion with respect to that point. It happens to be convenient to take the center of the Sun as such a point when doing calculations relevant to the solar system but it's not more 'valid' than literally any other point in the universe. You just have to change the equations a bit.

No, they actually dispute the „physical reality“ which is completely wrong: the actual words:

“there's no particular physical reality to the matter”

The "physical reality" of describing motion is transformations relative to a frame of reference. The origin (eg where you put 0,0,0) of that frame is a mathematical choice; it's not a real physical thing.

That the formulas can be calculated relative to any reference point doesn’t change the fact that the physical reality is ellipsoid movement of planets around the Sun.

https://spaceplace.nasa.gov/barycenter/en/

Even as you insist on choosing a privileged reference frame for, say, aesthetic reasons, it's still not all the planets moving around the Sun. Did you not read the article? It's all the planets and the Sun moving around the barycenter. If you try to think through what your words even mean, you'll realize that they don't even mean anything, much less describe a physical reality.

> you'll realize that they don't even mean anything, much less describe a physical reality.

Wrong.

https://en.wikipedia.org/wiki/Ellipse#Planetary_orbits

"In the 17th century, Johannes Kepler discovered that the orbits along which the planets travel around the Sun are ellipses with the Sun [approximately] at one focus, in his first law of planetary motion. Later, Isaac Newton explained this as a corollary of his law of universal gravitation.

More generally, in the gravitational two-body problem, if the two bodies are bound to each other (that is, the total energy is negative), their orbits are similar ellipses with the common barycenter being one of the foci of each ellipse. The other focus of either ellipse has no known physical significance. The orbit of either body in the reference frame of the other is also an ellipse, with the other body at the same focus."

The existence of barycenter it a physical reality. The elliptic movement is a physical reality. Compared to all other distances, the barycenter is for all the motions of all the planets effectively Sun. Even it it is approximation, it's a good approximation. Even if it moves and is sometimes a little outside of the Sun surface, it's still compared to the other distances practically there.

Sun.

It was known even three centuries ago, but now some "philosophers" think that they "relativize" that away. No. It's there.

> The existence of barycenter it a physical reality.

A barycenter is a mathematically defined point that we choose because it makes equations simpler. There's nothing physically real (i.e. directly observable) at the location.

Consider: if you fire a cannonball it will follow a parabolic path, and that parabola will have a focus, right? But that doesn't mean there's anything physically real about the focus of the parabola - it's a mathematically abstraction we invent because it's useful for describing the cannonball.

> some "philosophers" think that they "relativize" that away.

The relativity we're talking about comes from Einstein, not philosophers. Deciding whether the Earth revolves around the sun or vice-versa ultimately boils down to choosing a frame of reference, and one of the grand results of relativity is that there really is no absolute frame of reference we can measure from.

> Consider: if you fire a cannonball it will follow a parabolic path, and that parabola will have a focus, right? But that doesn't mean there's anything physically real about the focus of the parabola

The parabolic path is physically real, it will not go any other way.

The same is with the paths the planets make: their form is real, they don't take any other.

If you try to draw these paths on scale, you have to draw the ellipse (which for many planets is hard to distinguish from circle, the measurements had to become precise to learn that). Also, you have to place the Sun directly in one of the foci of the ellipse.

All of these steps you have to do to make a picture that corresponds to what is measured and observed -- to make a picture reflect the physical reality.

You obviously agree that much. So when you then write "whether the Earth revolves around the sun. ... I don't think there's any valid answer besides "you can define your terms and points of reference such that it does or doesn't; there's no particular physical reality to the matter"."

You are confused with the fact that the calculations can be done using different frames of reference to make a statement that "there's no particular physical reality to the matter."

The particular reality is the ellipsoid paths and the Sun in one of the foci, and whichever calculations you do, you have to reconstruct that physical reality. These shapes and that the Sun is actually in one of the foci is what you can't "relativize away."

> Deciding whether the Earth revolves around the sunb or vice-versa ultimately boils down to choosing a frame of reference

It doesn't. The Sun is in the focus of the ellipses made by planets around it. The opposite doesn't hold.

> there really is no absolute frame of reference we can measure from.

And that has nothing to do with the fact that the Sun is in the focus of the elliptic path of each planet and not the vice versa. The planets do make that path around the Sun, what can be simplified to "they rotate around the Sun." If you ever tried to draw it it would be obvious to you too.

So you were just confused after taking that "Philosophy of Physics" class.

> The Sun is in the focus of the ellipses made by planets around it. The opposite doesn't hold.

Certainly the opposite holds - if you draw the Sun's orbit from a planet's frame of reference, you'll draw an elliptical path with the planet at one focus. That's the whole point here, that neither drawing describes observable reality any better than the other.

I don't think I'm making any headway here so I'll defer to Einstein:

> Can we formulate physical laws so that they are valid for all CS [coordinate systems] ... ? If this can be done ... the struggle, so violent in the early days of science, between the views of Ptolemy and Copernicus would then be quite meaningless. Either CS could be used with equal justification. The two sentences, 'the sun is at rest and the Earth moves', or 'the sun moves and the Earth is at rest', would simply mean two different conventions concerning two different CS. Could we build a real relativistic physics valid in all CS; a physics in which there would be no place for absolute, but only for relative, motion? This is indeed possible!

