What are the simplest experiments or calculations that give evidence that the earth revolves around the sun? Can you please explain them and reference the history? Many simple explanations such as this cite observations such as that relative position of two stars are observed from earth vary every night - which would not be true if the stars orbited the earth. But isn't the observation also consistent with a model where the stars orbit the earth but do so at different speeds, while the earth still orbits the sun? Simple explanations would be helpful.

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    $\begingroup$ Actually, as @MarkOlson notes, the geocentric view is actually quite correct for the Sun/Moon/stars, since we can view all motion as relative. The problem is with the planets: they clearly don't orbit the Earth in simple circles or even ellipses. You can compensate by using epicycles, but having the planets revolve around the Sun requires fewer artificial constructs. From there, it's a small leap to treating our solar system as heliocentric, instead of having the Sun and Moon orbit the Earth and the other planets orbit the Sun. $\endgroup$ – barrycarter Jul 9 '18 at 14:43
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    $\begingroup$ It doesn't If the Earth tried to move that fast, the stack of turtles holding it up would fall apart. $\endgroup$ – Carl Witthoft Jul 9 '18 at 17:06
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    $\begingroup$ @barrycarter That's basically Occam's Razor, which is useful as a guiding principle, but not really a proof. $\endgroup$ – Barmar Jul 9 '18 at 18:13
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    $\begingroup$ Does "simple" include accepting the modern theory of gravity? Because if you start accepting the relative masses of the sun and planets, "Everything orbits the earth" can't work. $\endgroup$ – swbarnes2 Jul 9 '18 at 21:00
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    $\begingroup$ The sun and the stars do orbit the earth--but the math is very complicated. The choice of reference frame (the earth is stationary, the sun is stationary, the mass-center of the solar system is stationary) is chosen for convenience, and "earth is stationary" makes the math really hard. $\endgroup$ – chrylis Jul 11 '18 at 2:20

The answer is ironic: Without good instruments, there is no evidence. The people who thought that the Sun went around the Earth were perfectly correct as far as the actual evidence went until the early 1700s and mid-1800s when two lines of evidence opened up that showed that the Earth moved.

Aberration of Starlight Wikipedia has a correct but over-complicated explanation. The easiest way to think about it is to imagine yourself at a stop sign in a car in the rain, and the rain is falling straight down. When you start moving, the rain's apparent direction of fall changes so that it appears to be falling from ahead of you and slanting down towards you. That's aberration.

In the early 1700s, the stars were discovered to be shifting position, and in 1727, James Bradley correctly identified it as abberation of starlight due to the motion of the Earth around the Sun. (For any star in the ecliptic, the Earth is moving towards it and some time of the year and away from it six months later.)

Parallax Wikipedia's article on parallax is better, and I refer you to it for details. Basically, if you hold up your finger before you and look at it with your left eye closed, and then with your right eye closed, it appears to jump with respect to the background -- the wall beyond or the trees outside of whatever. Switch back and for between eyes quickly to see it clearly.

As the Earth circles around the Sun, nearby stars also appear to shift their position relative to the more distant stars. A key point here is that there was good scinetific reasons to suppose that the stars were much smaller than the Sun. Seen through a telescope, stars showed disks and from those disks their distance could be deduced. They were close enough that if the Earth went around the Sun, parallax should have been observed. But it wasn't and the lack of any noticeable parallax was a strong empirical argument against Heliocentric theories.

In reality of course parallax exists, but the parallax of all stars is small, because they are much further away than was estimated from their disks. (The visible disks were actually diffraction disks and not true disks at all -- but it was not until nearly a century later that diffraction began to be understood.) Friedrich Bessel first measure the real parallax of a star in 1838.

