Concepts explained
How the Distance to the Moon Was Measured
There is only one way to measure a distance you cannot reach with a tape: make a triangle. With that single method, people worked out the distance to the Moon, then the Sun, then the stars, then galaxies.
Walk fifty metres along the bank. From each of the two spots, sight the tree and measure the angle.
Now you have a triangle: the fifty metres you walked is one side, and you know the two angles at its ends.
So what about the Moon?
The same, except for the baseline.
For a tree across a river, walking fifty metres changes the angle noticeably. The Moon is so much further that fifty metres changes nothing. The baseline has to be far longer.
And this is not a one-shot measurement. Triangulate what is near, use it to calibrate a method for what is further, then use that to reach further still — a ladder.
A little further in
Consider measuring the distance to a far mountain. If you cannot walk there, look at it from two places. Know the distance between them and the angle to the mountain from each, and the rest of the triangle is fixed.
Applied to the sky, the hard part is the baseline. The further the target, the longer the baseline must be for the angles to differ measurably. For the Moon, two points on Earth suffice. For stars, nowhere near.
Using a shadow as the baseline
Aristarchus built his triangle differently. At half moon the Sun, Moon and Earth form a right angle, and from that he computed how many times further the Sun is than the Moon. His angles were not precise enough and the answer was badly off, but the method was sound.
Hipparchus was cleverer. He used a lunar eclipse: measure the size of the Earth's shadow falling across the Moon and you get the ratio of their sizes. The Earth's size was already known, thanks to Eratosthenes.
Stars were far harder
For stars the same method needs a much longer baseline. The longest available is the distance the Earth travels in half a year — the diameter of its orbit. Using it is what stellar parallax means.
Even with that baseline the angle came to less than one arcsecond. For three centuries nobody caught it, and that failure was used as an argument against the moving Earth. Bessel finally succeeded in 1838.
Leaving a mirror behind
Since 1969 the distance to the Moon has been measured without any triangle. Apollo astronauts left retroreflectors on the surface; fire a laser from Earth and time the return.
| Method | Era | Uncertainty |
|---|---|---|
| Eclipse shadow | 2nd century BC | a few per cent |
| Refined triangulation | 18th–19th century | ~0.1% |
| Radar echo | 1950s | kilometres |
| Laser retroreflector | 1969– | centimetres |
That precision revealed something: the Moon is receding by about 3.8 centimetres a year. Tides slow the Earth's rotation very slightly, and the rotational energy lost goes into the Moon's orbit.
The ladder
Astronomy's distance measurements are described as a ladder: triangulate what is near, use that to calibrate a method for what is further, and use that in turn to reach further still.
Triangulation is the bottom rung. If it is wrong, everything above it is wrong. Which is why the size of the universe usually gets revised when a lower rung is corrected.
The question that remainsEvery distance beyond reach was computed starting from something we already knew. If that first rung were wrong, how would we find out?