Why the Sun doesn’t go around the Earth

January 18, 2015 • 3:15 pm

Earlier I asked readers to think about (and comment on) why, if motion is relative, it still makes more sense to say that the Earth orbits the Sun than vice versa.  I had my own take, but the answer is not super-obvious. So I asked Official Website Physicist™ Sean Carroll for the answer, and here’s his response.

The short answer would be that it is possible to choose whatever coordinate system you like, including ones centered on the Earth, and then say “in that coordinate system the Sun goes around the Earth.” Hell, it’s possible to choose coordinate systems in which neither the Earth nor the Sun move at all! But some coordinate systems are better than others, and for understanding Solar System dynamics, an Earth-centered one is particularly dumb. If some Orthodox Jews want to argue that they have the right to be dumb, who am I to stop them?
Somewhat more careful (dare I say “rabbinical”?) discussion by me here:
Note, however, that while you can say “I am using a coordinate system where the Earth is at the center,” you can not say “Coordinate systems where the Sun [or the Solar System’s barycenter] is at the center are wrong.” So “geocentrism” is flatly incorrect.
Also, not to belabor the obvious: early geocentrists were not relying on coordinate invariance, and attempts by modern ones to save the old ideas are kind of pitiful.
This comes close to the response of Torbjörn Larsson, who gets a Warm Handshake from Professor Ceiling Cat™ for best explanation.

49 thoughts on “Why the Sun doesn’t go around the Earth

  1. In addition to Sean Carroll’s remarks, it’s not really just about the Sun and Earth, it’s about the other planets.

    If you just had Earth and the Sun you could centre your coordinate system on either readily enough.

    But, the question was, do the other planets go round the Sun or do they go round the Earth?

    There is no way you can get the planets to go round the Earth, in any simple fashion, even if you centre your coordinate system on Earth — or, rather, if you do try, you need all sorts of epicycles.

    But then there is no way of explaining epicycles by any sensible theory of gravity, whereas you can explain Sun-centred ellipses with Newton’s gravitational law or by General Relativity.

    1. That was my thinking–you have to look for some system that “works” for all the bodies affected by it…but I guess that’s just too simplistic.

    2. But then there is no way of explaining epicycles by any sensible theory of gravity

      I’m no expert by any means, but my impression is that general relativity is that theory. By whirling a massive Sun around a stationary Earth, you’d generate gravitational waves and frame-dragging effects that could in principle explain the motions of all the planets in that coordinate system (although the math would be intractable). They’d all be tracing convoluted geodesics though that pathologically warped spacetime.

      Or to turn it around, it was the presumed interchangeability of coordinate systems that led to the predictions of gravity waves, frame-dragging, and so on that have since been experimentally verified.

    3. Yeah. If your goal is to model what is actually happening rather than merely devise a coordinate system that enables you to predict locations you have to consider the forces, accelerations and inertia the individual components of the system are experiencing.

      Something like, if you put accelerometers on each of the planets what model would best explain the readings you’d get? Epicycles? Would the readings indicate that Mars accelerated in one direction for a while, slowed down and then accelerated in the opposite direction? Imagine the force necessary to repeatedly reverse the orbit (or whatever you want to call the path of travel in your model) of a planet, even one the size of Mars.

      1. If you replaced Mars with an accelerometer following the same orbit, it would read zero. Planetary orbits are geodesics in curved space and feel no net acceleration.

        This would still be true even in a coordinate space convoluted enough to produce epicycles.

  2. Congrats Torbjörn! I actually read Torbjörn’s answer thinking it made most sense. I didn’t have the intellectual fortitude today to attempt pondering it myself.

  3. We have more than just the Earth and the Sun to worry about. If the Sun goes around the Earth, then so must all the other planets, “fixed” stars, and distant galaxies. In fact, the further away something is from the Earth, the fastest it would have to move in order to circle around it entirely in just around 24 hours.

    The distance would only have to be around 7.6 light hours, just over 8 billion km, for something to have to go the speed of light to go around us in that time. Voyager 1 is over twice as far as that from us, so it would need to be moving more than twice the speed of light in order to move fully around us once per day.

    It seems sensible to apply Occam’s razor and adopt the coordinate system that requires the minimal overall motion of the observable universe.

    1. Well you just end up with epicycles – the ancient system of calculating ephemera which is so dastardly complex compared to using a sun-centered frame of reference.

      1. I remember reading somewhere that the old geocentric model with epicycles was not too inaccurate about predicting the locations of planets.

        1. Actually, the epicycles can be shown to be equivalent to a Fourier Series which becomes increasingly accurate as the number of terms is increased.

    2. Mark, I don’t think it works quite that way. Consider that the Sun is around 8 light minutes from Earth, yet both are about 4 light years from Alpha Centauri. So, whether you accept geocentrism or heliocentrism, you’re still going to end up with faster-than-light travel by your method of calculation. I THINK that, vis-a-vis distant objects, the solution is Earth rotating on its axis versus Earth rotating around the Sun (or Sun around the Earth); but perhaps someone truly knowledgeable can enlighten us.

