Fundamentals of astrodynamics and applications 4th Edition (2013)

6 EQUATIONS OF MOTION 1.1
occurred about the center of the deferent. This was actually a departure from the circular
motion.
It may, however, fairly be doubted whether Hipparchus or Ptolemy ever had an abstract
belief in the exclusive virtue of such [circular] motions, except as a convenient and easily
intelligible way of representing certain more complicated motions, and it is difficult to conceive
that Hipparchus would have scrupled any more than his great follower, in using an
equant to represent an irregular motion, if he had found that the motion was therefore represented
with accuracy. . . . The earlier Greeks, . . . and again many astronomers of the Middle
Ages, felt that it was on a priori grounds necessary to represent the perfection of the heavenly
motions by the most perfect or regular of the geometric schemes. (Berry, 1961:71–72)
Although Ptolemy had devised unique methods to explain the motion of the Sun and
planets, he still faced the problem of fitting the observations to one of his new theories.
He separated the problem for the inferior planets (Mercury, Venus, and the Sun), and the
superior planets (Mars, Jupiter, and Saturn). The difficulty that all the ancient astronomers
faced was explaining the observed irregular motions of the Sun and planets. In
fact, some planets exhibit retrograde motion at times, or a backwards motion, when
observed from the Earth. The effect is the same as the perceived velocity change as you
pass another car.
Ptolemy’s explanation of orbital motion greatly increased its complexity. He even
accounted for the inclination of the planets by slightly tilting the epicycles. Finally, in
his Almagest (c. 150), Ptolemy described the construction of an astrolabe, a fundamental
tool of the time, and the basis of some tools still used today. The instrument permitted
angular measurements of the motions of the planets and stars.
The Ptolemaic tables in the Almagest were the last major astronomical endeavor for
many centuries. Indeed, the fall of the Roman Empire in 476 eliminated financial support
for many scientific efforts. Because of the prevalence of Catholicism after the fall
of the Roman empire, the correct dates of religious festivals were required by Church
officials well in advance. In particular, the correct date of Easter was of prime concern.
According to the resolutions of the Nicene Council in 325 A.D., Easter was to occur on
the first Sunday following a full Moon after the first day of spring (the vernal equinox).
This meant the date could fall anywhere between March 22 and April 25. Determining
this day was difficult for most scholars and continued to perplex scientists until almost
1800 when Karl Frederick Gauss (1777-1855) found a solution. Pannekoek (1989:219)
records the finding:
Dividing the year by 19, by 4 and by 7, the remainders are called a, b, and c; put 19a + 15 =
multiple of 30 + d (d < 30); put 2b + 4c = multiple of 7 + e (e < 7). Then the date of Easter
is March 22 nd + d + e.
In the 7 th century, the rise of Islam demanded more accessible star tables so worshippers
could determine the direction of Mecca; thus, the Almagest was eventually translated
into Arabic. *
* In fact, the 9 th -century title (Almagest) was created from the Arabic superlative mageste (meaning
largest or biggest) with the added al prefix.