Q: Is geocentrism really so wrong? Is the Sun being at the “center” (i.e. the Earth orbiting the Sun) just an arbitrary reference frame decision, and no more true than the Earth being at the center?

Physicist: When you walk around in this big crazy world, there aren’t any immediate reasons to suspect that the ground under your feet is doing anything more than sitting perfectly still (ring of fire notwithstanding).  Given that, when you look up at the sky and see things pinwheeling about; why not assume that they’re moving and that you’re sitting still?  On its face, geocentrism makes sense.

But there are a lot of physical phenomena that poke holes in it pretty quick.  For example, Foucault pendulums (more commonly known as “big pendulums“) swing as though the Earth were turning under them and in a way that exactly corresponds to the way everything in the sky turns overhead (not a coincidence).

The classic way that heliocentrism (the idea that the Sun is at the center of the solar system) is demonstrated to be better that geocentrism (the idea that the Earth is at the center of the solar system) is by looking at the motion of the other planets.  This was essentially what Copernicus did; point out that with the Earth at the center the motions of the other planets are crazy, but with the Sun at the center the motion of the planets (including Earth) are simple ellipses.  His original argument was essentially just an application of Occam’s razor: simpler is better, so the Sun must be at the center.

Occam’s razor is a great red flag for detecting ad-hoc theories, but it’s not science.  With that in mind, it’s impressive how much Copernicus got exactly right.  Fortunately, about a century and a half after Copernicus, Newton came along and squared that circle.  Newtonian physics says a lot more than “gee wiz, but ellipses are pretty”; it actually describes exactly why all of the orbits behave the way they do with a remarkably simple set of laws for gravity and movement in general.  Newtonian physics goes even farther, describing not just the motion of the planets, but also why we don’t directly notice the motion of our own.

If we still assumed that the Earth was sitting still in the universe, physicists would have spent the last couple centuries desperately trying to explain what’s hauling the Sun (and the rest of the planets) around in such huge circles. We’d need a bunch of extra, mysterious forces to explain away why the center of mass in the solar system doesn’t sit still (or move at a uniform speed), but is instead whipping by overhead daily.

What follows is a bunch of Newtonian stuff.

Position and velocity are both entirely subjective, but acceleration is objective.  What that physically means that there is absolutely no way, whatsoever, to determine where you are or how fast you’re moving by doing tests of any kind.  Sure, you can look around and see other things passing by, but even then you’re only measuring your relative velocity (your velocity relative to whatever you’re looking at).  So, hypothetically, if you’re on a big ball of stuff flying through space, you’d never be able to tell.  Acceleration on the other hand is easy to measure.

Whether you're juggling in a place (upper left), a different place (upper right), or even a different speed (lower left), the laws of physics are indistinguishable.

The laws of physics are exactly the same regardless of where you are or how you’re moving.  Therefore there is no experiment that can tell you your “true” position or velocity.  Acceleration however does change things.  That’s why you can juggle in exactly the same way in a place (upper left), a different place (upper right), or even a different speed (lower left), but you can’t juggle, or you have to juggle differently, when accelerating (lower right).

At first blush it would seem as though there’s no way, from here on Earth, to tell the difference between the Earth moving or sitting still.  If the Earth is sitting still, we wouldn’t be able to tell.  If the Earth is moving, we also wouldn’t be able to tell.  But we’re doing more than just moving; we’re moving in circles and as it happens traveling in a circle requires acceleration.  The push you feel when you speed up or slow down comes from the exact same source as the push you feel when you turn a corner or spin around: acceleration.

The Moon orbits the Earth, and the Earth sorta orbits the Moon by wobbling.

The Moon orbits the Earth, and the Earth sorta orbits the Moon.  By wobbling.

If the Earth were “nailed to space” and never accelerated, then we‎’d only have one each of the lunar and solar tides.  If the Earth never moved, then the Moon’s gravity would pull the oceans toward it and that’s it.  But the Earth does move.  The Moon is heavy so, even though the Earth doesn’t move nearly as much, the Earth does execute little circles to balance the Moon’s big circles.  The Moon’s big circles generate enough centrifugal force to balance the Earth’s pull on it (that’s what an orbit is), and at the same time the Earth’s little circles balance the Moon’s pull on us.

