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"Every particle in the universe attracts every other material
particle with a force that is proportional to the product of the
masses of the two particles, and inversely proportional to the
square of distance between their centers. The force is
directed along a line joining their centers. "

Seven Ideas that Shook the Universe-- Spielberg & Anderson

Aristotle, the great Greek philosopher, believed in a homocentric

model of the solar system. This model placed all the planets with

one object--the unmoving Earth-- at the center of concentric

spheres holding the planets and moon. He divided the universe

in two "worlds"--the heavenly and the sublunar, The sublunar world was made
of four substances--earth, water, air, and fire. The heavenly world was made of
"ether". To Aristotle the laws of physics governed both worlds but were
different for each world. Unlike Eudoxus who had a model of eight geocentric
spheres carrying the moon and the planets, Aristotle had 56 spheres linked to
a large sphere called the "Prime Mover". The weakness in the Aristotelian
system was noticed because the brightness of the heavenly bodies varied
which indicted a change in distance from the Earth and thus an imperfect
heaven. In 150 AD and using mathematics, the Hellenistic astronomer, Ptolemy
devised a planetary system where Earth was a bit off center and even at times
moving slowly! He also used epicycles. This answered the Aristotelian
criticisms. A geocentric system still, but the modifications were important!
Ptolemy made no attempt to explain "how" the motion happened but as many
students do, simply wanted a 'correct" answer mathematically. Aristotle was
the first scientist to attempt to set forth a set of simple assumptions to explain
physical phenomena.

For approximately 2000 years, it was believed that the Earth

was at the center of the universe, "in reality and in divine

conception". The first, and possibly the most traumatic

scientific revolution, was the theory that the Earth is not the

center of the universe (Copernican Astronomy). The

Heliocentric Centric Theory (the sun was the center of motion

for all the planets of the solar system) had been proposed

(by Aristarchus) and rejected as early as the time of Aristotle.

A minor church official in Crakow, Poland, began studies in mathematics,
astronomy, theology, medicine, cannon law, and Greek philosophy. His
church duties let him much time to undertake a thorough study of
astronomy. From such, he concluded that the Ptolemaic System was too
complicated and too inconsistent with its mathematical treatment of orbits.
Ockham's Razor is a rule that states that simpler explanations are preferable
to complicated ones. Copernicus proposed (as Aristarchus had) that the
fixed stars and the sun should be regarded as stationary and the Earth, as
well as other planets, circled about the sun. He also proposed that the Earth
rotated on its axis. This shift of point of view from the Earth to the sun made
motion much less complicated. He completed his work in 1530 but did not
publish in fear of the reaction of the establishment. His work, On the
Revolutions of the Heavenly Spheres was published in 1543 on the day
Copernicus died.

Born in a time of religious and political strife in northern Italy,
Galileo Galilei demonstrated extreme talents in many areas. A
talented painter and a medical student at the University of
Pisa (one of the best schools in Europe), he became more
interested in mathematics and science. He displayed so
much talent inn mathematics that he was appointed professor
of mathematics at Pisa while still in his mid twenties.

Early in his career, Galileo became convinced that Aristotle was wrong in many
aspects of physics. He became a Copernican while young but did not
publicize his beliefs until he was almost forty-six. He was quite sure Aristotle's
ideas on motion were very incorrect. Galileo felt that the medium the object fell
in affected its speed. Aristotle felt that the mass of the object was the direct
cause of a difference in speed. His experiments on the incline plane were
critical to his theories. At that point in history, it was not easy to time
accurately. After trying many methods, Galileo used a water clock. He then
graphed his data to help explore and explain the results. For all his inclines,
his position-time graphs were parabolas. He was able to recognize that the
speed that matched this type of graph would be a straight line with uniform
slope--uniform acceleration. Thus Galileo was able to determine that objects
fall with uniform accelerated motion. He emphasized that the natural state of
an object was to move at constant speed.

