Can we determine for sure if the Sun revolves around the Earth?

Question

Rabbi Menachem Mendel Schneerson was the most recent (and final) rebbe of Chabad.

In 1975 he published a series of correspondence with a scientist about whether the Sun revolves around the Earth and not the other way around.

[Schneerson's first response]

It is my firm belief that the sun revolves around the earth, as I have also declared publicly on various occasions and in discussion with professors specializing in this field of science.

[Schneerson's second response]

One of the conclusions of the theory of relativity is that when there are two systems, or planets, in motion relative to each other—such as the sun and earth in our case—either view, namely, the sun rotating around the earth, or the earth rotating around the sun, has equal validity.

My knowledge of physics is limited to the undergraduate level, but, after reading up on relativity and a biography of Albert Einstein, everything he said seems to be correct as regards the current scientific knowledge.

Answers here and here tackle this question, but the answers, to my understanding, ultimately come down to "Mathematically modelling the Earth revolving around the sun and not the other way around makes our models simpler and physics calculations easier". While true, I don't see how this constitutes any sort of proof of an underlying physical truth.

Nevertheless, I remain skeptical. Is Rabbi Schneerson indeed correct: that we have no absolute way to determine whether the Earth revolves around the sun or the other way around and that his belief is no less valid than the one accepted by scientists?

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Mod Note

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I don't normally do this, but this question has garnered an incredible range of answers - often contradictory! - that do not belong on this site. Please read our Welcome to New Users before answering. It is not sufficient to share your philosophy of science. It is not sufficient to assert that modern physics says something without references. Answers and comments that don't follow the site's standards will be deleted. - Oddthinking.

Answer 1

The referenced link is correct; all frames of reference are equally valid in general relativity -- with a catch or two. One catch is that the mathematics can get a bit ugly (or more than a bit ugly), but it is possible to describe the behavior of the solar system from a geocentric perspective. Another catch is that in general relativity, frames of reference are local, where local means extremely local (i.e., infinitesimal).

However, in the rabbi's second response make his point of view much clearer:

It is my firm belief that the sun revolves around the earth, as I have also declared publicly on various occasions and in discussion with professors specializing in this field of science.

This Earth-centered (geocentric) point of view being the only valid point of view, which is shared amongst geocentricists, is nonsense. It is however a series of big leaps from "all frames of reference are equally valid" to "that means a geocentric point of view is valid" and then to "that means that only a geocentric point of view is valid". Just because it is possible to explain the behavior of the solar system from a geocentric perspective does not mean that that is the only valid perspective.

Ignoring the rest of the universe, the equations that describe the behavior of the solar system take on their simplest form when expressed in terms of a non-rotating frame of reference with the solar system's center of mass as the origin of the frame. This is the solar system barycentric frame of reference. The equations of motion take on their simplest form in a non-rotating, non-accelerating frame of reference such as this. Complex mathematics are involved in transforming from a barycentric frame to a geocentric frame. One way to look at it is to apply those complex mathematics (and we do do this, all of the time, for spacecraft orbiting the Earth) so as to come up with a geocentric view of those spacecraft's orbits. Another way to arrive at this point of view is to claim that these complex mathematical expressions are the right (and only) way to do it. Occam's razor (the simplest answer is most likely the best answer) comes into play here.

The best ephemerides (postdictions / predictions of the positions of the planets as a function of time) of the solar system (there are three competing organizations, the Jet Propulsion Laboratory in California, the Russian Academy of Science in St. Petersburg, and the Observatoire de Paris) all use a barycentric frame of reference in which the nastiness of general relativity is reduced to perturbations on top of Newtonian physics. A barycentric frame of reference makes the extreme ugliness of a geocentric frame vanish. Occam's razor prevails.

Answer 2

TLDR: the Rabbi is correct in a very specific technical sense, but it is not helpful to think about the question in the way he advocates.

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Detailed answer:

The Rabbi's claim raises an interesting issue that can be best understood if you apply his logic in a more extreme situation — a famous experiment sometimes described as Newton's bucket (see also here: 1 2 3, and the related topic of Mach's principle).

