For our ancient ancestors, the NIGHTSKY was "the only show in town"! Gawking led to realization that the celestial bodies seem to move in a regular manner that could define TIME and DIRECTION ON THE EARTH. Further interest in astronomy was induced by problems originating with the first civilizations:Fortunately, the sky exhibited manyregularities:
- The bright sun (dividing daytime from nighttime)always rose each morning from one direction, the east, moved steadily across the sky during the day, and set in a nearly opposite direction, the west.
- At night more than 1000 visible stars followed a "solar path", seeming to rotate in permanent groupings ("constellations") around a fixed point in the sky: "the north celestial pole".
- In the North Temperate Zone, people observed that daytime and nighttime were unequal in length.
- On "long days" the sun rose north of east and climbed high in the sky at noon;
- on days with "long nights", the sun rose south of east and didn'y climb so high at noon.
- stars appearing in the west after sunset or in the east before sunrise indicated that the relative position of the sun among the stars changes gradually. (Egyptians were perhaps the first to discover that the sun moves completely around the sphere of the fixed stars in approximately 365 days and nights.)
- The sky also displays, besides the moon, five bright planets which (together with the sun) move around a star sphere within a narrow belt ("the zodiac").
- The moon traverses the zodiac quickly, overtaking the sun about once every 29.5 days ("the synodic month"). This and "irregularities" of the sun complicated calendar-makng.
- The sun and moon always traverse the zodiac from west to east.
- But the five bright planets (Mercury, Mars, Venus, Jupiter, and Saturn) which also have a generally eastward motion against the background of the stars, yet move westward ("retrograde") for varying durations during each synodic period, providing perhaps the major puzzlement astronomy until heliocentrism was adopted.
With the exception of the Venus tables of Ammiza-duga, which probably originated in the seventeenth century BC, most of the surviving Mesopotamian astronomicaltexts were written between 650 and 50 BC. These clay tablets with cuneiformwriting are called astronomical diaries, and they are the unmistakable observations of specialists: professional astronomer-scribes.
A typical diary entry begins with a statement on the length of the previous month. It might have been 29 or 30 days. Then, the present month's first observation - the time between sunset and moonset on the day of the first waxing crescent - is given, followed by similar information on the times between moonsets and sunrises and between moonrises and sunsets, at fullmoon. At the end of the month, the interval between the rising of the last waning crescent moon and sunrise is recorded.
When a lunar or solar eclipse took place, its date, time, and duration were noted along with the planets visible, the star that was culminating, and the prevailing wind at the time of the eclipse. Significant points in the various planetary cycles were all tabulated, and the dates of the solstices, equinoxes, and significant appearances of Sirius were provided.
The Babylonian astronomers used a set of 30 stars as references for celestial position, and their astronomical diaries detailed the locations of the moon and planets with respect to the stars. Reports of bad weather or unusual atmospheric phenomena - like rainbows and haloes - found their way into the diaries, too. Finally, various events of local importance (fires, thefts, and conquests), the amount of rise or fall in the river at Babylon, and the quantity of various commodities that could be purchased for one silver shekel filled out the diligent astronomer's report.
By the sixth century BC, Neo-Babylonian astronomers were computing in advance the expected time intervals between moonrise or moonset and sunrise or sunset for various days in the months ahead. These calculations were based on systematic observations. Later, when combined with numerical tabulations of the monthly movement of the sun, the position of sun and moon at new moon, the length of daylight, half the length of night, an eclipse warning index, the rate of the moon's daily motion through the stars, and other related information, these computations enabled reasonably detailed and accurate predictions of what the moon would do and when it would do it.
Planets received similar attention, but because their movements were not uniform, the Mesopotamian astronomers had to devise mathematical techniques that would take variations in motion into account. As Jupiter, for example, makes its way through the zodiac in almost exactly 12 years, each year it more or less moves into a different zone, or constellation. Each year it also is seen in opposition to the sun - rising at sunset, setting at sunrise - but because Jupiter's motion is not uniform, it won't reach opposition on the same date each year. The Babylonians expressed this a little differently than we do and preferred to specify the position of Jupiter at each opposition rather than the date. The effect is the same, however, and their tables show that they compensated for Jupiter's nonuniform motion by increasing its shift in position by the same amount for each opposition in one half of the 12-year cycle and by decreasing the shift by the same amount each time during the other half. When the shift in position is plotted through the successive oppositions of the planet, a zigzag line results.