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    $\begingroup$ The change in solar zenith was known from prehistoric times and convinced no one of a heliocentric world, so, no, it doesn't strongly suggest anything until you make other assumptions (e.g., that the Sun is massive w/respect to the Earth or that something like gravitation creates the motions of the heavenly bodies) that are incompatible with geocentrism. It's not direct evidence of heliocentrism. (It's worth remembering that the lack of a visible parallax was already in ancient times one of the arguments used against heliocentrism.) $\endgroup$ – Mark Olson Jul 9 '18 at 17:17
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    $\begingroup$ Part 9 of TheOFloinn's "The Great Ptlemaic Smackdown" details the historical accretion of the evidence you mention as well as Guglielmi's 1791 measurement of lateral Coriolis force showing rotation. The prior eight parts are also a fun read of the detailed replacement of geocentric with heliocentric models and probable evidence tampering against Galileo (by a justifiably angry large political institution). $\endgroup$ – Eric Towers Jul 9 '18 at 17:27
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    $\begingroup$ Good answer. We tend to think of early cosmologists as flat-earther,denying an obvious truth. In fact they had good technical arguments for believing in things like 'a fixed dome of stars'. Without a good understanding of optics, how point sources can appear much larger than they actually are, they thought distant stars would have to be vastly bigger than our Sun in order to show no parallax. $\endgroup$ – MichaelB76 Jul 10 '18 at 6:50
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    $\begingroup$ It is also worth noting the observation of phases of Venus (en.wikipedia.org/wiki/Phases_of_Venus) in 1610 which ruled out the possibility that planets orbit Earth, although it is consistent with both Earth orbiting the Sun and Sun orbiting Earth while other planets orbit the Sun. $\endgroup$ – Martin Modrák Jul 10 '18 at 12:03
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    $\begingroup$ @littleO: Not a stab in the dark, exactly, but it seems to have been a combination of him thinking the heliocentric hypotheses was more elegant -- which it was -- and his own cantankerous nature. (Even without the near sainthood later myth-makers gave him, he was a very good scientist for his age. But he was also one of the more unpleasant people around and enjoyed driving off his friends and benefactors. He probably liked it because it would annoy people.) Read Owen Gingerich's book on him -- or read the "The Great Ptlemaic Smackdown" recommended a dozen comments above. $\endgroup$ – Mark Olson Jul 11 '18 at 17:49

You cannot prove that the Earth orbits the Sun rather than vice versa because this goes very much against the grain of all frames of reference being equally valid (but some make a lot more sense than others). For example, it makes much more sense to use an Earth-centered, Earth-fixed point of view rather than a non-rotating geocentric, heliocentric, barycentric, or galactocentric point of view when modeling the weather or the tides. One could, for example, use a heliocentric or even galactocentric point of view to model the Earth's weather, but doing so would be beyond stupid.

On the other hand, when modeling the behavior solar system it makes much more sense to use a heliocentric, or even better, a solar system barycentric point of view. One could however use an Earth-centered, Earth-fixed point of view because all frames of reference are equally valid (in theory). Doing so would of course make the equations of motion quite ugly, and uglier yet on trying to make those equations of motion relativistically correct. A geocentric point of view nonetheless remains theoretically valid -- even for modeling the behavior of the Milky Way.

The problem with a geocentric point of view isn't that it's invalid (which it isn't). The problem is that advocates of geocentricism argued (and sadly, continue to argue) that this is the one and only valid point of view. This argument is invalid, because once again, all frames of reference are equally valid.

Note well: Just because inertial frames are special in some sense does not mean that non-inertial frames are invalid.

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    $\begingroup$ As an aside, one of my favorite tests of the orbital dynamics framework I developed for NASA's Johnson Space Center was to place an object in orbit about the Earth's moon, but to model the time evolution of that object from the perspective a Neptune-centered inertial point of view. It worked, at least for a short period of time. While all frames of reference are equally valid in theory, some choices are rather dimwitted compared to others due to numerical accuracy concerns. My choice of Neptune-centered inertial was intentionally dimwitted. $\endgroup$ – David Hammen Jul 9 '18 at 20:44
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    $\begingroup$ Nah, you just needed more numerical precision! :-) $\endgroup$ – Tristan Jul 9 '18 at 22:27
  • $\begingroup$ all frames of reference are equally valid Not true. Both Newtonian mechanics and general relativity distinguish between inertial and noninertial frames of reference. (In GR, an inertial frame is a free-falling frame.) $\endgroup$ – Ben Crowell Jul 10 '18 at 0:07
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    $\begingroup$ @BenCrowell while equations of motion in inertial frames are generally nicer, this doesn't make non-inertial frames invalid – just introduces fictitious forces. $\endgroup$ – Ruslan Jul 10 '18 at 6:54
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    $\begingroup$ Also, the basic postulates of general relativity apply in exactly the same way in all reference frames, inertial or otherwise. Newton's postulates do not. $\endgroup$ – Ken G Jul 10 '18 at 13:14

If you start with the idea that the planets, the sun, the moon and the earth are all bodies that all move through space, exclude the apparently fixed stars, and then see what evidence there is as to how they move relative to each other, then in that context there is some evidence to be found in naked-eye astronomy aided by navigational instruments available even to the ancients.

The patterns of observed movement of the planets is evidence of heliocentric orbit. The visible planets follow certain patterns. First, Mercury and Venus:

  • They are always seen in the vicinity of the sun.
  • The observed angular separations of both Mercury and Venus from the sun have a regular pattern.
  • Mercury has a much closer maximum separation than Venus, and its angular separation changes at a much faster rate.
  • Both planets stay close to the ecliptic, and never oscillate normal to it.
  • Both planets' orbits around the sun can be documented and predicted with relative ease. This can be done imprecisely even without a telescope, though it is much harder for Mercury, being so close to the sun.

Beginning with the premise of bodies moving through the heavens, I believe the evidence is there for Mercury and Venus having a heliocentric orbit. Kepler described it precisely, but the ancient Greeks were able to model their motion very well without telescopes in the Antikythera Mechanism in geocentric terms.