The experiment is as follows: imagine if I take a bucket of water tied to a rope and spin it around me. Most people looking at this would say that the bucket is spinning around me. However, from the point of view of a frog sitting in the bucket, it would look like the entire universe is rotating around it. By the Rabbi's argument, neither of these two ways of thinking about the situation is more valid or correct than the other.

When faced with this claim of an apparent very extreme symmetry between two points of view which do not intuitively seem at all symmetric, we have two options:

1. Argue that, actually, no, one of the views is in fact more correct than the other.

2. Acknowledge that the "both points of view are valid" camp does have a point.

If we choose option 1, we have to defend our claim that it's more correct to say that the bucket is spinning around me. The explanation for this is the same one in the physics.stackexchange answers you found, namely that while in fact we can write down equations that describe the situation from either point of view, making them both valid in some sense, the equations become considerably simpler and more intuitive in one point of view than in the other.

The problem with this is that while we have defended the claim, we were also forced to acknowledge that both points of view are valid! So, we end up with option 2 after all, or, if we don't like that idea, we have to pile on additional arguments about Occam's razor, as @DavidHammen's answer does. These arguments are pretty wishy-washy and subjective IMO, and a lot of people don't find them very convincing.

Now, on the other hand, the problem with option 2 is that, while logical and correct in a theoretical sense, it is completely removed from our normal intuition and sense of reality about the physical world. It basically means accepting a world view in which motion and acceleration of physical objects is always understood to be a purely relative phenomenon: it's not just that we cannot decide whether the Earth is rotating around the sun or vice versa, we cannot even meaningfully regard the entire universe as fixed. This, to most people who care about physics and have thought about this issue, seems like too steep a price to pay, particularly when the only benefit we receive in exchange is a minute, almost imperceptible, gain in logical consistency.

So, the end result of the discussion is that we (meaning, physicists and other scientifically literate people) make a very small compromise, and accept that when we say "the earth revolves around the sun", it means something very specific (that all people who study physics understand quite well, and can explain fairly easily if called upon to do so), which is nonetheless subtly different than the literal meaning of "the Earth revolves around the sun" as someone like Rabbi Schneerson might interpret it. This small semantic compromise is a kind of intentional sloppiness, analogous to what mathematicians call abuse of notation.

Bottom line: it is ultimately much, much more helpful to regard the Earth as revolving around the sun than the other way around, even if, in a narrow, abstract, technical sense, both points of view are "equally valid".

Another way of saying this is that if you have two groups of people, one of which clings to the notion that the sun revolves around the Earth, and the other accepting the modern (circa 1822) point of view about the relative motion of the Earth and the sun, together with the scientific approaches and ways of thinking about the world tied to that point of view, it is the latter group that will become a lot more successful in harnessing the laws of physics to its needs, and come up with useful inventions such as planes, rockets, satellites, global positioning systems, etc. So, personally I'm happy to count myself as a member of the second group, while your Rabbi appears to prefer the first...

Answer 3

I don't think you need to understand much math to judge whether a heliocentric or geocentric model of our solar system is better. I think all that is needed is to ask some simple questions about which model has better predictive power before it devolves into tautologies ("that's just the way it is" / "we don't know"). This is generally how "the scientific method" works. This is explicitly what the question is about though, so allow me to post the "scientific" part of the answer (i.e., what can be answered on Skeptics.SE), and then address the philosophical question.

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One curiosity about our solar system is about once every 26 months it appears that Mars slows down its orbit, travels backwards for a bit, then resumes as before. And this same phenomenon is visible about Earth on Mars!

source: https://mars.nasa.gov/all-about-mars/night-sky/retrograde/

Ptolemy, working from a geocentric model of the universe, solved this problem by explaining the orbits of celestial bodies using "epicycles": you can attach a circle to another circle and suddenly Mars retrograde orbit is explained.

The interesting thing about epicycles, is that you can actually create (almost) any shape you want. For example

source: https://mathematica.stackexchange.com/a/171756/60731

So here is the challenge.

Q: Why should Mars prefer a simple epicycle and instead not trace an outline of Bart Simpson?
Geocentric answer: There is no logical explanation, all epicycles are equally valid. (Or perhaps, some planets prefer some epicycles, while others do not, and there is no explanation why).