(from The Evolution of Physics)

The orbits of the planets don’t behave “regularly” when observed from the Earth, exactly because they orbit the Sun and not the Earth.

https://en.m.wikipedia.org/wiki/Apparent_retrograde_motion

The laws of motion are the same in every reference frame, which means that statements like "X revolves around Y and not vice versa" are not "physically real" in the same way as "X and Y attract each other gravitationally" is, because they select one reference frame as privileged.

> The laws of motion are the same in every reference frame

Inertial reference frame, right? Otherwise you need to add in fictitious forces.

Rotation is different from motion.

Rotating around a point still applies in any frame of reference. Spin a top and the axes of rotation is independent of your frame of reference. Pick an atom on that top and it’s rotating around a specific point in any frame of reference.

This goes back to the ambiguity of the definition of orbit. If I have a system with two points involved in some sort of rotational motion, then there isn't a "best choice" for which point should be considered the origin of my coordinate system.

If you mean exactly 2 abstract points in Euclidean geometry then sure. 3D objects are not points which is the first issue. Relatively also cares about accelerating or rotating reference frames which applies to both point masses.

The center of mass in a two body system is a nice inertial reference frame which simplifies calculations.

No, they said "there is no physical reality to the matter", where, judging by context, "the matter" is the question of whether the Earth revolves around the Sun.

The conclusion that there is no physical reality to this is based on the what @aluren mentioned - you can take any immutable point of reference and describe the movements of the others from it using the same laws of physics, thus "the matter" becomes one of philosophy and choice of point of reference rather than physics itself.

You may disagree with this point but I don't think anyone disputed the existence of a physical reality, they simply moved one particular question out of its domain.

Changing the point of reference will change your mathematical model, sure, but it will still describe a movement around a barycenter, and the statement remains true whatever your philosophy. Numerous ways to model a phenomenon don't deny its existence.

Again: not denying the existence of the phenomenon, only removing it from the realm of physical reality to that of philosophy and mathematical point of reference.

Still very much existent.

What I mean is, if two people disagree about whether the Earth orbits the sun, there aren't any experiments where we'd expect them to predict different results. They're both describing the same physical reality, viewed from different frames of reference.

It's analogous to talking about someone throwing a ball on a train. A person on the train can say the ball moves relative to the train, and someone outside can say the ball and train are both moving relative to the Earth, and a guy in a spaceship can say that all three are actually moving relative to the sun. But choosing one of those claims over the others is purely a matter of convenience or perspective, not of physical reality.

You might find Bertrand paradox interesting regarding this aspect.

While I think the connection with what GP wanted to convey is tenuous, Betrands paradox _is_ interesting, and even more so E.T. Jaynes' solution.

As with most paradoxes, it's about how a seemingly innocuous question turns out to either be underspecified to have an answer, or tricks even the mind of mathematicians to assume too much.

Here it's about what it means to have a "random chord of a circle"; several simple ways to generate random chords lead to very different results, but true randomness should not be easy distinguishable from other true randomness...

E.T.J's solution to invoke the maximum ignorance principle to require any source of random chords to be size- and translation-invariant (because those dimensions are not specified in the problem) seems elegant.

Now, comparing to orbits, or to balls on a train, the thing here is: all these different viewpoints, although very different, do lead to the same result. Even if you calculate stuff; and if I'm not mistaken, that's because of relativity (Galilean relativity should be sufficient for the train example to work, the more modern ones for the rest).

IIRC objects experiencing acceleration (e.g. planets orbiting each other) are not subject to Galilean relativity like objects that are moving at a constant velocity (e.g. ball being thrown on a train). So when planets orbit each other, there is only a singe valid frame of reference.

See: https://en.wikipedia.org/wiki/Mach's_principle

But that is not what "there is no physical reality to the matter" means, if one chooses not to use any relative point there is still an objective distance between each object with respect to every other object and accelerations for each of those distances.

"The matter" in that quote is the matter of whether the Earth orbits the sun or vice versa. Naturally there's observable physical reality to distances and whatnot, but if you use the laws of physics to make predictions about those observables, the math works regardless of which body you assume the others revolve around.

The disagreement can exist because "orbits" is left under-defined. If you say A orbits B if A makes circles around B and B creates a bigger gravity field, then everyone will agree; they'll also agree on the fact if both objects have roughly equal masses, then it is true to say that both A orbits B and B orbits A.

> points of reference such that it does or doesn't

It's too bad (but not surprising) that you couldn't have gotten a bit deeper into general relativity where even the idea of "points of reference" gets a lot tricker. Even though there's a lot of pop-science talked about "space time" I find most people don't really grasp how really challenging of an idea it truly is.

Newtonian physics and special relatively are quite happy to imagine one observer looking at another from a particular frame of reference. The classic example is of course watching someone driving while you are in a train. Special relativity seems really crazy at first because you realize the length of the car can change if either of them are going close to the speed of light.