If an ancient Greek astronomer had wanted to precisely model the motion of the inner planets in heliocentric terms, he could have. The way to do it is to assume the fixed stars are rigidly fixed, and measure the angular distances between them all, and then plot the motions of the moving planets among them. Sextants and other devices were used by ancient mariners who were highly skilled even with primitive ones. So this could have been done to realize the "simple experiement or calculation" you are asking for. Whether it ever was done, with that question in mind, is a bit different issue.

Now for the earth itself. Even in the ancient world the relationship between the sidereal day and the solar day has been well understood. The precession of the sun around the ecliptic plane is evidence of a heliocentric orbit. One just has to model it to make this clear. Ancient calculations relating to sidereal time and the Metonic cycle reveal that the earth's heliocentric motion could have been mathematically modeled, if conceived of and desired.

As for the outer planets, to my mind this is the least intuitive, but there is evidence for a heliocentric orbit for them too, but only by building on the idea that earth and the inner planets orbit the sun. This comes from observing their retrograde motion. These planets will move retrograde against the "fixed background stars" at certain times, and those times can be correlated to their angular separation from the sun. Also the different planets move through the zodiac at different speeds, which also correlate with the amplitude of retrograde motion.

If you simulate all this with a heliocentric orrery, it is very plainly evident that we on an inner, faster planet observe an outer, slower planet in its orbit. The ancient Greeks had enough skill to model the motions of Mars, Jupiter and Saturn in their Antikythera Mechanism in geocentric terms. So it follows that a precise, mathematical model of heliocentric motion for the outer planets was within their reach, if they ever reached for it.

There is also some evidence that at least some ancient thinkers were able to decode all this into a heliocentric model. The ancient Greek Aristarchus of Samos had a heliocentric model. However, Plato and others seemed to disfavor it, and this reconstruction of the Antikythera Mechanism which is believed to come well after Aristarchus' day features a geocentric orrery which models planetary retrograde motion. And heliocentric thinking stayed within the minority in the west until the modern age. Perhaps the obvious geocentric orbit of the moon, or the question of the stars (whether they should be included in any correct model or not), or the lack of a universal theory of gravity, sufficiently obscured for them what to us is clear.

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    $\begingroup$ I think you're disregarding the fact that the heliocentric model doesn't do a much better job of actually modeling the system until you give up on circles. The first attempts at heliocentric models (even at the time of Galileo) had the issue of having even more exceptions than the geocentric ones due to using circles which don't actually work well. tofspot.blogspot.com/2013/10/… does seem to do a great job of explaining this. $\endgroup$ – DRF Jul 10 '18 at 11:10
  • $\begingroup$ @DRF You can probably tell I approached this from the point of view of, did the Greeks have enough information and theory, if not the insight, to prove heliocentricity at their level of mathematics, physics and technology? Following that same line, I don't know, but I wonder if you have to have good quality lenses in order to disprove circular orbits. Galileo had pretty good lenses, so maybe the Greeks were not capable of his level of precision. I'm not sure. $\endgroup$ – wberry Jul 10 '18 at 23:32
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    $\begingroup$ The Antikythera Mechanism amazingly had an eccentric gear in its lunar module, accounting for the moon's elliptical orbit, which I imagine is close enough to us for a half-decent sextant to measure eccentricity. But for the others it looks like all circles in Antikythera, with the caveat that not all of the device was recovered. Nor have I seen any reference online to the Greeks discussing such issues with the visible planets. $\endgroup$ – wberry Jul 10 '18 at 23:32
  • $\begingroup$ Although your blog author you linked to makes a pretty good case that the Greeks could have proved even elliptical orbits at their level, if they had followed all the thought processes of the later European astronomers, without lenses. $\endgroup$ – wberry Jul 11 '18 at 0:00

The best experimental evidence is probably retrograde motion. The data is not easily acquired: it takes a long time to collect, not to mention an astronomer would have to stay up every night keeping painstaking measurements of the positions of each object. But it can be done (ancient Greeks were aware of it) and in the modern world you can simply use a simulator like Stellarium.

Download Stellarium, start it up, and navigate to your local position. Then set the simulation running and speed it up many times. You should see the sun and stars rotate around you. Then turn the ground off (so you can see through the Earth), turn the atmosphere off (so you can see stars during the day), switch to the equatorial mount (Ctrl + M; this is the mount where most of the sky is stationary), and zoom out until the Sun, the Moon, and all the planets appear to move in a circle.

