Rung 04 · 1672 (Mars) · 1761 & 1769 (Venus)

The Distance to the Sun

Cassini · Halley · Cook · the Transit of Venus

Astronomers on opposite sides of the globe timed the same rare event — and triangulated the scale of the whole solar system in one stroke.

Two observers at different latitudes see Venus trace slightly different paths across the Sun's face. The timing difference reveals the parallax angle, which combined with Kepler's known Venus–Earth distance gives the absolute scale of the solar system.

The first breakthrough came in 1672, when Giovanni Cassini observed Mars simultaneously from Paris and French Guiana — two locations nearly 7,000 km apart. By measuring how much Mars appeared to shift against background stars (stellar parallax), he estimated the Earth–Sun distance to within about 7% of the true value.

But the definitive measurement came from Venus. On rare occasions Venus passes directly in front of the Sun — a transit. Edmond Halley realised before his death that if observers spread across the globe timed exactly when Venus touched the Sun's edge, the slight differences in timing between sites would reveal Venus's parallax precisely.

In 1761 and 1769, astronomers including James Cook sailed to Tahiti, Siberia, Canada, and India to observe. From different latitudes, Venus traces slightly different chords across the Sun. The measured timing difference revealed the parallax angle — and since Kepler had already given the Earth–Venus distance as a ratio of 1 AU, a simple triangle solved for the actual length of 1 AU.

1 AU = 149.6 million km — every planet's distance now known in km

One real measurement + Kepler's law = the entire solar system measured at once. Transits of Venus come in pairs 8 years apart, separated by over a century. The next are 2117 and 2125.

⚑ Assumptions that made it work

Kepler's laws are correct — the entire rung rests on Rung 3. By 1761, Newton had explained why Kepler's law holds (universal gravitation), so confidence was high.
The contact moment when Venus touches the Sun's edge is sharp. It was not — an optical smearing called the black drop effect blurred the edge and introduced timing errors that plagued the 1761 campaign and reduced accuracy.
Observers' clocks are synchronised and their positions known precisely. Expeditions carried fragile pendulum clocks across oceans and had to establish their own latitude/longitude from scratch. Clock errors and positional uncertainty directly corrupted the parallax calculation.
Venus's thick atmosphere does not significantly distort the measurement. It does — Venus's atmosphere refracts and blurs its silhouette, which contributed to the black drop effect. This was not understood at the time.

✋ Try it yourself — find out why Cook had to sail to Tahiti

This is the one experiment on the ladder that is supposed to fail. Do it anyway: the failure is the point, and it takes about twenty seconds.

Hold your thumb up at arm's length, in front of something a good distance away — the far wall, a tree, a building across the street.
Close your left eye, then your right, then swap back and forth.

Your thumb jumps sideways against the background. It has not moved; you are looking at it from two slightly different places, because your eyes are about 6 centimetres apart. Measure how far it jumps against the far wall and you can work out how far away your thumb is without ever reaching for it. That is triangulation, and it is the whole method of this rung.

Now bring your thumb slowly towards your nose, and then push it right out again. The nearer it is, the more it jumps. Push it far enough away and the jump becomes too small to see at all.

So now try it on the Moon. Go outside, blink one eye and then the other, and watch the Moon jump against the stars.

Nothing. Not a flicker. And that is the entire difficulty of rung 4, which you have just felt in your own face.

Your two eyes are 6 cm apart, and the Moon is 384,000 km away. To make something that far off shift by a visible amount you need your two viewing points to be thousands of kilometres apart — which means two observers, on different continents, looking at the same thing at the same instant and comparing notes afterwards. For the Sun, which is four hundred times further still, you need the widest baseline the planet can offer and an event timed to the second.

That is why this rung is not a clever idea someone had at a desk. It is why Halley designed a campaign he knew he would not live to see, why Cook sailed to Tahiti, and why astronomers died on expeditions trying to get one number. The idea is your thumb. The difficulty is the size of the Earth.

And the honest part: you cannot repeat the actual measurement. Transits of Venus come in pairs eight years apart and then not again for over a century. The last was in 2012. The next is in 2117, so nobody reading this page will see one, and that is simply how it is.

Never with unprotected eyes

Only through a filter made for looking at the Sun, checked for damage every single time — or by projecting its image onto card, which is safer still.

The full rules

The Sun can burn the back of your eye permanently, and it does not hurt while it happens, so there is no warning to react to. An adult must be in charge of this.

Only ever use a filter made for looking at the Sun — eclipse glasses marked ISO 12312-2, or a proper solar filter that fits over the front of a telescope or binoculars.
Check the filter every single time before you use it. Hold it up to a bright lamp and look at the filter itself, not through it at anything else. If you can see any scratch, pinhole, crease, bubble or peeling edge — or if you can see the lamp through it clearly — throw it away. A damaged filter is more dangerous than none, because it feels comfortable while it lets the harmful light through.
Never use sunglasses, smoked glass, exposed camera film, a CD, or several pairs of sunglasses stacked up. None of these stop the invisible light that does the damage.
Never put a filter on the eyepiece end of a telescope. The instrument concentrates the Sun's heat onto it and it can crack without warning, while your eye is already there.
The little finder scope on the side needs capping too. It is a burning glass pointed at the same Sun.
Safest of all, and rather good fun: don't look at the Sun at all. Poke a small hole in a piece of card, hold it up, and let it throw a little image of the Sun onto a second card in the shade. The gaps between leaves on a tree do the same thing — during an eclipse the ground under a tree is covered in dozens of tiny crescents.

The Distance to the Sun

When Astronomers Measured the Sun...