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Your Sundial Is Watching the Earth Turn

About 11 minutes

Your plate worked because a shadow always points away from the light, and because the Sun's position in the sky changes through the day. Both of those are exactly what you saw.

This article is about what causes them, and about the thing your sundial did that the last article admitted and did not explain: put the plate out again months later and the hour marks land somewhere else.

The Sun is not the part that moves

Standing on the ground, the Sun climbs, crosses and sets. Nothing about that looks like it is your doing.

But the Earth is a ball turning steadily on its axis, and it takes about twenty-four hours to come all the way round. You are standing on the outside of it. Your plate is turning. Your pencil is turning. Your whole garden is swinging round to face a different part of the sky, and the Sun — which has not moved at all — slides across your view because your view is the thing being carried.

That is the same reason a tree you drive past appears to slide backwards past your car window. It is not the tree.

It gives you a number you can check

Once you know the Earth is turning, you know exactly how fast. A full turn is 360 degrees and it takes 24 hours, so:

360 ÷ 24 = 15 degrees every hour.

That is a real prediction about the plate on your doorstep. The shadow does not shuffle vaguely along — it sweeps a specific amount, and it sweeps the same amount every hour, all day.

Go and look at the marks you already made. Two marks an hour apart should be about a fifteenth of the way round a full circle from each other. Three hours apart, about forty-five degrees. Your pencil has been measuring the rotation of a planet.

The slower motion

So much for the day. Now the part your two plates disagreed about.

The Earth's axis — the line it spins around — is not upright. It leans over by about 23 and a half degrees. And here is the piece that does all the work: that lean stays pointing the same way all year. It does not swivel to follow the Sun. It points at the same distant spot in the sky in January as it does in July.

The tilt stays pointing the same way all the way round the Sun The Sun sits in the middle with rays around it, and a dashed oval path runs round it. The Earth is drawn twice on that path, once on the left and once on the right. Each Earth is a circle with its axis drawn straight through it as a line leaning over to the right, and both lean by exactly the same amount in exactly the same direction. A faint upright line beside each one shows how far over the lean is. Because the lean never changes, the Earth on the left has its top half leaning towards the Sun while the Earth on the right has its top half leaning away, and that is the difference between summer and winter.
The same lean, both times, in the same direction. On one side of the orbit that puts your half of the world tipped towards the Sun; six months later the identical lean has you tipped away.

Because the Earth carries that fixed lean all the way round the Sun, your half of the world spends half the year tipped toward it and half the year tipped away.

Tipped toward: the Sun rides high across your sky, the days are long, and shadows at midday are short.

Tipped away: the Sun stays low, the days are short, and shadows at midday are long.

The Sun is not tracing the same path across your sky in December as in June — it traces a lower one. A lower Sun means a longer shadow, falling at a different spot on your plate. Your hour marks moved because the Sun's whole daily arc moved.

Two motions, two speeds. Your sundial feels both of them, but each of these effects comes from only one. Put each into the right group.

  • The shadow creeps round the plate while you watch
  • The shadow sweeps about 15 degrees every hour
  • The Sun comes up on one side and goes down on the other
  • Midday shadows are much longer in December than in June
  • Summer days have more daylight hours in them than winter days
  • Your hour marks land in a different place months later

The thing almost everybody gets wrong

It is tempting to say summer happens because the Earth is nearer the Sun. It sounds sensible and it is not true.

The Earth is actually closest to the Sun in early January — deep midwinter for everyone north of the equator, and high summer for everyone south of it. If distance were the cause, both halves of the world would have summer at once, and they plainly do not: it is July in Australia when it is July in Canada, and only one of them is at the beach.

The seasons are the tilt. Nothing else.

Six months from now the Earth is on the far side of its orbit. Which way is your half of the world leaning?

Two plates, side by side

Make the sundial again in the same spot, months later, and lay the two plates next to each other. You now have a record of both motions at once.

The marks are still fifteen degrees apart on each plate, because the Earth still turns at the same rate — that has not changed and will not.

But the whole set has shifted, and the shadows have a different length, because the Sun is running a different track across your sky than it was.

One plate is a day. Two plates are a year. All from a pencil in a lump of clay.