    3. If you want to apply the Occam’s razor, which is indeed a sensible idea, then use the barycenter to center the coordinate system. The barycenter in our solar system is most of the time in the near vicinity of the sun, but not always within the sun. If we were living on a planet belonging to a multiple stars system, this would probably be our first choice, as in such a place all other choice for the center make a mess much worse than the Ptolemean epicycles

  4. Wait…is Professor Ceiling Cat actually trademarked now?

    Suddenly I have Professor Ceiling Cat plushies and Hili and Cyrus action figures (or inaction figure in Hili’s case) dancing in my head.

  5. Astronomers use earth centred co-ordinate systems all the time. It is the only way to work out sanely where and when something should appear in the sky.

    As Mark Hanna points out having everything revolving around the Earth leads to some “interesting” results. This is because such a revolving co-ordinate system is not an inertial frame of reference, and then to explain the motion you have to do all sorts of mathematical gymnastics with General Relativity, horrible tensors, ugly manifold manipulations and complex partial differential equations. Anyone choosing to do this over the simple Newtonian model is obviously insane. 🙂

  6. If two objects, A and B move in uniform motion relative to each other, which one travels faster – with consequent greater mass and less volume than the other?

    1. Assuming equivalent rest masses and volumes, in the frame of reference of A, the answer is B and, In the frame of reference of B, the answer is A.

  7. I’ve tried unsuccessfully to envisage a coordinate system in which neither the earth nor the sun move at all.Yes,if the earth’s orbit around the sun was circular, that would be easy, but the earth sun distance changes constantly, which is where I fall down. It’s probably my advancing years. Perhaps one of your contributors could explain in words of not-too-many syllables.

    1. I suspect “move rotationally” was intended. As you suggest, the proposed coordinate system would still have the earth-sun distance increase and decrease periodically.

          1. And the sun’s (rotation, that is). We can point cameras at it and watch it rotate, so it would be difficult to explain how it’s not moving with respect to us.

  8. Frames of reference vary all the time. Even the sun’s position isn’t really quite fixed because it’s affected by the planets, but the sun is so massive that the planets only make the sun gyrate about a fairly small orbit which is insignificant even when compared to the distance between the sun and Mercury. So for our solar system’s dynamics a stationary sun is a great point of reference. When flying aircraft I like to have the earth as the stationary point of reference; that makes the GPS calculations much easier.

  9. If being at the center implies being the one that moves least, the only way the Earth can be at the center is if our understanding of gravity is all wrong. And it’s not . . . because, well . . . Cassini, Rosetta and every other space mission.

  10. There is a well-made series on YouTube that completely annihilates geocentrism, and thereby conveys a lot of interesting astronomy.

    CoolHardLogic: Testing Geocentrism // Part 1

    There are 9 parts already, which seems like way over the top, but it’s just an excuse to explain the scientific method (hypothetically assuming geocentrism was true and see what happens when you do the math) and to look at the science (and how we know what we know) from all angles.

  11. It would be more accurate to say that the Earth and Sun rotate around their common center of mass (barycenter). However since the Sun is so much more massive than the Earth the barycenter is a lot closer to the Sun than the Earth, and is usually inside the Sun itself.

  12. I’m curious – how would Earth’s and Sun’s positions be made fixed? Can Sean – or someone else – comment on this briefly?

  13. Solar system models work just fine regardless of which planet (or the sun) is stationary. And everything else in the solar system will eventually make its way around (though in a bizarre fashion). You can also maintain the earth and sun as static in relation to one another, the other planet orbits just appear to slow down and have their orbits expand and contract in concert since their motion is relative to the earth-sun which should be getting further and closer together.

      1. Absolutely, gravity and the sizes of planets remaining constant are issues too. But as far as perspective of the orbits are concerned, instead of the earth moving closer to the sun, all the other orbits appear to expand. Instead of the earth moving away all the other orbits appear to contract.

  14. This makes me feel good that I’ve hit the nail on the head in past discussions about Galileo and the Church with religious people. I always pointed out that the Church claimed heliocentrism is wrong, not just that geocentrism was right. Game over, there’s no rescuing it by pretending ancient iron age writers were foretelling relativity via Divine intervention.

    1. Also if one wants to get relativistic, he not just posit that I am the center of the universe? or that you are? When I walk or drive my car, I stay in place and cause the Earth to roll under me.

      Since very point in space is equidistant from the locus of the Big Bang, we can each claim that we literally are the center of the universe anyway.

  15. Speaking of frames of reference, I was curious what the path of the Moon relative to the sun looks like. I made a diagram to scale using CAD software and found that the Moon does not seem to go in an ellipse around the Earth, but rather in a low-amplitude sinusoid along the ellipse of Earth’s path around the sun.

