sky , with underlying cycles of 15 – 17 , 47 , and 79 years . Jupiter returns each 399 days , with cycles of 12 , 71 , and 83 years . While the shortest periods may easily be discovered by a single person ’ s careful observations through a lifetime , longer periods are less obvious to discern — but the Babylonians had been scrupulously noting down , rather regularly , everything that happened in the kingdom and neighboring ones as well as in the skies . For example , a scribe might have written a weather report , together with the prices of various commodities such as those of wheat or beer , the king ’ s health and the state of political affairs , famine or drought , war or epidemics , etc ., along with — and here ’ s our cue — the position and aspect of planets and the Moon . To Babylonian “ star-diviners ,” six points were important in monitoring planets Mercury and Venus , whereas five were their concern for Mars , Jupiter , and Saturn . For the first two , these were :
• First visibility , first station , and last visibility in the west after sunset
• First visibility , first station , and last visibility in the east before sunrise For what we now call “ superior planets ,” these were :
• Heliacal rising ( first visibility in the east before sunrise )
• First station in the west before sunrise
• Acronycal rising in the east just after sunset ( sometimes spelled “ acronical ”)
• Second station in the east after sunset
• Heliacal setting in the west just after sunset ( last visibility ) Recording the movement of planets allowed star-diviners to notice patterns and repetitions , but the stroke of genius came when someone decided to put all that in numbers — it is indeed much more precise to say , for example , that Jupiter is 1 ° away from the brightest star of Virgo and to say that it ’ s “ two fingers ” away from it ; how big are the fingers ? how far from the eye are they held ? Since planets always travel along a specific band of the sky , now known as the zodiac , it was decided to divide it into 360 uš , a unit that is the direct ancestor to our degree . Why 360 and not , for example , 231 ? A definitive answer has never been found , but we may guess at least two possible factors :
• It ’ s close to the number of days in a year , with the added advantage of having more mathematical factors ( 365 can only be divided by 5 and 73 , whereas 360 can be divided by 2 , 3 , 4 , 5 , 6 , 8 , 9 , 10 , 12 , 15 , 18 , 20 , 24 , 30 , 36 , 40 , 45 , 60 , 72 , 90 , 120 , and 180 — sadly , though , it is impossible to divide a circle in 360 equal parts with a compass and unmarked straightedge , so it took a long time before humans were able to manufacture precise protractors and other angle-measuring devices )
• A degree is about twice the apparent size of the Sun , so it might have been found by “ dividing the
horizon ” into “ Sun-portions ” With the zodiac thus divided , it became easy to bring out the mathematical relationships of the Universe , starting with the movement of planets . For example , from one year to the next , it was found that Jupiter would move ahead by 33 ° on average . Babylonians even came up with a system ( simply called “ System A ” by modern historians ) to calculate the past and future positions of planets using so-called step functions : for example , between the 25th degree of Gemini and the 30th degree of Scorpius , Jupiter would move by 30 °/ year ; between Scorpius 30 and Gemini 25 , by 36 °/ year . Another system , which probably came later although extant cuneiform tablets describing or based upon it are of roughly the same time as those pertaining to System A , is System B , in which the calculation follows a zigzag function : for example , in one version , Jupiter ’ s progression was reckoned as growing steadily from 28 ° 15 ′ 30 ″ at Virgo 15 up to 38 02 ′ at Pisces 15 . How precise were these systems ? Just for fun , I ran a simulation starting from the values in a cuneiform tablet ( called ACT 620 ) dated 185 BCE all the way to 2040 CE , and the average error for Jupiter was 0.624 °, the largest errors being −4.29 ° and + 6.184 °— not bad , for a 2,500-year-old algorithm ! In the next installment of Figuring Out How the Universe Works , we ’ ll travel from Babylonia to Greece . Stay tuned ! n n n Pierre Paquette has been an amateur astronomer for more than 35 years . He has been secretary ( 1990 – 1992 ) and president ( 1993 – 1994 ) of the Centre francophone de Montréal of the Royal Astronomical Society of Canada , board member of the Fédération des astronomes amateurs du Québec ( 1993 – 1994 , then 2010 – 2014 ), and vice-president of the Club des astronomes amateurs de Laval ( 2014 ). From 2012 to 2016 , he was the editor and publisher of Astronomie-Québec , a freely available PDF magazine , and he still sometimes publishes on its website and Facebook page . He was main presenter at National Geographic Night-Sky Odyssey , the first-even open-air planetarium with augmented reality , in Sutton , Québec , from 2018 to 2021 . He has been an Ambassador of the Royal Astronomical Society of Canada since 2013 . In 2016 , he received the Fred Clarke Award of the Montréal RASC for his lifetime achievements . He has given talks and workshops in Montréal , Québec City , Toronto , Whitehorse ( Yukon , where he is Subject Matter Expert for the Aurora | 360 Experience ), and Brazil .
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