But GR does away with this idea that you can understand the universe at all while sitting on a train. In GR frames of reference only exist locally in infinitesimally small units of space and time and are defined by being simple such that all particles being observed move in straight lines. The big insight of GR is that the question "which 'revolves' around the other" is the wrong question because the only way to understand the universe is in slices of space and time where everything moves straight (well you can't ever get 'everything' straight, so even then you just worry about getting it right for a few particles at time).

In GR when you jump forward and land on the ground in front of you, you moved in a straight line the entire time. This sounds impossible because we can't imagine a single frame of reference where we could observe this. And that's what makes GR so hard to understand because the jump forward can only be understood by looking at the way those infinitesimal local reference frames change, but there is no general frame of reference that we can find where we can clearly observe this. In the exact same way that calculus understands a curved line as an infinite sequence of perfectly straight lines, GR understands curved space time as an infinite sequence of perfectly straight frames of reference.

It is, in fact, much more complex than the simple case of trying to understand who is right from the two reports of two observers seeing each other on passing trains.

> In college I took a great "Philosophy of Physics" class, where on the first day the professor asked everyone to write one page on whether the Earth revolves around the sun, and the final project was another paper on the same topic, so we could see how nuanced a question it was and how our views had evolved over the course.

A lengthy and enjoyable read of the original controversy is "The Great Ptolemaic Smackdown."[1] (I prefer to start there, as it's easy to tell whether you are interested in reading after the first few paragraphs, but he did put a ToC together, too.[2])

[1]: https://tofspot.blogspot.com/2013/08/the-great-ptolemaic-sma...

[2]: https://tofspot.blogspot.com/2013/10/the-great-ptolemaic-sma...

> With that said, I don't think there's any valid answer besides "you can define your terms and points of reference such that it does or doesn't; there's no particular physical reality to the matter".

Isn’t the article linked here exactly the correct and valid answer of whether the earth orbits the sun? Philosophy likes to make things all seem like perception and mental frame of reference, and sometimes it is with people, but the earth’s trajectory relative to the sun doesn’t change if we think about it different or define terms differently.

Maybe the whole problem is asking an invalid binary right/wrong question, when the actual valid answer is that it’s not binary. This one hinges on your definition of “orbit”, when the real valid answer is that there are more than 2 masses, so using orbit in the first place is misleading. Another valid answer to whether the earth orbits the sun might be 99.87% yes and 0.013% no.

> Philosophy likes to make things all seem like perception and mental frame of reference, and sometimes it is with people, but the earth’s trajectory relative to the sun doesn’t change if we think about it different or define terms differently.

That's exactly the point here - answering the question of which revolves around what boils down to deciding which body is stationary, and that depends entirely on your frame of reference. Viewed from the Earth the sun is moving, and viewed from the sun the Earth is moving, and viewed from somewhere else they both move relative to one another. But none of those viewpoints is any more physically real than the others - they're just choices for where to put the origin of the coordinate system, as it were.

That is, if you wanted to predict how the planets will move in the future, you could start from any of those assumptions and still make correct predictions. That's what I mean by saying there's no physical reality to the matter of which frame of reference you choose.

> Isn’t the article linked here exactly the correct and valid answer of whether the earth orbits the sun?

Is it though? I'm genuinely curious. For example, in our current reference, earth almost always is orbiting the sun, but what would happen if the entire system was not contained in the galaxy but in the middle of space (not attached to any galaxy), how would the planetary orbit change?

Another question would be if our solar system was closer to the center of the galaxy, would the orbits of the planets stay the same or would they be skewed because of gravitational forces from the center of galaxy + other solar systems?

> Another valid answer to whether the earth orbits the sun might be 99.87% yes and 0.013% no.

I'm not sure if you're an astronomer or have a weather of knowledge or PhD in this topic but from the article, the answer is given as "Technically, what is going on is that the Earth, Sun and all the planets are orbiting around the center of mass of the solar system," writes Cathy Jordan, a Cornell University Ask an Astronomer contributor." That would be the only correct answer it seems. If the center of mass happens to be direct center of the sun or skewed one way or other is irrelevant to the fact. However, I could be wrong in my understanding.

> there's no particular physical reality to the matter"

Completely wrong. The physical reality is reflected by calculating Newton‘s formulas, which give the center of mass somewhere inside or very close to the Sun, as the article explains.

By that argument we actually orbit the centre of the galaxy, with the sun causing a minor wobble on top of that orbit.

It depends on your frame of reference.

looks towards the great attractor and sighs

Some frames of reference are very close to being inertial frames, and others aren't. There's a big difference between inertial and non-inertial frames. In non-inertial frames, you have to introduce fictitious forces in order for the physics to work out.

In short, the universe cares about acceleration, but not constant motion. Accelerating frames are different from non-accelerating frames.

We are accelerating away from the center of the universe though.

There is no center of the Universe. If the Universe is flat or negatively curved, then it is infinitely large, and if it is positively curved, then the volume is finite, but space is periodic.

Space is intrinsically expanding, and that expansion is accelerating. That's quite different from acceleration in Newtonian physics. The statements I made about acceleration are in the context of Newtonian, pre-Relativistic physics, and are only approximate in a Relativistic framework.

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