Of course, the Babylonians never developed completely accurate representations of nonuniform motion, but in the later dynasties of Mesopotamia, and especially in the Seleucid period (301-164 BC) following the death of Alexander the Great, Babylonian (during this period called Chaldean) astronomers approximated the cyclical accelerations and decelerations of the moon and planets withthe "zigzag functions." They did this numerically, not graphically, but the technique worked well enough for their purposes.
The phases of the moon are important in a society not lighted by electricity. The new moon allows a little more time in the day for hunting and gathering and provides more security from animal and human predators.
A lunar eclipse was frightening to many people, so its prediction was helpful. (Of course, solar eclipses are the most frightening, but their prediction came later.) So the ability to count backward and see "how it got that way" was of great value to the priests and "scientists" of ancient societies.
We've become very blasé about "expecting" lunar and solar eclipses and return of recorded comets.
There are recorded cases wherein in a ruler -- his priests having predicted a solar eclipse -- sent his soldiers to wait outside an enemy city to take it over during the panic of the solar eclipse.
In 1504, Christopher Columbus used an edition of Regiomantanus' Ephemerides to predict a total eclipse of the moon on Feb. 29. This so frightened Native Americans that they allowed Columbus and his crew to escape.
In the 1930's, a solar eclipse viewed in India panicked an immense crowd of people -- many thinking a demon was "eating the sun" -- so that thousands of children, women, and old people were trampled to death in the stampede.
Newton's friend, the astronomer Edmund Halley -- after taking measurements on the Comet named for him -- was able to WORK BACKWARD to other times when it appeared -- for example, at the Battle of Hastings, 1066, when the Normans of France defeated the Anglo-Saxons and took over the throne. Halley's prediction of future times for the Comet's return have been confirmed.
Among the ancients, Babylonians achievements excelled. To perfect their calendar, they studied the motions of the sun and moon. They began each month the day after the new moon's lunar crescent first appeared after sunset.Going beyond observations to calculate it in advance (about 400 BC), they realized that the motions of the sun and moon from west to east around the zodiac seem to move with increasing speed for half of each revolution to a definite maximum, then to decrease to the former minimum. Arithmetically, they gave the moon a fixed speed for its motion during half its cycle and a different fixed speed for the other half. Later they represented the moon's as a factor that increases linearly from minimum to maximum during half a revolution, then decreases to minimum at end of the cycle. These calculations of the lunar and solar motions predicted the time of the new moon and the day on which the new month would begin. As by-product, they knew daily positions of moon and sun for every day during the month.
Similarly, planetary positions were calculated, with both eastward and retrograde motions represented. Archaeologists have unearthed hundreds of cuneiform tablets showing these calculations. A few tablets, originating in the cities of Babylon and Uruk, on the Euphrates River, bear the name of Naburiannu (flourished about 491 BC) or Kidinnu (flourished about 379 BC), astrologers who may have invented the systems of calculation.
"It was perhaps in algebra that the Babylonians did their most important work, for by 4000 BC they had developed an extensive rhetorical algebra. A particular favourite of Babylonian puzzle masters was to determine the values of x and y, given the (positive) values of x + y and xy. This is equivalent to solving a quadratic equation, which they could do using the equivalent of a general formula. Indeed, they went on to discuss both third and fourth order equations, and also simultaneous equations in several unknowns. They had an effective algorithm for computing square roots, and generated a remarkable approximation to (2)1/2. Using their version of log tables they solved problems in compound interest using linear interpolation, in almost exactly the same way that British school children would solve them six thousand years later. ....The number base 60 allowed the Babylonians to adopt a simple technique for dividing one number by another, because inverses could easily be determined for the many divisors of 60 (the sexagesimal digits are represented here in decimal, separated by commas):
"Avoiding both our long division and the Egyptian duplation technique, a Babylonian engineer would calculate a/b by first finding 1/b in the table, and then multiplying this by a. This technique is extremely efficient, and is still used in computational look-up tables, but was limited by the numbers for which an inverse was easily found."(Mike Stannett, noisefactory.co.uk/research/sci-math/history/hist012.html)
They had tables of squares, square roots, cubes, cube roots, reciprocals, exponential functions, log functions..... They had knowledge of trigonometry, the Pythagorean theorem 1200 years before Pythagoreas did, and pi. They knew that certain equation solutions reduced to log tables based on a non repeating fraction that they approximated as 2.43 in base 60 (163/60 or 2.716666.. in base 10). This is the base to the natural logarithm "e". They reduced equations to the quadratic form and solved some polynomial equations to the eighth degree. Unlike the Greeks, to follow 1000 years later , the Babylonians thought in terms of algebra and trigonometry instead of geometry.