Q: We have just observed a new planet/moon/heavenly body. How does it move around the sun/host planet/solar system?
Geocentric orbit: It is impossible to know until we have observed one complete orbit around its parent.

Q: Is space travel even possible -- can we send a probe like Voyager out and it suddenly succumbs to an unknown epicycle orbit?
Geocentric answer: Who knows.

This is a very unsatisfactory answer, and helps very little in providing a useful model of the universe.

However, this is all resolved quite nicely with a heliocentric model of our solar system.

Q: Why does Mars occasionally travel backwards in its orbit?
A: Because Earth and Mars orbit at different distance/speeds around the sun.

Q: We have just observed a new planet/moon/heavenly body. How does it move around the sun/host planet/solar system?
A: We only need a few hours/days/weeks of measurement to predict where this will be in the future. (depending on distance)

A heliocentric model explains Mars' orbit, and the orbit of any other body we care to ask about. A heliocentric model allows us to estimate that Eris will orbit the sun once every 559 years. A geocentric model means we need to wait at least until the year 2564 (2005+559 years) before we will know what the orbit of Eris really looks like.

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Now for some philosophical discussion. This section has perhaps more opinions, but the intent is to address the following:

"Mathematically modelling the Earth revolving around the sun and not the other way around makes our models simpler and physics calculations easier". While true, I don't see how this constitutes any sort of proof [em. added] of an underlying physical truth.

There are all kinds of prickly issues about what "truth" is, what "knowledge" is, and how us humans can come to know such things. Many people have an intuitive belief that science "trends towards truth" but succinct descriptions like that are complicated by the fact that humans are unpredictable and only-sometimes rational.

So I think I would have to say, with a few carefully worded caveats, that maybe you are correct. Just because a model is very useful does not mean it is "true." And further, even if a model had 100% predictive power, there will always be room for even just the tiniest, smallest, practically-impossible reason to have just a little bit of doubt that it is "true" (e.g., negligible errors in execution, whether the future will behave like the past, negligible errors in measurement, etc). But, for all practical purposes, what does that matter?

Before proceeding, I want you to stop and reflect for a moment -- how would you decide your question? What must be in place for you to say, "yes this model is preferred over that one?" You have already ruled out better predictive power, and you have ruled out "easier to use." What sort of criteria could possibly remain? Perhaps some kind of appeal to authority, e.g., religion?

One more example to finish this discussion. Consider that for some few hundred years Galilean/Newtonian physics was the most accurate model of the universe. Was it "true?" Not compared to modifications introduced in the past century or so. Is our current understanding of the universe with special/general relativity "true?" We already know that's not the case, because the models fail under certain conditions. Does it matter that we don't have a "true" model of the universe? I mean, philosophically, yes it matters, it gives a reason to keep searching. But practically, i.e., since we don't (yet) use black holes in our every day life, what difference does it make?

I say that to steer you towards a conclusion, if perhaps not an answer. If there is no room in your worldview to accept "the scientific method" then how are such questions (heliocentric vs geocentric) ever resolved?

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Generally such questions are resolved from a pragmatic point of view. That is, "the scientific method" resolves questions of skepticism because that is the dominant view of society. We search for models with better explanatory power, and replace them as needed. That is all that can be said with authority; we use a heliocentric model because it has the best explanatory power. Whether or not this is actually "true" is a (number of) philosophical questions that can't ever be fully, completely, 100% resolved -- there will always be room for skepticism, and it is up to your own philosophical foundation to resolve. (and other people will have different foundations that will object to your skepticisms, etc)

Answer 4

Is Rabbi Schneerson indeed correct: that we have no absolute way to determine whether the Earth revolves around the sun or the other way around and that his belief is no less valid than the one accepted by scientists?

There are incorrect premises to this question, and a fundamental disconnect.

The Rabbi is correct: physicists do not accept one view as valid and hold the other not to be. So this part of your question, based upon "scientists" only regarding one thing as valid, has an incorrect premise.