Galileo's net contributions to science were great. He described how objects
fall, introduced the idea of inertia, corrected Aristotle's misconceptions about
falling objects, and answered how projectiles move as they do. However, he
did not give the "why" of the motion. That was left to Newton. Galileo was
an outgoing, hard living individual. He was so devastating in written and oral
debate that he made many enemies as well as friends. Misjudging the
political climate, he published a book, Dialogues Concerning the Two Chief
World Systems. Using the Socratic Dialogue approach, two characters --one
an advocate of a Ptolemaic Universe and the other an advocate of the
Copernican Universe--debate each other. At the end the Copernican
advocate concedes the debate to the Ptolemaic character. But the Ptolemaic
is portrayed as a simpleton and it is clear which debater really won the
argument. The pope was not amused. Because of his age, Galileo was
punished by house arrest instead of torture. He recanted his theories but his
book had been read by thousands. He was cared for by his illegitimate
daughter and died shortly before age 78.

One of biggest weaknesses of Copernicus' work was his
lack of accurate data. In 1576, the Danish astronomer
Tycho Brahe built an observatory near Copenhagen. A
nobleman of quite unusual appearance--he had a silver
nose to replace his own that he lost in a duel--he was an
unusually meticulous observer. His measurements of
planetary position were more than twice as accurate as
previous data. He was the first to track the planets
throughout their entire orbit. All of this he did without the
aid of telescopes and used only "sighting tubes" that he
designed. He supported a modified theory of the solar
system; the Earth is at the center but other planets revolve
about the sun. This is known as a Tychonic Theory.

Kepler was born 28 years after Copernicus' great work was
published. His childhood was an unhappy one--plagued by
poor health and a lack of friends. His talent in mathematics
soon surfaced and he obtained a position as a teacher of
mathematics. Because of his mathematical gifts, his deficiency
as a teacher was overlooked. In fact, being such a poor teacher
meant he had fewer students. This allowed him more time for
research ( a somewhat prevalent theory at modern universities).
He turned to the study of orbital motion.

There are two methods of logic used in science. In the first,
evidence is collected and from that evidence or series of
experiments a general rule is produced. The general rule is
obtained directly from experimentation. This is the
inductive process. The other method is the deductive
process. Starting at a general rule, the logical process
concludes that certain expected outcomes should result
from the general rule.

Isaac Newton successfully combined the inductive and deductive methods to
produce amazing results. He would start by making observations to reach a
general rule. From that rule he would then deduce that certain phenomena
should occur. From his observations, Newton produced The LAW OF INERTIA,
F=MA, ACTION-REACTION FORCES & THE UNIVERSAL LAW OF
GRAVITATION. It is impossible to overrate the impact these laws had on the
world. Newton's influence was to establish the belief that the Universe was a
Mechanical Clockwork Arrangement. Laws of science could be found to
explain everything in simple related terms. Faith in the "scientific process"
became a part of modern culture. This was the start of "the age of reason". The
American and French Revolutions owe much to Sir Isaac Newton's laws of
motion.

As a person, Newton was strange and difficult. He was jealous, ego ridden,
complex and morose at times. He lived his life as a bachelor cared for by his
niece. He was admired by Voltaire and Alexander Pope and detested by
Jonathan Swift and William Blake. His work constitutes some of the most
important achievements in science and mathematics. (He is credited as the co-
father of calculus along with Leibniz.) In short, he gave us the "why" of
Galileo's "how". His greatest work was "Principia" written in Latin. It contained
his Laws of Motion as well as Laws of Conservation of Momentum and Energy.

Kepler was not content to propose laws for the motion of the planets. These laws
had to be consistent with Tycho Brahe's data. In 1600, Kepler became Brahe's
assistant. Kepler and Brahe did not always get along but Kepler knew that he
needed Brahe's data. Brahe, in turn, was aware of Kepler's mathematical genius.
Brahe died in 1601 as a result of overeating and Kepler took custody of Brahe's
data. For two decades he struggled with Brahe's data and finally published his
Three Laws of Kepler. He did this in spite of interruptions that included many
changes in employment, the death of his beloved first wife, and a court battle to
defend his mother against charges of witchcraft. Kepler was the right person at
the right time to discover the laws governing the motion of the planets. He was
greatly respected as a mathematician and his work was taken seriously.