Babylonian Astronomical Geometry Drew the White Star Orbit of Jupiter

Summary: An astrophysicist in Berlin, Germany, recognizes the White Star orbit of Jupiter in 1,400-year-old Babylonian astronomical geometry tablets.

Full-disk image of Jupiter was taken Monday, April 21, 2014, via Hubble's Wide Field Camera 3 (WFC3): NASA, ESA, and A. Simon (Goddard Space Flight Center), Public Domain, via Wikimedia Commons

Mathieu Ossendrijver, astrophysicist at Humboldt University in Berlin, Germany, argues that Babylonian astronomical geometry precedes European calculus by 1,400 years in an article published online Jan. 28, 2016, in the journal Science.

Dr. Ossendrijver, an expert in the history of ancient science, bases his findings upon four 1,400-year-old Babylonian tablets preserved in the British Museum in London, England. The quartet and a fifth tablet, the 2-inch (5.08-centimeter) across and 2-inch (5.08-centimeter) high BM 40054, calculate the White Star’s motion relative to planets and stars. Dr. Ossendrijver describes the Babylonian astronomical geometry in the clay, cuneiform-scratched tablets as constructing the orbit of Jupiter, the planet known in Babylon as White Star.

The Babylonian astronomical geometry in the tablets expresses White Star’s orbit through “numbers and computations, additions, divisions, multiplications.”

Dr. Ossendrijver finds “drawing graphs of the velocity of a planet against time, and computing the area . . . thoroughly modern, that is not found until 1350.”

Specialists at the British Museum give the tablets, designated A, B, C, D and E by Dr. Ossendrijver, writing dates between 350 B.C.E. and 50 B.C.E. They have access to 450 mathematical astronomy tablets from Babylon and Uruk, respectively 85 kilometers (53 miles) and 270 kilometers (168 miles) south of Baghdad, Iraq. Three hundred forty of the 450 tablets preserving Babylonian mathematical astronomy involve arrangements of data derived from lunar and planetary computations into columns and rows.

One hundred ten of the 450 tablets join “procedure texts with computational instructions” to calculate or verify the tables.

Astronomers know that Babylonians invented the zodiac, the coordinate system used to compute celestial positions in the tablets, near the end of the fifth century B.C.E.

Dr. Ossendrijver looks at 110 tablets worth of texts as “branching chains of arithmetical operations (additions, subtractions, and multiplications) that can be represented as flow charts.” He mentions that “Geometrical concepts are conspicuously absent from these texts” even though the tablets that prompt his recent study “preserve portions of a trapezoid procedure.” He notes that tablet B names the White Star and, with C, E, and probably D, is “embedded in compendia of procedures dealing exclusively with Jupiter.”

A “nearly complete set of instructions for Jupiter’s motion along the ecliptic” occurs in the text preserved on tablet A.

Tablet A provides instructions whereby Jupiter can be followed from the White Star’s first visible rising at dawn through the planet’s last visible setting at dusk.

It quantifies a last visible rising at dusk between a first station beginning and a second ending apparent retrograde motion (illusory direction changes from Earth’s movements). It reveals the motion along the ecliptic (solar path) in terms of two consecutive intervals of 60 days by the fifth planet over from the Sun. Dr. Ossendrijver suggests that Babylonian trapezoid procedures predict the Mertonian mean speed theorem formulated at Merton College, Oxford, and proved by Nicole Oresme (1320 to 1382).

Trapezoids take Babylonian astronomical geometry to “configurations … in an abstract mathematical space defined by time and velocity (daily displacement).”

Text B (BM 34757); photo by Trustees of the British Museum/Mathieu Ossendrijver: Archaeology Magazine @archaeologymag, via Twitter Jan. 29, 2016

Acknowledgment

My special thanks to talented artists and photographers/concerned organizations who make their fine images available on the internet.

