Fundamentals of astrodynamics and applications 4th Edition (2013)

2 EQUATIONS OF MOTION 1.1
one, . . . the belief in it has undoubtedly been a powerful stimulus to genuine astronomical
study.
Perhaps the two greatest concerns of the ancient civilizations were agriculture and religion.
People were concerned about their crops, the summer rains, storms, or, in essence,
their very existence. As Barclay (1956:97) says,
The ancient world was dominated by the thought of the influence of the stars; and even the
greatest and wisest men would not act without consulting them. [They] believed that all
things were in the grip of an iron fatalism settled by the stars; and the science of astrology
professed to provide men with the secret knowledge which would rid them of their slavery
to the elemental spirits.
Because many events in nature are random (such as earthquakes and storms), astrologers
sought explanations in events that were consistent and predictable, such as the
movements of the Sun, Moon, and stars. In the absence of any other knowledge, astrology
took on almost a religious importance. The significance of determining heavenly
motions meant they attacked the problem with great vigor and made every effort to
improve their accuracy.
The Sun’s diurnal rising and setting motion was the easiest to observe; yet, its brightness
made accurate observations difficult. Early people studied solar eclipses in great
detail because these events terrified them. Studying the Sun and Moon quickly dominated
astrology.
The Chaldeans determined the Saros cycle by noticing the regularity of certain types
of eclipses over time (Green, 1988:449). The period between eclipses is 6585.32 days,
and consecutive occurrences are displaced approximately 120° to the west of the previous
event. An interesting side legend tells of Chinese astronomers who regularly predicted
eclipses, probably using the Saros cycle (Asimov, 1971:18–19). The night before
an eclipse they had predicted, the astronomers went out drinking. Unfortunately, in their
inebriated state, they forgot to tell the emperor. When the eclipse frightened the
emperor, he ordered the astronomers executed. If true, this legend has important lessons
for us even today, for mistakes in our field of astrodynamics can have grave consequences!
Observing the cycles of the Moon was slightly easier than for the Sun, and it permitted
more precise observations. The early Babylonians, who had reasonably good
weather conditions for observing the Moon’s phases, developed the lunar month (about
29½ days) (Pannekoek, 1989:21).
The planets presented a greater challenge because their motions appear transient and
inconsistent. The early Babylonians accomplished tremendous feats and were even able
to predict the phases and period of Venus. Still, as Pannekoek (1989:33) points out,
some of their predictions were based on incorrect phenomena or intervals from erroneously
copied values and rough averages. So their mathematical understanding is suspect.
Thales (c. 640–546 B.C.) of Miletus, was perhaps the first astronomer to receive notoriety.
He is credited with determining the length of the year and founding the Ionian
school of astronomy and philosophy. He predicted eclipses, probably using the Saros
cycle. Moulton (1914:30) suggests that he may also have taught about the obliquity of