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.
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 at some time of the year and away from it six months later.)
Wikipedia's article on parallax is better, and I refer you to it for details. Basically, if you hold your finger up 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 or whatever. Switch back and forth between your 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 were good scientific reasons to suppose that the stars were much smaller than the Sun. Seen through a telescope, stars showed disks and if they were like the Sun, their distance could be deduced from those disks. And they were close enough that if the Earth really 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.
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.
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.
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.
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.
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?
With relatively simple equipment it is possible to observe the behaviour of the satellites of Jupiter. Assuming the hypothesis that Jupiter and all the planets rotate around the Earth, it should be expected that the occlusion of the satellites by Jupiter would happen on a highly regular basis. But what we see is the event happening at different times relative to Earth-bound clocks, even not very accurate ones, which proves that the orbit of Jupiter is not a simple epicycle around the Earth. Also the observation of any satellite not directly orbiting the Earth casts doubt on the Earth-centric view.
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."