This is a draft of a piece about sundials for the U(t)-Mathazine.
Sundials don’t measure time. They measure something much more interesting: the position of Spaceship Earth relative to its nuclear energy source, The Sun. To put it another way: a sundial is a dial aboard our spacechip which displays the apparant position of the sun. From this, one can determine the date and time.
If you want to measure time: check your phone or get a watch. If you want to understand some deep facts about the structure of the solar system: design your own sundial.
I’ve found that learning about sundials has taught me a lot about time. What is an hour, really? In this article, we’ll explore such questions.
We want to create something which will measure the position of the sun. The first thing to note is that the majority of the apparent motion of the sun in the sky is caused by the rotation of the earth about its axis. It looks like the sun is moving in the sky but what we’re seeing is the Earth is spinning. The sun is in a fixed position and we are rotating.
This suggests a simple sundial: keep track how much of a rotation the Earth has completed. Of course, we can’t stand at the North pole and watch the Earth turn, but we can make a small line parallel to the Earth’s rotational axis. The scale of the Earth-Sun system is such that any small line parallel to the Earth’s rotational axis will work just as well as the axis itself. This leads to the question: How do we, in Scarborough, make a line parallel to the rotational axis of the Earth?
To make the parallel line, we can use a little bit of geometry. Let $N$ be the north pole. Consider a line $OP$ from the center for the earth $O$ to your position on the surface of the earth $P$. If $ON$ is parallel to $PQ$.
“Rotation” refers to an object’s spinning motion about its own axis. “Revolution” refers the object’s orbital motion around another object. For example, Earth rotates on its own axis, producing the 24-hour day. Earth revolves about the Sun, producing the 365-day year.
Published: Mar 31, 2025 @ 16:54.
Last Modified: Apr 4, 2025 @ 09:17.
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