Ancient Babylonian astronomers calculated Jupiter’s position from the area under a time-velocity graph

Posted: January 29, 2016 by tallbloke in Astronomy, History, solar system dynamics

A new paper shows how a recently re-discovered 50 year old photo of a clay tablet holds the key to a geometrical method used by the Babylonians to calculate the position of Jupiter.

babylon-jupiterAncient Babylonian astronomers developed many important concepts that are still in use, including the division of the sky into 360 degrees. They could also predict the positions of the planets using arithmetic. Ossendrijver translated several Babylonian cuneiform tablets from 350 to 50 BCE and found that they contain a sophisticated calculation of the position of Jupiter. The method relies on determining the area of a trapezium under a graph. This technique was previously thought to have been invented at least 1400 years later in 14th-century Oxford. This surprising discovery changes our ideas about how Babylonian astronomers worked and may have influenced Western science.

Science, this issue p. 482



The idea of computing a body’s displacement as an area in time-velocity space is usually traced back to 14th-century Europe. I show that in four ancient Babylonian cuneiform tablets, Jupiter’s displacement along the ecliptic is computed as the area of a trapezoidal figure obtained by drawing its daily displacement against time. This interpretation is prompted by a newly discovered tablet on which the same computation is presented in an equivalent arithmetical formulation. The tablets date from 350 to 50 BCE. The trapezoid procedures offer the first evidence for the use of geometrical methods in Babylonian mathematical astronomy, which was thus far viewed as operating exclusively with arithmetical concepts.



  1. Trick says:

    “..from 350 to 50 BCE..”

    Makes me wince again about the loss of the Alexandrian Library. Over politics. Probably they had a complete understanding of global warming in there too.

    The top post paper mentions the Antikythera mechanism – majorly cool – that could actually compute the position of Jupiter et. al. Even the small perturbations in the moon orbit. Construction dated to 150 to 100 B.C. about the time of these tablets, the information was shared over long distances. Those ancients were really competitive – accomplished scientists/mathematicians/travelers – with labs/shops! Unfortunately then as now, science was pushed ahead to make war. And weather sank ships.

    Much of what was already known had to be re-learned the hard way coming out of the dark ages. Had they not happened, had the Alexandrian Library been preserved, we’d be all the richer in knowledge and philosophy.

  2. oldmanK says:

    Trick above is not the only one to wince about the loss of the Alexandrian library, and much much else besides.

    For example, in the text above it says “including the division of the sky into 360 degrees”. The origins of that according to Wiki is unknown but suggests possibly from calendar requirement. Evidence of that exists, and is in my view undeniable, but in the fourth millennium, and not in Mesopotamia, though the connection with that place is very strong.

    Trick says “Those ancients were really competitive – accomplished scientists/mathematicians/travelers”. Exceptionally so. Looking at how they developed the wild cereals into the staple crop that it is today, over 8000 years ago and how they passed that knowledge in the form of myths (the zodiac is one such case which can be traced to about 5000 bce), one will then fathom to what extent great knowledge has been lost. Unfortunately while the evidence is still under our noses we can’t seem to realise it.

  3. ren says:

    Tallbloke sorry.
    Center polar vortex moves in the direction of Scandinavia.

  4. pyromancer76 says:

    This post reminds me of an older one by E.M. Smith about measurements and our Babylon heritage. Perhaps it might be useful here.

  5. ren says:

    Tallbloke look at wind.

  6. tallbloke says:

    ren: Looks like heavy weather for Ireland and Wales incoming!

  7. ren says:

    Look at the distribution of temperature in the stratosphere. Neutrons exceed 6400 counts.

  8. oldmanK says:

    pyromancer76’s comment above reminds of the comment made by the late C H Gordon (decipherment of forgotten scripts) late in his career (and life) that there is convincing evidence of considerable diffusion of knowledge from very remote past.

    Archaeologists, guarding their patch of soil, don’t like this. It is only towards their end that they seem to dare to speak their mind frankly.

  9. tallbloke says:

    ren: We have had snow today in North UK

  10. Alan Poirier says:

    Oh my. the Anunnaki? 🙂

  11. oldmanK says:

    Alan Poirier said “Oh my. the Anunnaki?”

    I’ll believe that when I see their warp drive. 😉

  12. ren says:

    Tallbloke it seems to me that this will be a long winter in Europe.

  13. Wayne Job says:

    Alan poirier, There were giants in the land in those days. If you want to find gold in South Africa look for a hole or a tunnel that was dug about 100,000 years ago. That is the truth. They saw the daughters of men fair and came down into them and were born mighty men of renown. This is part of our distant history. Many 10Ft skeletons have been found and their skulls are not human Annunaki indeed. The secrets of many things have come down to us from this time, one only needs to look at architecture and the dimensions and hidden harmonics, the pyramid with the seeing eye on a Yankee dollar bill, some people to this day know the truth or a fair facsimile of it. We are but children floundering in the dark.

    Ren I am thinking that the winters are not going to get better for a long time, old sol is going into sabbatical mode. If it happens Ice fairs on the Thames will be a special tourist attraction.

  14. tallbloke says:

    Hi Wayne,

    Got a credible link for that?

    There is this:

  15. oldmanK says:

    Seeing how Alan Poirier’s Annunaki stirred something, here’s a little something that Wayne Job may be interested in. Some decades ago I started chasing two Women that took my fancy in abnormal ways. From just curious to dogged perseverance, seeing how their fashion changed.
    They are these

    You may recognise them in their latest outfit. Throughout the 6000 years plus it turned out (with more than enough proof) they were only a metaphorical representation of an agrarian practice, a way of passing down the generations an important lesson; the cultivation of the cereals. What is more it became evident that throughout the ages all new what it/they meant. It was only in the last one or two millennia, with the rise of fanaticism and abject ignorance, that we lost the way. You are right, we have become children floundering in the dark.

    Ancient texts contain ancient knowledge, but I would not take it at face value.

  16. oldmanK says:

    Another example that highlights the fact that ancient lore is primarily an information tool is the zodiac. The above paper says it was invented in 5th century bce, but actually much earlier. But for those interested see this link.

    The origin of the zodiac is as an agrarian calendar, where e.g. boothes the reaper, virgo the virgin corn seed and the plough follow in proper sequence as the actual works in the field.