Through the internet one discovers that for any thought, there is someone who thinks it. Of course, some of the minority positions you see advocated are reasonable, or -- at least -- not demonstrably unreasonable. Topics where there is no widely accepted explanation, or where the mainstream explanation is not entirely satisfactory, are natural and legitimate fields for speculation. If the proponents are genuine and their ideas well informed, then engagement with fringe ideas can be an interesting and productive exercise; if the idea is completely juvenile (e.g. electric universe) then it is best left alone. Then there are fervent pseudo-skeptics and poorly motivated conspiracy theories, some of which were well known to me (climate change denial, moon landing hoax); others new, but follow a familiar pattern (HAARP). When it comes to scientific matters -- especially in areas where I have some special knowledge -- I occasionally take the bait, but I know better than to expect a good outcome. But recently I encountered a position that actually shocked me; stunned me. Perhaps it was because it involved both the rejection of well-established science and the invocation of a truly grand conspiracy. It seems we have been lied to all these years: the Earth is stationary!
At first, I wondered if the post (and, indeed whole identity of the poster) was satirical. After a bit of poking around, I concluded that was wishful thinking on my part. Then, a few weeks later, I saw something very similar from a different person. There's more than one person who thinks this! Few people will deny things that can be demonstrated in a simple and straightforward way: I haven't yet seen "Planes don't really fly - the airline industry is a hoax!". But even many basic aspects of the way we understand the world to work are not so simply demonstrable - they often require a level of trust (that the information you're being given is true) and an evaluation of multiple pieces of evidence for a most probable, parsimonious explanation. If one is inclined to be suspicious then one might reject the evidence, or one might dissent in the evaluation of the "naturalness" of a given explanation; neither is necessarily crazy. So I started to think about the evidence for the motion of the Earth, in an effort to evaluate how crazy it would be to reject it.
From the point of view of pre-modern astronomy (before the telescope) the motion of the Earth is particularly thorny because there is an almost exact symmetry between heliocentrism and geocentrism. The sky changes either because the Earth is stationary and the sky ("Celestial Sphere") moves, or the sky is stationary and the Earth moves. The two propositions produce exactly the same observations. Hence both Copernicus and Kepler had to defend themselves from charges of "novelty": simply coming up with a new model because they could. Of course, the ancients realised that a moving Earth would have some physical consequences, although they weren't entirely correct about what those would be. We can't really blame them for that - mechanics in a rotating reference frame is actually quite tricky. Nevertheless, they looked for such effects, didn't find any, and -- quite correctly -- concluded that the Earth was stationary.
The observation of Venus through a telescope by Galileo and others from 1610 onwards provided a genuinely new piece of information. Venus, as observed from the Earth, goes through phases just like the Moon does. The Ptolemaic model, the dominant pre-modern (and geocentric) astronomical model, was pretty vague about the relative positions of the Sun and inner planets, but no matter which way you arrange things you can't get it to produce a complete cycle of phases for Venus. The Copernican model was consistent with the observations of Venus, but so was another geocentric model, the model of Tycho Brahe. In the Tychonic model, the Sun orbits the Earth, and all the other planets orbit the Sun. However, the Tychonic model would soon lose out to convenience.
During the first quarter of the 17th Century, Johannes Kepler produced a heliocentric model based on ellipses, which proved to be far more efficient at describing planetary motion than the circles of the Copernican and Tychonic systems. The ephemerides he produced, the Rudolphine Tables, were so convenient that the astronomical community adopted heliocentrism despite its physical problems; but at that time it was still not clear that physics and astronomy would ever have much to say about each other. In other words: Kepler's model could be a convenient computational device without being a realistic model of how things actually work. That changed in 1687 when Isaac Newton published his Universal Theory of Gravitation. Newton provided a precise physical theory that explained Kepler's model.
All that is nice and, for the physics and astronomy communities at the end of the seventeenth century, compelling. But that is still not actual proof that the Earth itself moves. Before going further, we should specify the two types of motion required by Kepler's model. Firstly, the Earth must rotate: this provides the alternation of day and night, depending on whether the bit of Earth you're standing on is facing the Sun. Secondly, the Earth must revolve around the Sun: this produces the procession of the constellations across the evening sky over the course of a year.