If the Earth were nailed to the sky, then the Moon's gravity would cause only one tide a day.  We experience two because the Earth and Moon both orbit the same point (red dot).

If the Earth were nailed to the sky, then the Moon’s gravity would cause only one tide a day as the seas are pulled toward it. We experience two because the Earth and Moon orbit each other around the same point (red dot).  The swinging of the backside of the Earth means that the water on the far side is “flung outward”.

The same basic thing happens between the Earth and the Sun.  Things closer to the Sun orbit faster and things farther away orbit slower.  But the Earth has to travel as one big block.  The side facing the Sun is about 4,000 miles closer, and traveling slower than it would if it were orbiting at that slightly lower level.  As a result, the Sun’s gravity “wins” a little in the “noon region” of the Earth and we get a high tide (pulled toward the Sun).  The side facing away is moving a little bit faster than something at that distance from the Sun should, so it’s flung outward a little more than it should be and we get another high tide at midnight.  These are called the “solar tide” and they’re harder to notice because they’re about half as strong as the lunar (regular) tides.  That said, the solar tides are important and they exist because the Earth is traveling in a circle around the Sun.

Long story short: If the Earth were stationary (geocentrism) then we’d have to come up with lots of bizarre excuses to explain why Newton’s laws work perfectly here on the ground, but not at all in space, and we’d only have one solar and lunar tide a day.  If the Earth is moving (specifically: around the Sun), then Newton’s simple laws can be applied universally without buckets of caveats and asterisks*, and we get two lunar and solar tides a day.

*or even †’s.

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12 Responses to Q: Is geocentrism really so wrong? Is the Sun being at the “center” (i.e. the Earth orbiting the Sun) just an arbitrary reference frame decision, and no more true than the Earth being at the center?

  1. micha says:

    Einstein already made up those excuses: General Relativity handles non-inertial frames of reference.

    The reason why geocentrism isn’t very useful is because it replaces the earth’s spin with a weird gravitational field that pulls everything else in the universe around in the opposite direction. Which would both complicate the math terribly, it would beg for explanation — where did this gravity come from?

    But geocentrism is not exactly false.

    NB: Heliocentrism is out. Barycentrism is what gives the simplest description of the solar system. Admittedly the two differ by the distance between the center of gravity of the sun and the center of gravity of the solar system as a whole, which isn’t much. But it it is there.

    I was kind of disappointed by this answer not addressing either of these issues.

  2. P says:

    micha ,it sort of did with earth moon wobble thus same thing happens between the sun and the rest of the solar system.

  3. micha says:

    And the issue of General Relativity deeming geocentrism as valid, if a poor and unuseful frame of reference? That’s the issue generally raised on religious cites, and answering with Newtonian physics doesn’t really address them.

    Speaking from a religious point of view, General Relativity makes the universe further from what they desire. If every frame of reference is equally valid, then our location here on earth is even less unique. The fact that geocentrism is valid may allow a literal read of scripture, but so does idiom. Neil deGrasse Tyson has no problem talking about sunrise, even though he knows it’s caused by the earth’s spin. It’s just idiomatic language. But if you make geocentrism valid because anything is valid, then nothing is special and we are even further from the center of the universe than Copernicus thought.

  4. Elvince ager says:

    On some other threads it has been discussed that in General Relativity the geocentric and heliocentric reference frames are equally valid. If you open any Earth Science or Introductory Astronomy textbook you will find the Aberration of Starlight discovered by James Bradley in 1727 and Parallax presented as evidence that the Earth is moving around the Sun.
    So textbooks are establishing the heliocentric reference frame as the preferred reference frame over the geocentric reference frame. In the Newtonian gravitational model this is correct, but this violates General Relativity since all reference frames are equally valid.
    The question then is – what are we supposed to be teaching students in school? Most are not ready for the complexities of relativity theory, but aren’t we misleading students if we teach that parallax is evidence the Earth orbits the Sun?
    Is there any conclusive evidence out there that cannot be interpreted in another way that requires that the Earth is orbiting the Sun? Any such evidence would immediately violate GR by establishing a preferred reference frame – right?

