Ancient Babylonians Used Calculus to Track Jupiter 1,400 Years Before Anyone Else

Move aside 14th century Europeans, Mesopotamians tapped that first. 


While the Ancient Greeks spent their time searching for meaning in the cosmos, the Babylonians attempted, to quote fictional astronaut Mark Watney, to “science the shit” out of space. The Babylonians were so good at developing mathematical and geometrical ideas, in fact, we now know they could calculate Jupiter’s position in relation to time and velocity.

For decades, historians presumed that this revelation hadn’t occurred until the Middle Ages. A recently discovered tablet from Ancient Babylon, however, warrants a historical revision: The Babylonians did it first.

Astroarchaelogist Mathieu Ossendrijver, who published his findings in Friday’s edition of Science, spent the last 14 years traveling between the British Museum and Humboldt University in Berlin to analyze five clay tablets — including the tablet that previously had escaped academic attention. Since the 1950s, researchers knew that four of the ancient cuneiform tablets, dated between 350 and 50 BCE, tracked Jupiter’s movement but were confused to the actual method employed.

“Some of these tablets contained a weird procedure, a weird little bit of text, that deals with trapezoids,” said Ossendrijver on the Science podcast. “People were wondering what were these strange procedures. . . It’s only now, last year, when I found a fifth tablet that also deals with Jupiter and contains computations, that are equivalent to these computations with the trapezoids, that I was able to decipher these weird tablets.”

A cuneiform tablet detailing the calculations involving a trapezoid. The distance travelled by Jupiter is computed as the area of a trapezoid.

Trustees of the British Museum/Mathieu Ossendrijver

Ossendrijver found that Babylonian astronomers used trapezoid calculations to figure out Jupiter’s movement each day along its ecliptic path. Relying on now-common basic calculus methods, they determined that plotting Jupiter’s velocity against time created a downward slope, forming the edge of a trapezoid. The area of the trapezoid revealed the distance that Jupiter moved the first 60 days it crossed the night sky.

The Babylonian method — computing a celestial body’s movement in relation to time and velocity — is 1,400 years older than thought, discovered long before 14th century Oxford academics and Parisian philosopher Nicole Oresme credited themselves with the discovery.


Earlier and more obsessively than any other ancient culture, Babylonians observed heavenly bodies and interpreted planetary motion. From their main temple in Babylon (located south of present-day Baghdad, along the river Euphrates), they observed the signs in the sky. Archaeologists have found approximately 340 tablets’ worth of planetary and lunar data — as well as 100 accompanying tablets with computational instructions. Near the end of the fifth century BCE, Babylonians created the zodiac as a organizational method to compute celestial positions.

When the ancient astronomers first observed the moon, sun, planets and stars, the purpose was to interpret these movements for their kings. They compiled huge lists of these signs and what they meant, hoping these celestial patterns could be read as godly omens. Jupiter was of particular interest — Marduk, the patron deity of the city of Babylon, was associated with the giant planet. But “as time progressed the Babylonians became less and less interested in interpreting messages from the gods,” wrote Texas Tech’s David Leverington in 2003, and “more interested in trying to see patterns in planetary and lunar movements to enable astronomical predictions to be made.”

Their extensive astronomical work included efforts like measuring planetary movements via ecliptic longitude and latitude coordinates, figuring the time it took other planets to rotate around the sun, and predicting lunar eclipses. Babylonian methods of astronomy became the blueprints for other astronomers to follow.

Marduk, Babylonian god of Jupiter.

RuM/Wikimedia Commons

Ossendrijver’s discovery can be added to the Babylonian list of we did it first’s. But because the astronomers’ names weren’t included on the tablets — as was Babylonian tradition — we have no idea exactly who deserves credit in the historical record.

Alexander Jones of New York University believes that the new inscriptions reflect “a more abstract and profound conception of a geometric object in which one dimension represents time.”

“Their presence,” Jones tells Science magazine, “testifies to the revolutionary brilliance of the unknown Mesopotamian scholars who constructed Babylonian mathematical astronomy.”

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