Thursday Evening Astronomy
Lecture, 9/15/05
•Summary of the Apparent Motion of
the Planets
•The Ptolemaic (Geocentric) Model
•Weaknesses of the Ptolemaic Model
•Copernicus’ Innovation
•Examples of the Predictive Power of
the Copernican Model
•Weakness of the Copernican Model
Red Sections are not yet completed.
Summary of the Apparent Motion of the Planets
Planet
Time to Cycle
Zodiac
Elongation Restrictions
Retrograde
Periodicity
Angular
distance
behind the
Stars per
Day
Moon
27.3 days
None
Never
13
Sun
365.25 days
None
Never
0.98
Mercury
365.25 days
28 Max. Elong.
116 days
0.98 avg
Venus
365.25 days
45 Max. Elong.
584 days
0.98 avg
Mars
687 days
None, Brightest at Opp.
780 days
0.52 avg
Jupiter
12 years
None, Brightest at Opp.
399 days
0.08 avg
Saturn
29 years
None, Brightest at Opp.
378 days
0.03 avg
The properties of the planets listed above, that we have studied for
the last few weeks, must be part of any model that explains their
apparent motion. We will first review the Aristotelian/Ptolemaic
Model of the Univerese.
The sketch to the
right illustrates the
basic model of the
Universe as
envisioned by
Aristotle. The outer
sphere is the celestial
sphere that carries
the stars and is the
home of the gods.
Within this stellar
sphere, the planets
are located on
concentric nested
spheres centered on
the Earth.
How was the order of
the planets
determined?
Aristotle set
the order of
the planets
using the
apparent
sidereal
periods (Time
to cycle to the
Zodiac.)
Notice that
Saturn the
planet farthest
from the Earth
is the one with
the longest
time period to
cycle the
zodiac.
Which of the
planets is missing
on this diagram?
Ptolemy (See the
Monday Class notes
for his history) devised
a geocentric model of
the Universe which
closely followed the
principles of Aristotle.
In particular, Ptolemy
devised a clever model
where by the planets
moved at constant
speed on perfect
circles as Aristotle
required, but they
moved on two circles
simultaneously; the
smaller epicycle
carried the planet and
the center of the
epicycle followed the
deferent each at a
constant rate.
This simple model was too simple to explain the
variable and complex motions of the real planets. To
try to improve the fit to the positions of the planets,
many complications had been added
Astronomers
• had moved the earth slightly
off the center of the solar
system to avoid needing have
the planets move at varying
speeds along their orbits.
• had used a different type of
epicycle to explain the
motions of Mercury and
Venus than were used for
Mars, Jupiter, and Saturn.
•The model got extremely
complex for Mercury (and
Mars). The figure to the right
shows Mercury riding on an
epicycle on an epicycle on an
epicycle with constant speed
measured from a point well
off-center! (From Scientific
American)
The following excerpt from
John Milton’s Paradise Lost
expresses the degree of
complexity that the
Ptolemaic model grew to
just prior to its rejection by
Copernicus.
“Hereafter, when they come
to model Heav'n,
And calculate the Stars,
How will they wield
The mighty frame, how
build, unbuild, contrive,
To save appearances, how
grid the Sphere
With Centric and Eccentric
scribbl'd o'er,
Cycle and Epicycle,
Orb in Orb.”
Problems with the Copernican Model
1. No Proof that the Earth moved.
•
Scientists and philosophers of the time argued that Copernicus’ proposal that Earth moved was
as ridiculous as a person on a ship proposing that it was the ocean, and not the ship, that
moved. No one could believe a mass as large as the Earth could move as Copernicus
proposed. A simple calculation using the radius of the Earth (6,378 km) and the approximate
rotation period of the Earth (24 hours), indicates that a person on the Earth’s equator is in fact
moving at 1,670 km/hr or about 1,000 mph. This high a velocity without visual effects like the
blowing down of buildings was unbelievable at that time.
•
In addition, in the Old Testament book of Joshua (10:13) scripture seemed to clearly indicate
that the Sun moved, not the Earth, as inferred from this description of God’s intervention in
Israel’s battle against the Amorites “And the sun stood still, and the moon stayed... So the sun
stood still in the midst of heaven, and hasted not to go down about a whole day.”
2. No mechanism by which the planets (Earth included) maintained a
circular motion around the Sun.
•
Aristotelian philosophers argued that the Earth was at rest in the center of the Universe
because of it’s “heaviness” drew it there. There was no physical theory that could account for
the Earth being maintained in constant circular motion away from this special location (the
center). The concept of gravity did not exist at this time nor would it for another 100 years.
Problems with the Copernican Model
3.
Challenged Deeply Held religious beliefs.
Kuhn wonderfully describes the impact of the Copernican model in his work The Copernican
Revolution. I quote from Kuhn directly. “ When taken seriously, Copernicus’s proposal
raised many gigantic problems for the believing Christian. If, for example, the Earth were
merely one of six planets, how were the stories of the Fall and of the Salvation, with their
immense bearing on Christian life, to be preserved? If there were other bodies essentially
like the Earth, God’s goodness would surely necessitate that they too be inhabited. But if
there were men on other planets, how could they have inherited the original sin, which
explains Man’s otherwise incomprehensible travail on an Earth made for him by a good and
omnipotent deity? Again, how could men on other planets know of the Savior who opened for
them the possibility of eternal life? Or, if the Earth is a planet and therefore a celestial body
located away from the center of the Universe, what becomes of Man’s intermediate but focal
position between the devils and the angels? If the Earth, as a planet, participates in the
nature of celestial bodies, it cannot be a sink of iniquity from which man will long to escape
to the divine purity of the heavens. Nor can the heavens be a suitable abode for God if they
participate in the evils and imperfection so clearly visible on a planetary Earth. Worst of all,
if the Universe is infinite, as many of the later Copernicans thought, where can God’s Throne
be located? In an infinite Universe, how is man to find God or God man? (Kuhn’s The
Copernican Revolution, pg 193.)
Problems with the Copernican Model
4.
Copernicus’ original heliocentric model did not predict the positions
of the planets any better than Ptolemy’s geocentric model
•Copernicus could not complete shake off the influence of
Aristotle even as he made the revolutionary proposal that
the Earth was a planet. He held fast to the Aristotelian
tenets that the planets moved on circles at constant
speeds. There is a common misconception that the
Copernican model did away with the need for epicycles.
This is not true, because Copernicus was able to rid himself
of the long-held notion that the Earth was the center of the
Solar system, but he did not question the assumption of
uniform circular motion. Thus, in the Copernican model the
Sun was at the center, but the planets still executed uniform
circular motion about it. As we shall see later, the orbits of
the planets are not circles, they are actually ellipses. As a
consequence, the Copernican model, with it assumption of
uniform circular motion, still could not explain all the details
of planetary motion on the celestial sphere without
epicycles. The difference was that the Copernican system
required many fewer epicycles than the Ptolemaic system
because it moved the Sun to the center.
This presentation is unfinished at
this time. I’ll be back at it as soon as
I’m able. I hope to have it finished
by Friday evening. In the meantime,
please study the assigned text
reading ( pg 40-54 ) and the reserve
reading in Kuhn.