A non-rotating frame of reference is considered a valid way of observing, and a rotating-frame of reference is considered a valid way of observing. Observing from the viewpoint of Terra is considered valid; and observing from the viewpoint of Sol is considered valid. The mathematics may be a whole lot more difficult, but the whole point of relativity is that these are valid views. Difficulty does not render something invalid.

There are many physics textbooks that make this point. Picking one at random, I select In Search of a Theory of Everything: The Philosophy Behind Physics by Demetris Nicolaides, physics professor at Bloomfield College, New Jersey. Dr Nicolaides addresses this very issue on page 51, and calls geocentric and heliocentric rotating frames of reference "equally correct" for 2-body systems far as modern physics is concerned.

It's not even true that a geocentric reference frame is not useful or not helpful, and only a heliocentric one is, as some have claimed. It actually is useful and helpful. Space agencies and astronomers regularly use geocentric, and even selenocentric, models for various things. A Selenocentric Reference Frame is used, as noted in this paper for example, for laser ranging measurements using reflectors on Luna. The Geocentric Celestial Reference System, a general relativistic space-time coördinate system centred on Terra, was adopted by this IAU resolution in 2000.

However, saying that physics allows multiple ways of viewing a 2-body system is not the same as the Rabbi saying:

the sun revolves around the earth

That's not a claim about some abstract, thought experiment, 2-body system in physics. That's a direct claim specifically about the real universe, about Sol and Terra, and an indirect claim about all of the other bodies in the Solar system.

To start with: in both the geocentric and heliocentric frames of reference, Venus and Sol are still orbiting their common barycentre. (To keep this answer short, like Demetris Nicolaides I'm not fussing too much about the difference between orbiting the centre of Sol and orbiting a common barycentre that is inside, or even slightly outside, Sol.)

And yes, the Rabbi is claiming things about the Solar system, and that one can check that scientists support his view, as his first letter says:

Of course, on the elementary and high school level, science in general, and the so-called Solar System in particular, is taught from relatively simple textbooks, and the change in the scientific attitude towards the subject under discussion is not emphasized. But, as stated, it would be quite simple to verify it with any scientist who knows this particular field.

Whilst you can consult modern physics textbooks that confirm that the Rabbi's 1970s account of modern physics and 2-body problems still holds, half a century later; the Rabbi's furtherance, that modern physics is saying that the Solar system can be equally correctly regarded as either heliocentric or geocentric, is flawed. The Rabbi has made a leap that is not, in fact, justified by modern physics.

From the not-quite-so-relatively-simple textbooks one can in fact verify that the Rabbi is wrong about modern physics; and his belief is not in accordance with it.

From the point of view of modern physics, the Solar system is a very complex, chaotic, N-body problem. A discussion of this can be found in textbooks such as Relativistic Celestial Mechanics of the Solar System by Sergei Kopeikin, Michael Efroimsky, and George Kaplan. (In fairness, note that Rabbi Schneerson writing in the 1970s could not have known about chaos theory, barely invented and not fully developed back then, or some of the other things developed over the past few decades that are discussed in that 2011 textbook. But you did say current scientific knowledge.)

Similarly, the 2014 Encyclopedia of the Solar System (edited by Tilman Spohn, Doris Breuer, and Torrence Johnson) in chapter 3 recounts that long term numerical modelling of the Solar system, over the scale of gigayears, has in a small percentage of cases ended up with some planets colliding or escaping the Solar system entirely.

So the Solar system is not viewed as either a heliocentric or a geocentric 2-body system by modern physics; and the statement that "the Sun revolves around the Earth" is not aligned with the view of how the Solar system works espoused by modern physics. But neither is the statement that "the Earth revolves around the Sun". The best Rabbi Schneerson interpretation of the understanding of the Solar system in modern physics would be "It's bloody complex.", to which one might add "… and there's a chance that they don't even keep revolving.".

Answer 5

The following quote from Einstein is the principle of equivalence for which this discussion is incorrectly stating. Two unequal masses orbiting each other do not provide 'physically exactly equivalent' frames on their surfaces. Also, since the orbits are also elliptical, there is no point on any surface that experiences perfectly uniform acceleration, which is another condition stated by Einstein. Hence, this whole argument is invalid.

