THE CELESTIAL SPHERE

THE GEOCENTRIC UNIVERSE

Plato (ca. 350 b.c.) suggested that to understand the motions of the heavens, one must first

begin with a set of workable assumptions, or hypotheses. It seemed obvious that the stars

of the night sky revolved about a fixed Earth and that the heavens ought to obey the purest

possible form of motion. Plato therefore proposed that celestial bodies should move about

Earth with a uniform (or constant) speed and follow a circular motion with Earth at the

center of that motion. This concept of a geocentric universe was a natural consequence of

the apparently unchanging relationship of the stars to one another in fixed constellations.

If the stars were simply attached to a celestial sphere that rotated about an axis passing

through the North and South poles of Earth and intersecting the celestial sphere at the north

and south celestial poles respectively all of the stars’ known motions could be

described.

THE RETROGRADE MOTION

A planet such as Mars moves slowly from west to east against the fixed background stars and then mysteriously reverses direction for a period of time before resuming its previous path . Attempting to understand this backward, or retrograde, motion became the principal problem in astronomy for nearly 2000 years . Eudoxus of Cnidus, a student of Plato’s and an exceptional

mathematician, suggested that each of the wandering stars occupied its own sphere and that

all the spheres were connected through axes oriented at different angles and rotating at various

speeds. Although this theory of a complex system of spheres initially was marginally

successful at explaining retrograde motion, predictions began to deviate significantly from

the observations as more data were obtained.

Hipparchus (ca. 150 b.c.), perhaps the most notable of the Greek astronomers, proposed

a system of circles to explain retrograde motion. By placing a planet on a small, rotating

epicycle that in turn moved on a larger deferent, he was able to reproduce the behavior of

the wandering stars. Hipparchus also created the first catalog of the stars, developed a magnitude

system for describing the brightness of stars that is still in use today, and contributed to the

development of trigonometry

Claudius Ptolemy (ca. a.d. 100) introduced refinements to the epicycle/deferent

The retrograde motion of Mars in 2005. The general, long-term motion of the planet

is eastward relative to the background stars. However, between October 1 and December 10, 2005,

the planet’s motion temporarily becomes westward (retrograde). (Of course the planet’s short-term

daily motion across the sky is always from east to west.)  Betelgeuse, the bright star in the constellation of Orion, is visible at (α, δ) = (5h55m,+7◦24′), Aldebaran, in the constellation of Taurus, has

 coordinates (4h36m,+16◦31′), and the Hyades and Pleiades star clusters (also in Taurus) are visible at

(4h24m,+15◦45′) and (3h44m,+23◦58′), respectively.

The Ptolemy model of planetary motion

System by adding equants , resulting in a constant angular speed of the epicycle

about the deferent (dθ/dt was assumed to be constant). He also moved Earth away from

the deferent center and even allowed for a wobble of the deferent itself. Predictions of the

Ptolemaic model did agree more closely with observations than any previously devised

scheme, but the original philosophical tenets of Plato (uniform and circular motion) were

significantly compromised.

Despite its shortcomings, the Ptolemaic model became almost universally accepted as

the correct explanation of the motion of the wandering stars. When a disagreement between

the model and observations would develop, the model was modified slightly by the addition

of another circle. This process of “fixing” the existing theory led to an increasingly complex

theoretical description of observable phenomena.

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