The Egyptian Town Where the Sun Stood Directly Overhead at Noon on the Summer Solstice

The southern Upper Egyptian town of Syene (modern Aswan, on the Nile’s first cataract) was approximately 24° north of the equator in the 3rd century BC. That latitude was — and this was the substantial astronomical-geographical curiosity Eratosthenes built his famous measurement on — the latitude at which the Sun stood exactly at the zenith at noon on the summer solstice. From every point south of Syene, the Sun crossed the substantially northern half of the sky; from every point north of Syene, the southern half. Syene was the transition.

The line of latitude through Syene is the Tropic of Cancer.

Why the Sun was overhead there

The Earth’s rotational axis is tilted by approximately 23.4° relative to the plane of its orbit around the Sun. The geometric consequence is that the latitude at which the Sun substantively reaches the zenith at noon substantively shifts through the year between 23.4° North (at the June solstice) and 23.4° South (at the December solstice). The line of latitude at 23.4° North is the Tropic of Cancer; the line at 23.4° South is the Tropic of Capricorn. Syene sat substantively exactly on the northern tropic in the 3rd century BC — substantively give or take a few minutes of latitude.

The Egyptian astronomers had identified the substantive solstice phenomenon at Syene long before Eratosthenes. The diagnostic test was a deep well at the centre of the town: on the noon of the summer solstice, the Sun’s reflection appeared at the bottom of the well, substantively confirming that the light was substantively descending vertically into the water. The well was a Egyptian tourist attraction in the Hellenistic period, substantively the annual destination for Alexandrian-Egyptian astronomy enthusiasts on the solstice day.

Eratosthenes’s measurement

Eratosthenes was the Chief Librarian of the Library of Alexandria from approximately 245 BC. Around 240 BC he substantively used the Syene solstice phenomenon to calculate the Earth’s circumference. The substantive method:

The Sun at noon on the solstice cast no shadow at Syene (because it was directly overhead). At the same noon, the Sun at Alexandria cast a shadow at an angle of approximately 7.2° from the vertical — measured using a vertical pole (a gnomon) of known height. The 7.2° angle was substantively the fraction of a full circle (360°) represented by the angular separation between the Alexandria and Syene latitudes — 1/50 of the full circle.

The distance between Alexandria and Syene was substantively known to the Egyptian government surveying tradition — approximately 5,000 stadia along the Nile-paralleling caravan route. Multiplying by 50 produced substantively the Earth circumference: 250,000 stadia.

The stadium was substantively a standard Greek-Egyptian distance unit, 157.5 metres for the Egyptian stadium that Eratosthenes substantively used. Substantially 250,000 stadia = 39,375 km. The modern Earth circumference is 40,075 km. The Eratosthenian measurement was substantively accurate to within 2%.

The substantive tropic shift

The Tropic of Cancer is not substantively fixed in latitude. The Earth’s axial tilt substantively varies on a 41,000-year cycle (the Milankovitch obliquity cycle) between 22.1° and 24.5°. The current value is 23.4° and substantively decreasing; the value in the 3rd century BC was 23.7°. The Tropic of Cancer is therefore substantively drifting southward at approximately 14 metres per year.

Syene/Aswan substantively sat on the tropic in Eratosthenes’s time. Modern Aswan sits substantively about 30 km north of the current tropic line. The solstice Sun is no longer substantively directly overhead at Aswan; the overhead-Sun line has drifted south to Lake Nasser. The Egyptian astronomers of the 3rd century BC substantively had a standing geographical advantage that the modern observer no longer has.

The scientific point survives the drift. The Eratosthenian method was substantively the first quantitative measurement of the substantive size of the Earth. The answer was substantively correct to within experimental error. The method substantively did not depend on any astronomical or geographical knowledge that was not substantively available to any Hellenistic-Egyptian observer of the period.