    So I wondered, why do we think the Moon goes ’round the Earth? How do we know the Moon isn’t really just orbiting the Sun with the Earth wobbling its orbit?

    But here’s how my tiny mind works: I figured I would have heard by now if astronomers thought that was a thing. Also, without any exposure to gravitationl calculations beyond 12th grade Physics, I assumed the sinusoid is an illusion and Earth orbit is the simplest way to explain how the Moon always shows the same face to the Earth and also gets ahead of the Earth on its path 12 times per year.

    My point being, one doesn’t have to understand much about science in order to trust the folks who know what they are talking about. If a lay person thinks of something the scientists have “missed,” it’s important to evaluate whether s/he is the one who is missing something. And this is why if a person will not trust science and will not consider that s/he might be mistaken in his or her assumptions, then there simply is no foundation for reasoning with that person.

    1. The Moon and the Earth revolve around their barycentre (which is about 3/4 of the distance from the Earth’s centre to its surface). As they do so, the Earth and the Moon also revolve around the barycentre of the Sun/Earth/Moon system (ignoring the effects from outide this system). As a result, both the Earth and the Moon follow a sinusoidal path around the Sun, with the Earth’s sinusoidal path being much lower in amplitude than that of the Moon.

  16. Considering only the Sun/Earth system the notion that the Sun goes around the Earth is preposterous. According to Newton’s laws (which are accurate for this problem; relativistic effects can be handled by perturbation theory), the Sun and the Earth revolve around a common center of mass. However, the two body problem can be shown to be described by an equivalent one body problem with a planet of reduced mass mM/(M+m), m being the mass of the earth and M being the mass of the Sun, revolving around a body of mass M where the body of mass M is fixed in space. Since M >> m, the reduced mass is nearly equal to m so it makes no sense to consider the Sun as revolving around the Earth.

  17. I am not sure I agree with comments claiming that all coordinate systems (“frames”) are equivalent. This is true as far as linear, constant velocity motion is concerned, but not when rotation is involved. “All” rotating frames are by definition non-inertial, and hence any “non-rotating” frame is by definition “special” in a way rotating frames are not. “Inertial” frames are special because these are the only frames in the which the laws of physics do not require any corrections/modifications.

    The question that arises from the previous discussion is which frames are “rotating” and which are not. This is what is called a “deep” question, so that the only valid answer (though seemingly circular) seems to be that we call a frame inertial (and hence non-rotating) if the laws of physics do not require any corrections in that frame.

    Under that definition, it does seem clear that the heliocentric frame of reference is closer to being inertial than the geocentric one, since the “corrections” require to correct for rotation in the geocentric frame are much larger than those required in the heliocentric frame.

    1. Again I’m no expert, but I thought it was a foundational assumption of general relativity that rotating frames are just a special case of accelerated frames, which in turn are just curved space.

      So if you hold the Earth stationary and spin the entire universe around it, the resulting curvature of space exactly mimics the Coriolis effects you’d get from a spinning Earth in a stationary universe. The two frames really are equivalent in that sense, at least as I understand it.

      Of course the calculations are much harder in one frame than the other, but the answers ought to be the same in either case.

      1. The equivalence between accelerated reference frames and gravity used in GTR is for linearly accelerated frames only, not for rotating ones. In particular, the fact that you have to add Coriolis (and centrifugal) terms in rotating frames basically show that the “laws” of physics have changed [these terms are precisely the “corrections” I was talking about].

        The thought experiment you suggest is a variant of the so called “rotating bucket” experiment, first described, I think, by Ernest Mach well before relativity theory was developed. However, any claims of equivalence then require you to assume the results of this though experiment, which are by by no means obvious.

        1. The rotating bucket experiment was first described by Newton. Amazing to think that the first demonstration of general relativity took place more than three centuries ago.

  18. Frames with constant speed are equivalent; accelerated frames are distinct.

    When you wake up in a train, you can’t tell whether your train is standing and the next one moves, or your train is moving and another stands still. However, if you were awake all the time, you could feel either the acceleration or its absense. You may feel the acceleration even with your eyes closed.

    Rotation is a kind of accelerated movement, so it may be proven on its own.

  19. I’m going to be cheeky and say they technically swing around a common centre, like a binary system, but the sheer mass difference means that central spinning point is much closer to the core of the sun than to the core of any of its orbiting planets. It’s this principle that’s used to find exoplanets of extremely large size and gravitational pull, mainly by looking for small wobbles in the star’s position like a hammerthrower swinging their hammer.

  20. Because the apparent motion of the sun about the earth comes from the rotation of the earth, not from either revolving about the other.

    And, we know the earth does revolve around the sun because of orbital mechanics and measuring relative the rest of the galaxy.

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