to plot spatial intervals that are less than whole returns, some means of dividing up
the great circle of the ecliptic was also needed. Sometime after 500 BCthis resulted
in the invention of the zodiac, whereby 30 USˇof arc were each assigned to 12 signs,
whose names were taken from nearby constellations, in a circle of 360 USˇ. We translate
these USˇas ‘degrees’, though they should not be confused with degrees describing
angles subtended from a point (Brown 2000 a: 106 ). They are fractions of a great
circle.
The ‘regulation’ of the luni-solar calendar and the invention of the zodiac were
primarily effected in order to assist in the further development of astronomy in
Babylonia from a non-mathematical variety to a fully mathematised one. Both found
far wider uses. The 19 -year scheme was adopted by Meton of Athens in the late fifth
century, and remains the basis of the Hebrew calendar to this day. The zodiac, of
course, went on to become the dominant tool of divination, particularly through the
spread of personal astrology, especially horoscopes. The division of the great circle
into 360 units became the standard means of dividing any circle.
We have ca. 80 full planetary ephemerides, several templates giving just longitudes
and no dates, and about 30 procedure texts. We also have a few texts of a mathematical
nature which deal with various aspects of planetary behaviour – variation in latitude,
errors in characteristic periods, subdivisions of the arc between successive phenomena
of the same type (the synodic arc). The earliest of these (BM 36301 ) dates back to
the fifth century BC, but the most advanced stage was reached during the third to
first centuries BC. While most attested planetary ephemerides calculate the location
and dates of the phases, ones for Jupiter and Mercury offered schemes giving the
location of the planet on a day-by-day basis, essentially fulfilling the same aim as
Greek kinematic astronomy (Neugebauer 1975 : 452 ). No doubt similar tables once
existed for all the planets (see further Steele 2000 on text A 3405). We must, therefore,
entertain the notion that one of the most important aims of the planetary ephemerides
was to provide data that would have been of use to those writing horoscopes, for
which the location of the planets at any given moment was crucial. Much as we might
wish to imagine that the most advanced Babylonian astronomy was undertaken by
scholars who were interested in planetary behaviour for its own sake (e.g. Neugebauer
1975 : 412 ; contraBrown 2000 : 220 ), that view does appear to be little more than
the projection of modern sensibilities.
The aim of non-mathematical astronomy may also have increasingly become devoted
to providing data useful to those doing zodiacal astrology, and away from providing
data on the ominous phases of the planets, which would have been useful to those
divining with omens. The Almanacs, for example, from early in the Hellenistic period
and perhaps as early as the invention of the zodiac itself, give, among other things,
calculated data on when planets entered zodiacal signs for a given year. At the moment
of any birth, the horoscoper could easily have read from the Almanacs the sign in
which each planet was located.
The masterpieces of cuneiform astronomy are the lunar ephemerides. These
determined the moments of luni-solar conjunction and opposition (the so-called
syzygies), the lengths of lunar first and last visibilities, and the details of eclipses.
The intervals between syzygies depend on the varying velocity of both Moon and
Sun, the latter having the dominant effect. The authors of the lunar ephemerides
successfully modelled both, and how they managed this remains a topic of some
— Mesopotamian astral science —