Now look carefully at the motions of all the planets. You should see that the Moon (and the Sun) goes in circles without ever slowing down. This is what you'd expect if they went around the Earth. However Mercury does not follow this motion - it visibly disappears around the Sun. Mars behaves differently as well: it goes round and round, then stops, goes backwards, and then goes round and round again. This last behavior is called retrograde motion and its explanation occupied a lot of ancient astronomy. Ancient Greeks came up with a complicated theory of epicycles to explain it, given that the planets orbited the Earth and moved in perfect circles (neither of these are true in modern knowledge).

However retrograde motion can be easily explained if Mars didn't go around the Earth, but went around the Sun instead. This would simply mean that Mars goes retrograde when we overtake it on its orbit. In addition, this also explains how each time Mars goes retrograde, it is at its brightest, plus it is on the opposite side of the sky relative to the Sun. It also explains why Mercury does its loops around the Sun.

This doesn't mean that the geocentric model is not able to account for the same observations, but it's drastically simpler. In the heliocentric model, every planet goes round the Sun on a simple path, an ellipse. In the geocentric model, every planet goes round the Earth, but on epicycle after epicycle. That's when we apply Occam's Razor and conclude that the simpler explanation is correct.


Well... the seasonal cycle is evidence enough that the Earth and Sun are orbiting each other. Whether A orbits B or B orbits A is an argument about relative mass. If you find that the movement of all the other planets are consistent with them orbiting the Sun but not the Earth, you can conclude that the Sun's mass is enormous and therefore barely affected by the pull of the Earth.


This might oversimplify things but here's my go:

  • Create a flat surface (the larger the better as long as it stays flat), e.g. by placing a board on a still surface of water.
  • Put up a long pole (the longer the better) vertically on that surface at noon.
  • Measure its shadow (direction and length), which needs to be completely on the flat surface.
  • Have someone do the same (esp. same length of pole) at the same time far to the north of you (the further the better).
  • Have a third of the exact same measurements far to the south of you.

Evaluating the measurements should establish:

  • Earth's surface is roughly spherical (actually earth is an oblate ellipsoid but you need more than 3 measurements to confirm that)
  • Earth diameter is within reported values (+/- expected deviation for measurement error and the fact that you only measured a very rough estimation)
  • Rough estimation of earth-sun distance by triangulating

Using a pinhole camera you can now achieve a rough estimation of sun's actual diameter by its apparent diameter and the distance estimation from above. Even accumulating all the measurement errors, the difference in size between sun and earth should be some orders of magnitude.

Attach two balls to the opposite ends of a rod (the lighter the rod compared to the balls the better). The balls need to be rough approximations of the above established measurements (e.g. you could guess the sun is pure hydrogen and the earth is pure iron to achieve an estimation of mass). Attach a string to the rod and find the point of balance. Most likely it will be way to the ball representing the sun (you need to accommodate for weight of the rod).

You can now make the two balls circle each other while hanging from the string.

Which one revolves around the other?

  • $\begingroup$ Feel free to extend/correct this answer. I thought about how to have the described experiment/model as simple as possible. The only hope for this to achieve anything is that the difference in diameter and mass between earth and sun is so staggering large that the numbers work out although they are likely to be 50% (or more) off from the actual values. $\endgroup$ – NoAnswer Jul 12 '18 at 15:59

Detailed observations of any star in the sky reveal that the Earth moves in an elliptical orbit with a speed of approximately 30 km/s.

When the line of sight velocities of stars are measured using the Doppler effect, they have to be corrected for the motion of the Earth. If they are not, then one would see an unexplained modulation of the velocities, with a period of 1 year and an amplitude of up to 30 km/s that would differ depending on the direction of the star with respect to the Earth-Sun orbital plane.

Likewise, a geocentric model fails to explain why an observer on the Earth sees the positions of stars on the sky execute periodic ellipses on the sky with amplitudes (a.k.a. the trigonometric parallax) that appear to be inversely correlated with how far away they are, but all with a period of one year.

Perhaps these are not the"simple" experiments that you were thinking of, but the universe cannot always be understood with what is visible to the naked eye and common sense.


Very simply: because of relative motion, no proof exists. Any situation that you come up with can be explained by a tweaked geocentric module. Albert Einstein came to the same conclusion when he said "I have come to believe that the motion of the Earth cannot be detected by any optical experiment." and "...to the question whether or not the motion of the Earth in space can be made perceptible in terrestrial experiments. We have already remarked... that all attempts of this nature led to a negative result. Before the theory of relativity was put forward, it was difficult to become reconciled to this negative result."

  • $\begingroup$ It really makes sense to elaborate on this particular quote. You are being downvoted, because this well-known quotation is often seen torn out of its contest to show as if E. supported the geocentric model. I am surprised, however, that no one except you has so far mentioned the GR in this context. This looks like an introduction to a very good and educational answer, if only abruptly ended. $\endgroup$ – kkm Jul 12 '18 at 4:51
  • $\begingroup$ @kkm thanks I will edit my answer. $\endgroup$ – Vladimir_314159 Jul 12 '18 at 12:52

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