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Egyptian and Mesopotamian achievements
The organization of the universe that is created and governed by all-powerful gods is told in myths.
Astronomical achievements are for practical and/or religious reasons, not for the achievement of a world view.

EGYPTIANS:
Because the Egyptian approach to astronomy is non mathematical, their astronomy will never become predictive, as does that of the Babylonians. The Egyptians could add, subtract, multiply, divide, and calculate simple areas (e.g. squares, triangles, rectangles). Despite those skills, there does not appear to have been a complex geometric knowledge.
Their astronomical focus will remain on fixed stars rather than on planets. Many of their buildings will be oriented to fixed stars with amazing accuracy.  This can be readily understood if we realize that the egyptian religion was based on Ra the sun god and emphasized stability and the correspondance between the heavens and the earth. By 3000 BCE they have identified groupings of stars(=constellations) which represent likenesses to mythological beings or animals, along with a zodiac which marks the ecliptic, the sun's yearly path through the 12 zodiacal constellations.
No doubt they were aware of precessional motion also although we have no records to support that.
The egyptian astronomical tradition was much more extensive than we know, and there are clear indications that much of it had been preserved in the great library of Alexandria. Unfortunately, with the destruction of the Library and the temples and their records in 391 CE under the edict of Theodosius insured that virtually all the knowledge of the egyptians disappeared. What we know is mainly reconstructed from archeological records from the past two centuries.

The Egyptian Civil Calendar

The Egyptians used the periodic events in the heavens for calendar, both civil and religious. The civil calendar focused primarily on the sun hence they used the solar year (365 days) rather than a lunar calendar (although parts or even most of some of the religious calendars were based on the moon). Beginning of the year occurs at the first rising of the star Sothis (our prensent day Sirius) as the sun is setting. The year is divided into 12 months of 30 days. The month is divided into three 10 day segments (=decans therefore 36 decans in a year). At the end of the year, there are 5 extra days added for a 365 d. year.

Just as the path of the sun over a year is divided into 12 constellations so is the day and the night divided into 12 parts, the hours. Originally of different lengths depending on the seasons, the 12 day hours and the 12 night hours will evolve into fixed length hours of 60 minutes. During the day time is based on on the gnomon (sun dial). It is thought that some, if not most, of the obelisks were used as sun dials.  At night, time is measured with first appearance of stars on the horizon and later also with water clocks.

BABYLONIANS
The Babylonians focus on numerical rather than geometric relationships associated with a felt need for accurate prediction
2000 BCE identified the motions of planets. calculations are based on arithmetic progressions to describe recurring phenomena
Identify the ecliptic, the sun's yearly path through 12 constellations (the zodiac). After 1500 BCE, there are systematic mathematical tables that note conjunctions of the moon and planets with stars, using mathematical tables. position of the sun, moon and planets re computed for regular intervals, so that planetary and lunar phenomena could be predicted. base 60 math and place notation. could compute reciprocals squares, square roots, cubes and cube roots.add subtract multiply divide mathematical theory of movements of bodies using such variables as the velocity of the sun and monn  angles between the ecliptic and the horizon, magnitude of eclipses
By 500 BCE they have such an enormous observational data base thatcan predict lunar eclipses and somewhat solar eclipses. They probably knew how to do this much earlier. The predictions are based on a mathematical (numerical rather than geometric) algorithm, based on millenia of observations. Some evidence that they thought the earth was spherical. The celestial sphere is an imaginary sphere that rotates from E-W
Sun, Moon 5 Planets move relative to the background of stars
Mesopotamian calendar is lunar. Because the lunar year is about 11 days shorter than the solar year, therefore they have to aqdd an extra monthh about every 3 years. This addition is haphazard until~500 BCE when the metonic cycle is introduced. Every 19 years, the lunar and solar calendar come back in phase if we add 7 months during this 19 year cycle. Babylonian month (as jewish and islamic) begins with first sighting of the new crescent moon.
 
 
 

Greeks
acquire babylonian knowledge beginning 1000 BCE developed geometry and simple trigonometry; focus was and remained on geometrical explanations of heavenly motions rather than numerical
Acquired constellations from Babylonians have a total of 48 constellations