by dfabulich | 2025-07-31 22:06:20+00:00
Here's another good example of a series of slow experiments: the cosmic distance ladder.

https://www.youtube.com/watch?v=YdOXS_9_P4U https://en.wikipedia.org/wiki/Cosmic_distance_ladder

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. Aristarchus guessed 6 hours, which was off by an order of magnitude, but showed an important point: that the sun was much larger than the earth, which was the first indication that the earth revolved around the sun. (Aristarchus' peers mostly didn't believe him, not simply out of prejudice, but because the constellations don't seem to distort over the course of a year; they were, as we now know, greatly underestimating the distance to nearby stars.)

Next, you can compute the shape of the orbits of the planets, by observing which constellations the planets fall inside on which dates over the course of centuries. Kepler used this data first to show that the planetary orbits were elliptical, and to show the relative size of each orbit, but with only approximate measures of the distance to the sun (like the θ measurement above) there's not enough precision to compute exact distances between planets.

So, scientists observed the duration of the transit of Venus across the sun from near the north pole and the south pole, relied on their knowledge of the diameter of the earth, and used parallax to compute the distance to Venus, and thereby got an extremely precise measurement of the earth's distance to the sun, the "astronomical unit." It took decades to find the right dates to perform this measurement.

The cosmic distance ladder goes on, measuring the speed of light (without radar) based on our distance to the sun and the orbit of Jupiter's moon Io, using radar to measure astronomical distances based on the speed of light, measuring brightness and color of nearby stars to get their distance, measuring the expected brightness of variable stars in nearby galaxies to get their distance, which provided the data to discover redshift (Hubble's law), measuring the distance to far away galaxies (and thereby showing that the universe is expanding).