  5. Rob says:

    “…heliocentrism (the idea that the Sun is at the center of the solar system) is demonstrated to be better that geocentrism (the idea that the Sun is at the center of the solar system)…”

    Whoops!

  6. MadhuS says:

    Moving in circle requires acceleration. Since earth is in constant orbit around the Sun, why don’t we feel the acceleration? is this acceleration g ? 🙂 or is it that the orbital path is big so we don’t feel a thing when the earth accelerates? or, as GR says are we moving actually in a straight line around (?!) the Sun? Thanks

  7. The Physicist The Physicist says:

    @MadhuS
    The acceleration balances the acceleration caused by the Sun’s gravity, which is what keeps our orbit stable. Since all of the forces on the Earth are balanced, we don’t feel a net force in any direction.
    From a GR perspective, the Earth is traveling in a straight line through spacetime (though clearly not a straight line through space alone).

  8. pablo says:

    Geocentrism would be theoretically as silly as putting myself at the centre of universe.
    But as we recognise what is really going on, earth going round the centre of sun plus planet solar system centre of gravity, then in turn that going round centre of whole galaxy of stars , then our milkyway galaxy going around in some sense the centre of the cluster of “near” galaxies etc.

    Copernicus gets a bunch of nearly circular ellipses which is totally much simpler than horrid spirographic mayhem. Then Newtons derivation of the elliptic orbits. It is really very clear what goes around what.

    Perhaps in a very sophisticated machian cosmology perspective one may try and have physical laws for general reference frames. But if you really follow the physics and advanced mathematics of this journey, then at the end you are not suddenly going to get all sentimental about the earth ! No, You might as well choose the nearest football or proton or the moon.

  9. Angel says:

    @micha & Rob:

    General Relativity tells us that all frames of reference are equally valid, but that statement DOES NOT prohibit us from assigning a preferable reference point. In fact, without a convention, it would be impossible to study physics; or rather, it would be way too complicated, and that is unneeded. Heliocentrism is more natural to laws of physics than geocentrism is. Although now we know the Sun is not the center of the universe either. It’s all about orbits within orbits.

    You must know that everything in science is pure convention. There is nothing special about the meter as unit of length (well, now it is). We could very well be using refrigerators as unit of length. That doesn’t make any difference except for the fact that meters are simply better for humans (1: because refrigerators are freaking heavy, 2: because the meter is now defined by a natural constant). Get this: objects don’t have a length as a property. I mean, you can never measure an object to be 0.5 meters long, or 25 m squared. You can only compare its length to the length of another object which we consider the fixed standard (in our case, the meter). That is how science metrics work — well, actually, I suppose it is more complicated than that, but if you want to get down to the basics, that’s it. Humans observe physical phenomena, and the assign those phenomena as fixed standards, and then everything else is compared to that. Geocentrism isn’t better than heliocentrism when it comes to human observations. But maybe if we were of the size of bacteria (or if we were bacteria), then geocentrism could make more sense. Why didn’t we choose the radius of a helium atom to be the standard unit of length? Well, humans can’t see individual atoms and distinguish them, to start with. But we could do that if we were of the size of cells. But because we are human sized and not cell sized, we are stuck with other units like the meter and the inches.

  10. peace says:

    Really gravoty os kust an effect of curved space-time and neither helio nor geocentric model are correct. Both orbit a central point equal to the gravational center.

  11. martin says:

    the sun is the solar system the planets are just a little bit of left over materials. thats how we know its at the center because the solar system would survive without the earth. but not witout the sun.

  12. Guest says:

    “This was essentially what Copernicus did.”

    True, but he did plagiarise the idea from Aristarchus, millenia before. I believe he even put a reference to Aristarchus in his original manuscript which he later removed.

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