Image credits:

Full-disk image of Jupiter was taken Monday, April 21, 2014, via Hubble's Wide Field Camera 3 (WFC3): NASA, ESA, and A. Simon (Goddard Space Flight Center), Public Domain, via Wikimedia Commons @ https://commons.wikimedia.org/wiki/File:Jupiter_and_its_shrunken_Great_Red_Spot.jpg;
CC BY 4.0 International, via ESA/Hubble @ https://esahubble.org/images/heic1410a/

Text B (BM 34757); photo by Trustees of the British Museum/Mathieu Ossendrijver: Archaeology Magazine @archaeologymag, via Twitter Jan. 29, 2016, @ https://twitter.com/archaeologymag/status/693142839455125504

For further information:

AAAS‏ @aaas. 28 January 2016. "Ancient Babylonians used advanced geometry to track Jupiter." Twitter.
Available @ https://twitter.com/aaas/status/692811207422640130

Achenbach, Joel. 28 January 2016. “Clay Tablets Reveal Babylonians Discovered Astronomical Geometry 1,400 Years Before Europeans.” The Washington Post > Speaking of Science.
Available @ https://www.washingtonpost.com/news/speaking-of-science/wp/2016/01/28/clay-tablets-reveal-babylonians-invented-astronomical-geometry-1400-years-before-europeans/

Archaeology Magazine‏ @archaeologymag. 29 January 2016. "The Babylonians calculated the position of Jupiter using geometry around 350-50 B.C." Twitter.
Available @ https://twitter.com/archaeologymag/status/693142839455125504

Ball, Philip. 28 January 2016. “Babylonian Astronomers Used Geometry to Track Jupiter.” Nature > News.
Available @ http://www.nature.com/news/babylonian-astronomers-used-geometry-to-track-jupiter-1.19261

Chang, Kenneth. 28 January 2016. “Signs of Modern Astronomy Seen in Ancient Babylon.” The New York Times > Science.
Available @ http://www.nytimes.com/2016/01/29/science/babylonians-clay-tablets-geometry-astronomy-jupiter.html?_r=0

Derla, Katherine. 29 January 2016. “Clay Tablets Show How Babylonian Astronomers Tracked the Planets Using Ancient Geometry.” Tech Times > Science.
Available @ http://www.techtimes.com/articles/128879/20160129/clay-tablets-show-how-babylonian-astronomers-tracked-the-planets-using-ancient-geometry.htm

Griffin, Catherine. 28 January 2016. “Ancient Babylonian Clay Tablets Reveal People Used Astronomical Geometry to Chart Jupiter.” Science World Report > Space.
Available @ http://www.scienceworldreport.com/articles/36531/20160128/ancient-babylonian-clay-tablets-reveal-people-used-astronomical-geometry-chart.htm

Ossendrijver, Mathieu. 29 January 2016. “Ancient Babylonian Astronomers calculated Jupiter’s Position from the Area under a Time-Velocity Graph.” Science, vol. 351(6272): 482–484. DOI: 10.1126/science.aad8085
Available @ http://science.sciencemag.org/content/sci/351/6272/482.full.pdf

O’Hare, Ryan. 28 January 2016. “Babylonians Used Geometry to Track Jupiter Long Before the Europeans: Stone Tablets Reveal Ancient Astronomers Used Calculations 1,700 Years Earlier.” Daily Mail > Science > ScienceTech.
Available @ http://www.dailymail.co.uk/sciencetech/article-3421190/Babylonians-used-geometry-track-Jupiter-long-Europeans-Stone-tablets-reveal-ancient-astronomers-used-calculations-1-700-years-earlier.html

Scalise, Joseph. 28 January 2016. “Babylonian Astronomers Used Advanced Geometry to Track Planets.” Science Recorder > News.
Available @ https://www.sciencerecorder.com/news/2016/01/28/babylonian-astronomers-used-advanced-geometry-track-planets/

Science Magazine. 28 January 2016. "Math whizzes of ancient Babylon figured out forerunner of calculus." YouTube.
Available @ http://www.youtube.com/watch?v=Rx-5dCXx1SI