But we arrive at a very satisfactory interpretation of this law of experience, if we assume that the systems K and K' are physically exactly equivalent, that is, if we assume that we may just as well regard the system K as being in a space free from gravitational fields, if we then regard K as uniformly accelerated. This assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual theory of relativity forbids us to talk of the absolute velocity of a system; and it makes the equal falling of all bodies in a gravitational field seem a matter of course.

— Einstein, 1911 "On the Influence of Gravitation on the Propagation of Light" §1,¶3

Answer 6

The question of whether the sun revolves around the earth, or vice versa, has nothing to do with the Theory of Relativity. It has everything to do with gravity, which allows only one conclusion. I will discuss relativity below, and begin by explaining the correct answer.

Newton’s Law of Gravity, one of the most famous discoveries in scientific history, is F=Gm₁m₂/d². Here m₁ and m₂ are two masses, d is the distance between them, F is a force which acts on each mass, directed toward the other, and G is a constant. In the case of the earth m₁ and the sun m₂, the sun experiences a force F pulling toward the earth. From Newton’s law of motion, F=ma, the sun accelerates toward the earth by F/m₂. The earth experiences the same force, pulling toward the sun, so it accelerates by F/m₁. The sun has a mass of about 1030 kg, about 333,000 times the mass of the earth. That means that F/m₁ is 333,000 times larger than F/m₂. So the earth’s acceleration toward the sun is far greater than the sun’s toward the earth. The situation is not symmetrical. It is not a matter of opinion, despite Schneerson’s “firm belief.”

To produce a stable orbit requires a precise relative velocity of the two bodies. This is the actual case for the sun and earth, as evidenced by the fact that the earth has not fallen into the sun, which would happen if the earth’s orbital velocity was too small. Nor has the earth flown off into space, which would happen if the earth’s orbital velocity was too large. The earth is in a stable orbit, in accordance with Newton’s laws. Its orbital velocity, which can be measured, is about 30 km/s. https://en.wikipedia.org/wiki/Earth%27s_orbit

In general, it is approximately true that the lighter body orbits the heavier one. The strictly correct answer, which can be worked out mathematically from Newton’s laws, is that the two bodies rotate around their mutual center of gravity, called the barycenter. https://en.wikipedia.org/wiki/Barycenter When one body is much, much heavier than the other, the mutual center of gravity is often somewhere inside the larger body. That is the case with the earth/sun system: the center of gravity is 449 km from the center of the sun, which has a radius of 696,000 km. The verbal simplification, that the light body is the one doing the rotating while the heavy body remains still, is almost exactly correct.

The basic mathematics of planetary motion, along with a significant amount of empirical evidence, emerged from the work of Copernicus, Galileo, Brahe and Kepler by 1630. https://www.physics.unlv.edu/~weistrop/ast104s05/ch4nic.htm Newton’s Laws of motion, including gravitation, were published in 1686. It is true that Newton could not explain why gravitational attraction occurred, but his law nevertheless described how it worked with great accuracy. That provided sufficient insight to prove that the earth, and all the other planets, revolve around the sun and not the reverse. [https://education.seattlepi.com/newton-explain-planetary-motion-6264.html] When Schneerson claimed that relativity theory settled the question of planetary motion, “half a century ago” as he was writing in 1975, his time line was off by about a factor of seven. The issue was actually settled before 1700, long before Einstein was born. Schneerson ignores all the previous developments in the field.

Schneerson’s claims about relativity can be refuted in more than one way, the simplest of which, perhaps, is reducto ad absurdum. If one thinks that relativity justifies a belief that the sun revolves around the earth, then exactly the same argument can be used to justify a belief that the earth revolves around the moon. As Schneerson says, both views “have equal validity.” The same logic leads to a belief that the sun revolves around Halley’s Comet. The earth revolves around the International Space Station, or any other satellite of your choice. An airplane in flight is stationary while the entire earth moves rapidly beneath it, since both plane and earth are equally valid vantage points. The earth conveniently slows down when the pilot wants to land.

These are obvious absurdities that no one believes. Yet Schneerson suggests, in the case of the sun and earth, that it is a matter of “personal choice and belief” how the orbital dynamics actually function. The reducto ad absurdum tells us that something is seriously amiss with his reasoning.

