Terence Tao on the cosmic distance ladder

About geocentrism vs heliocentrism, 3blue1brown has recently released a video [1] that talks about about it. It is about the cosmic distance ladder, but geocentrism is mentioned, and it makes a lot of sense in context. To summarize: heliocentrism was known to the ancient Greeks, who realized the Sun was much bigger than the Earth, so it would seem logical to have the Earth go around the sun. But the counterargument was that if the Earth goes around the Sun, the stars should move relative to each other during the year, because of parallax, and they didn't have instruments that were precise enough to see it, so they assumed that they didn't. Copernicus major contribution wasn't heliocentrism, but the orbital periods of planets. And the model wasn't complete until Kepler calculated the shapes of the orbits. For details, watch the video, it is really good. [1] [this video]

Here's another good example of a series of slow experiments: the cosmic distance ladder. [this video] [link] You can compute the distance to the moon if you know the radius of the earth by looking at how long lunar eclipses take, data gathered over years of observations. Eratosthenes computed the radius of the earth by clever trigonometry in ancient times, and Aristarchus computed that a 3.5-hour lunar eclipse indicates that the moon is ~61 earth radii away. Once you have the distance to the moon, you can compute the size of the moon by measuring how long it takes the moon to rise. It takes about two minutes, and so the radius of the moon is about 0.0002 of the distance to the moon. By cosmic coincidence, the sun and the moon appear to be approximately the same size in the sky, so the ratio of radius/distance is approximately the same for the sun and the moon. If you measure phases of the moon, you'll find that half moon is not exactly half the time between the full moon and new moon. Half moon occurs not when the moon and the sun make a right angle with the earth, but when the earth and the sun make a right angle with the moon. You can use trigonometry to measure the difference between the half-time point between new/full moon, and the actual half moon, giving you an angle θ. The distance to the sun is equal to the distance to the moon divided by sin(θ). To get θ exactly right, you need a very precise clock, which the Greeks didn't have. It turns out to be about half an hour. Ari