Fundamentals of astrodynamics and applications 4th Edition (2013)

4 EQUATIONS OF MOTION 1.1
modern technological society, we often take for granted the flow and availability of
information, but that flow was very limited in ancient times. To copy a few pages of calculations
or a book required scarce materials, knowledgeable scribes, and days, weeks,
or even years of effort. It’s no surprise that scholars in the same country often didn’t
know of their contemporaries’ accomplishments and findings in towns a few hundred
miles away.
Hipparchus also noticed an increase in the longitude of the stars (Green, 1988:51). To
observe such a small phenomenon during the second century B.C. is extraordinary and
illustrates the dedication, time, and diligence that the ancient Greeks applied to particular
tasks. Hipparchus likewise developed the first system of cataloging star magnitudes.
The list categorized about 1000 stars by brightness. He did this by separating the stars
into six categories of brightness, each of which was separated by about 2.5 times the
brightness. The brightest was first magnitude, whereas the dimmest, about 100 times
dimmer, was sixth magnitude. It’s remarkable to imagine the naked eye being able to
detect gradations accurately enough to place nearly 1000 stars in the correct categories.
Hipparchus also developed theories to describe orbital motion. He made very accurate
observations, which presented some problems when trying to describe the orbital
motion. As mentioned earlier, ancient astrology had strong ties to religion, so people
thought the heavens were holy and perfect. Because the circle was the only geometric
shape considered to be perfect, they relied on circular motion. Hipparchus, and probably
Apollonius before him, was caught in a difficult dilemma—fitting observational data to
a theory which (as we know now) didn’t represent the data adequately. Hipparchus continued
developing the basic excentric and epicycle systems. The excentric system consisted
of the Sun revolving about the Earth in a circular path, called the excentric, which
is a convenient way to represent the Sun’s apparently irregular motion while preserving
perfect circular motion from the center of the circle. For the epicycle system, the Sun
was placed on a small circle called the epicycle, the center of which rotated about the
Earth. The circular orbit of the epicycle center was called the deferent. Both the excentric
and epicycle systems resulted in the same apparent motion of the Sun and planets
about the Earth. Ptolemy used the term excentric instead of the deferent. Figure 1-1
shows the two theories.
Julius Caesar introduced the Julian calendar in 46 B.C. as a sophisticated way to
track time. That particular year had 445 days due to the large error which had accumulated
(Berry, 1961:23). * The Julian year of 365.25 days is quite familiar because it contains
a leap day every four years to account for the Earth’s non-integral motion about the
Sun. (the actual period is 365.242 189 7). A Julian century has exactly 36,525 days.
Unfortunately, the Julian year doesn’t account for the remainder (about 11 minutes and
14 seconds per year, or about one day in 128 years). Thus, the system was fairly accurate
over a few centuries but accumulated appreciable errors over longer periods. The
Council of Trent (1545–1563) ultimately proposed changing the calendar. In 1582, Pope
* The astronomer Sosigenes actually recommended the change to Caesar after the Roman calendar
(10 months with 304 days and 12 months with 355 days) had produced a three month shift in
the seasons. 46 B.C. is sometimes called the year of confusion.