In Einstein’s book “Relativity,” he states carefully what he calls the “principle of relativity.” The word “principle,” as opposed to “theory,” is very important. They are not the same thing. In fact the principle is one of the postulates on which the theory is based. Here are some excerpts from chapter V, page 13 [Crown Publishers, New York 1961].

“If K is a Galilean co-ordinate system, then every other co-ordinate system K’ is a Galilean one, when, in relation to K, it is in a condition of uniform motion of translation.”

In preceding paragraphs, he defined a “Galilean” coordinate system as one whose motion is that of uniform translation, i.e., its motion is in a straight line and it is neither accelerating nor rotating.

“Relative to K’ the mechanical laws of Galileo-Newton hold good exactly as they do with respect to K.” The italics are mine. What is invariant here is the laws of physics, not the verbal descriptions made by observers in two different locations.

“We advance a step farther in our generalization when we express the tenet thus: If, relative to K, K’ is a uniformly moving co-ordinate system devoid of rotation, then natural phenomena run their course with respect to K’ according to exactly the same laws as with respect to K. This statement is called the principle of relativity.”

Again the point is very clear. What the principle asserts is the invariance of the laws that govern the motion of objects. This principle does not offer the slightest justification for saying that the statement “the earth revolves around the sun” is equivalent to the statement that “the sun revolves around the earth.” In fact, just the opposite: the principle indicates that Newton’s Law of Gravity is equally true on the earth as it is on the sun. The first statement – the earth revolves around the sun - is consistent with Newton’s Law of Gravitation. The second statement is not.

Before leaving the subject of relativity, I would like to mention the next paragraph, which begins as follows:

“As long as one was convinced that all natural phenomena were capable of representation with the help of classical mechanics, there was no need to doubt the validity of the principle of relativity.” Again, italics mine. Einstein is saying here that the principle of relativity was accepted by physics long before his own time. He did not invent it; not even close. It was already a principle of classical mechanics, at least as old as Newton.

The nineteenth century saw the development of electrodynamics and optics, and the deduction by James Clerk Maxwell that the vacuum speed of light was a constant. This, too, was established science before Einstein. But the two principles appeared to contradict each other; as he says, in that same paragraph, “it did not appear impossible” that the principle of relativity was, in fact, wrong. It was Einstein who removed this doubt. The Theory of Relativity explains what sort of universe permits both the principle of relativity and a constant speed of light. The resulting picture, explained by Einstein with compelling logic, is the one unversally held by physicists today.

None of that has anything to do with the motions of the planets. To be very precise, relativity makes a small correction to Newton’s laws of motion. For objects that move much slower than the speed of light, such as planets, this correction is insignificant.

I will acknowledge one truth about Schneerson’s claims: if the only thing you know about physics is the principle of relativity, it would be quite difficult to understand how the solar system works. It would be especially true if the only visible celestial bodies were the earth and the sun, and one did not have observations of the other planets. Galileo, in Dialog Concerning Two World Systems, offers empirical evidence that all the other planets orbit the sun. From this knowledge, even though he was lacking a theory of gravity, he made a strong case in favor of a heliocentric solar system. He reasoned that placing the earth at the center of the solar system, and requiring all the other celestial objects to revolve around it while somehow also revolving around the sun, did not make any geometric sense. He also found evidence that Jupiter had moons of its own, further reinforcing the idea that not everything revolves around the earth. Nevertheless, it was Newton’s Law of Gravity that formed the strongest proof that the solar system revolves around its center of mass, which is of course its heaviest object, the Sun.

All of Schneerson’s analysis in his second letter ignores the law of gravity and all its implications. It also, as I have said, misinterprets Einstein and the principles on which his theories are based. It uses simple sentences as a substitute for accurate scientific reasoning. He considers the sentence “the earth revolves around the sun,” and then uses his cartoonish view of relativity to justify exchanging the words “earth” and “sun.” That’s not how science works, at least not for about the last four hundred years. As I pointed out, continuing such a line of reasoning quickly leads into absurdities.

That Schneerson’s misinterpretations are theologically convenient, given his stated belief in the scientific accuracy of an ancient religious text, should not escape our attention.