Galileo had proposed that the moons of Jupiter could be used as a clock with which to determine longitude on Earth. This method was not useful on ships, where the required observations were impractical, but was successfully used on land. However, those who produced the necessary tables noticed a problem: sometimes their predictions were out a bit. Ole Roemer realised that if Earth and Jupiter orbited the Sun, then the distance between the two planets changed with time. If the speed of light were finite, then the time at which a particular Jovian moon would be observed in a particular position would depend on the travel time for the light. In 1676 he estimated that it takes light 11 minutes to travel from the Sun to the Earth: a bit slow, but of the right magnitude.
The clearest consequence of a revolving Earth is that of stellar parallax: the observed position of a star should shift over the course of the year as the position of the Earth changes. It was whilst looking for this that James Bradley discovered a more surprising, and subtle, effect: stellar aberration. In a series of observations from 1725 to 1728, Bradley observed an annual oscillation in the position of star gamma Draconis. In 1729 he published an explanation: the speed of light is finite (as demonstrated by Roemer), so for that part of the year when the Earth is travelling perpendicular to the direction of the star's light, the telescope moves while the light is travelling down its tube! This results in a shift in the apparent position of the star. From the size of the aberration he was able to deduce the relative speeds of the Earth and light, and hence the time it takes light to get from the Sun to the Earth: 8 mins 12 seconds. Not bad!
It turns out that the distances to the stars are so large, and therefore the angle of parallax so small, that it was not conclusively observed for another hundred years. It was Friedrich Bessel who finally made a positive measurement, on the star 61 Cygni, in 1838.
But what about the Earth's rotation? A freely falling object will experience an apparent deflection in the direction of rotation: the Coriolis force. This is somewhat counter-intuitive; it is perhaps useful to think in terms of conservation of angular momentum, e.g. the increased rate of rotation of an ice skater as they pull their arms in. In 1771, Giovanni Guglielmini dropped spheres from a tower. A fall of 241 feet resulted in an eastward deflection of about seven tenths of an inch! Artillerists would eventually have to correct for Coriolis force if they wanted to hit their target, and today it is central to our understanding of weather.
However, there is a simpler way to see the motion of the Earth. In 1851, Leon Foucault installed a large pendulum in the Pantheon in Paris. As the pendulum swings back and forth, the Earth goes through its daily rotation, rotating under the pendulum. The direction of the pendulum's swing, in terms of the room in which it is installed, changes. At the poles, the line of the pendulum's swing rotates 360 degrees per day; at the equator it rotates not at all.
Today we live on a planet surrounded by artificial satellites; we routinely use them for communication and navigation. The Gaia observatory uses parallax to measure the distances of stars tens of thousands of light-years away. We have sent probes to every planet in the solar system, and New Horizons is starting the exploration of the Kuyper belt. But what do these things matter to the true crackpot!? The history of science is all lies: the above remembrances ignore the many contradictory results. And the reported effects are tiny, dependent on expensive equipment and the product of elite knowledge. The various space programs of all those countries: lies. Why should all those people, irrespective of nationality, politics or religion engage in a multi-national, multi-generational conspiracy? I don't know, but I'm sure someone does!
Well, our crackpot could find a Foucault pendulum and spend a few hours observing it, if they have the patience; but they might suspect some interference. There is usually some driver to keep the pendulum going. They might build one themselves, but ensuring it swings straight is tricky, and it will need regular re-starting.
Instead, how about the old water swirling down the drain phenomenon? The notion that the direction a water swirls out a sink/toilet/bath is determined by which hemisphere it's in (via Coriolis) is a myth: local conditions -- the way the water was poured in, the shape of the basin etc. -- dominate. But, if the experiment is performed carefully, Coriolis can produce the expected effect. This is beautifully demonstrated by Derek Muller and Destin Sandlin in a pair of Youtube videos: https://www.youtube.com/watch?v=ihv4f7VMeJw and https://www.youtube.com/watch?v=aDorTBEhEtk (I recommend going to the effort of synchronising the videos - it really is pretty cool). I think most of us would be happy to accept that this is a true record of an honest and competent experiment, but the experiment is simple enough that the skeptic could perform it at home, at least for one hemisphere. Perhaps the skeptic travels, or perhaps they know someone they trust in the other hemisphere, who could repeat the experiment there. Maybe they could find someone on the internet - you meet all sort of people there.