A Modern Almagest

Ptolemy Today

The ancient science of the sky, retold with modern diagrams

The earth is also a sphere

The earth itself is also shaped, to a good approximation, like a sphere. Several observations make this clear.

Flat Earth in Antiquity

Educated observers in Ptolemy's day, and for centuries before, already knew the earth was roughly spherical. The modern myth that ancient people believed in a flat earth is largely false. What Ptolemy does in the Almagest is not discover the earth's shape for the first time but show rigorously why it must be so.

The sun, moon, and stars do not rise and set at the same moment for everyone on earth. Observers further east see them rise earlier, and observers further west see them rise later. This is what causes modern time zones: the sun rises in Moscow before it rises in Madrid, even though it is the same sun. At sunrise in Moscow, the sun is still below the horizon in Madrid, hidden by the curvature of the earth.

This pattern makes sense only if the earth's surface is curved. A steady, even curvature means that each observer's horizon cuts the sky at a slightly different angle, so the sun and stars appear to rise and set at slightly different moments for each of them. No other shape would produce this result. If the earth were flat, everyone everywhere would see the same star or the sun rise and set at the same time. If it were shaped like a triangle or a square or any other flat-sided figure, observers on the same flat side would all see rising and setting together. None of these patterns match what people actually observe.

But the east-to-west curvature alone only proves that the earth curves in one direction. It could, in principle, be shaped like a cylinder, curved around the east-west direction but flat from north to south. To rule this out, consider what happens when an observer travels north or south. As you move northward, constellations in the southern sky (such as Centaurus) gradually sink below the horizon and disappear from view, while northern constellations like Ursa Major climb higher and become visible all night. Moving south reverses the effect: Ursa Major sinks and southern stars appear. The sky shifts steadily and smoothly with latitude, which means the earth curves from north to south just as it curves from east to west.

Use the slider to move the observer from the north pole to the south pole. The dark hemisphere shows the visible sky at each latitude. Stars above the horizon are bright; those below it are greyed out. Ursa Major (the Big Dipper) sits deep in the northern sky; Centaurus sits deep in the south. From a northern latitude like 50°N, Ursa Major is always visible while Centaurus is hidden below the horizon. From the equator, parts of both can be seen. From 50°S, the situation reverses.

The clearest evidence for the east-to-west curvature comes from lunar eclipses. A lunar eclipse is a single event happening to the moon itself; the moon passes into the earth's shadow and darkens. Everyone who can see the moon at that moment sees the same eclipse at the same instant. But when observers at different places record the local time at which the eclipse happened, they get different answers. The further east an observer is, the later the local clock reads when the eclipse occurs; the further west, the earlier. And the time differences are proportional to the distances between the observers.

The same curvature also explains why the sun climbs higher in the sky the closer you get to the equator. In the tropical regions (the band of latitudes near the equator) the noon sun passes nearly overhead year-round, while in places further north or south it always sits lower in the sky. This difference in solar angle is why the tropical regions are hot and the polar regions cold.

The earth, therefore, curves in every direction, not just one. It is a sphere.