Caption: A copy of the Venus Tablet of Ammisaduqa which reports observations of Venus. The original (from which many copies were made) was compiled circa mid 17th century BCE (see Wikipedia: Venus tablet of Ammisaduqa). The copy is from the Neo-Assyrian period (934--609 BCE).

Features:

1. We have many texts from Ancient Mesopotamia (or, loosely speaking, Ancient Babylonia) since their inhabitants wrote on clay tablets and kiln-baked clay tablets buried in dry earth (like that in Tigris-Euphrates River area) last for thousands of years---millennia---a very non-volatile memory data storage medium:
   ---"They wrote on clay", Edward Chiera (1885--1933).

2. Many clay tablets giving details of Babylonian astronomy have survived, and so we know a lot about Babylonian astronomy. This figure explicates an important clay tablet from Babylonian astronomy: i.e., Venus Tablet of Ammisaduqa.

3. The predictive mathematical astronomy of the Babylonian astronomers had simple beginnings in using cycles of repeated astronomical motions.

   The Venus Tablet of Ammisaduqa is early evidence of this from as aforesaid circa mid 17th century BCE.

   Note Ammisaduqa (reigned c. 1646--1626 BCE, middle chronology) was a king of the dynasty of Hammurabi (reigned c. 1792--1750 BCE, middle chronology) (i.e., the dynasty of the First Babylonian Empire).

4. Venus tablet proves that the Babylonian astronomers knew of the Venus cycle from very early on in their history (see No-290).

5. To explicate the Venus cycle:
   1. First note that most Solar System arrangements repeat approximately if you wait long enough.

   2. The arrangements of Venus with the Sun and the fixed stars repeats approximately every 8 years. The cycle of these arrangements is the Venus cycle.

   3. To be a bit more precise, the Sun returns to the same position relative to the fixed stars every orbital period (which is also the sidereal year) equal to 365.256363004 days at epoch 2000 January 1 noon (J2000.0) (see Wikipedia: Earth).

   4. Now Venus returns to the same position relative to the Sun every 583.92 days which is called the synodic period (see ESO: Synodic Period of Venus).

   5. Say we have a particular arrangement Venus, the Sun, and the fixed stars today. For example, consider the arrangement greatest eastern elongation of Venus and the Sun in conjunction with fixed star X.

      The arrangement will happen again at time m*PS=n*PV later where PS is the sidereal year and PV is the synodic period and m and n are integers.

   6. In fact, there are no exact choices for m and n. The periods PS and PV are only known to within some error and they vary slowly with time. There is also the complication that the orbits of Earth and Venus have small, non-zero eccentricities---but let's NOT worry about that.

      If, however, we took the accepted values as exact values, we would find that

          PV     m        583.92          583920000000
         ---- = --- = ---------------- = --------------     ,
          PS     n      365.256363004     365256363004 

      where the right-hand side gives m and n as integers. In fact, the right-hand side is NOT an irreducible fraction or fraction in lowest terms since the numerator and denominator are divisible by 2 and perhaps other integers. But it is unlikely that we can exact m and n values that are of order a few---yours truly has proven numerically that we can't. In any case, our hypothesis that there are exact values to find is wrong as aforesaid.

   7. However, we can find and the Babylonian astronomers did find m and n of order a few such that m*PS≅n*PV.

      At time about m*PS≅n*PV after the arrangement, we will have an approximate repeat arrangement. The smaller |m*PS-n*PV|, the closer to the approximate repeat arrangement is to the original arrangement.

   8. Yours truly has done a numerical calculation and found m=8 and n=5 gives |m*PS-n*PV|=2.45 days and this is by far the smallest difference for m and n of order a few. To get a smaller difference, one has to go up to m=235 and n=147: the difference is 0.99 days. A offset of 2.45 days between exact repeats of two different Solar System periodic phenomena is small and unnoticeable without precise measurements.

      The m=235 value means a cycle period of nearly exactly 235 sidereal year. This period is so long that Babylonian astronomers could probably NOT have found it even if they wanted to.

      However the m=8 value means a cycle period of nearly exactly 8 sidereal year which was within their range and interest.

      So 8-year Venus cycle was what they discovered.

      To be precise m*PS=8*PS=2922.05 days and n*PV=5*PV=2919.600.

      So about every 8 years ≅ 2920 days, all Venus the Sun and the fixed stars arrangements repeat approximately---and that's the Venus cycle.

   9. To make use of the Venus cycle to construct ephemerides, one merely collects 8 years of observations of Venus's position on the sky.

      Then one can predict Venus's position on the sky for the entire future albeit with decreasing accuracy as time passes.

      One can correct the inaccuracy of the predictions, by simply updating one's Venus observations as needed.

6. The Venus Tablet shows that the Babylonian astronomers as early as 1600 BCE could rely on cycles to make relatively accurate predictions of the motions of Venus.

7. In fact, Babylonian astronomers used the Venus cycle and similar cycles for the other planets and for eclipses (i.e., the famous Saros cycle) to construct ephemerides.

   This is a step up from the alignment astronomy of prehistoric peoples---you had to be literate to do it---but it still ain't rocket science.