Towards a new world Model
From Galileo to Newton:
Physics Emerges
Newton's Many Accomplishments
BACKGROUND &
TIMES 
1. By the time Isaac Newton
entered college, the scientific revolution of the 17th century was well
underway.
2. Men like Copernicus, Kepler, Galileo, and Descartes had
all helped develop a new view of nature.
3. When Newton went to
Cambridge, everyone was still studying the old nature.
4. Newton
studied it too—but in his notebook he had written: "Amicus Plato;
amicus Aristoteles; magus amica veritas." "Plato is my friend,
Aristotle is my friend, but my best friend is truth." 

THE PERSON 
1. Isaac Newton was born on
Christmas Day, 1642, the same year Galileo died.
2. He did much of his
greatest work during a two year period from 1665 to 1667 when he was at the
village of Woolsworth to escape the Great Plague which was ravishing London.
3.
His life was troubled by angry conflicts and bitter feuds with colleagues and
friends.
4. Twice these feuds led to breakdowns; other times they led
to bursts of brilliant new achievements.
5. He died in 1727, at the age
of 85. Years later it was discovered that much of his erratic behavior may have
been caused by mercury poisoning. Recent samples of his hair showed he had forty
times the level of mercury considered normal. 

ACCOMPLISHMENTS 
1. Newton discovered the origin of
color.
2. He discovered the nature of gravity.
3. He invented
calculus.
4. He invented the first reflecting telescope.
5. He
wrote and published the book Mathematica Principia, which provided a detailed
explanation of the laws of gravity and motion, particularly as they applied to
astronomy.
6. He was knighted as Sir Isaac Newton and became
president of the Royal Society, a post he held until his death.  
UNIQUE
INFLUENCE 
1. He was one of the most creative
geniuses the world has ever seen and to many people the greatest scientist who
ever lived.
2. While Galileo's discoveries brought humankind to the
brink of a new age, Newton took it the rest of the way.
3. He unified
the work of Copernicus, Galileo, and Kepler into one scientific theory that has
stood the test of time.
4. Principia Mathematica is still considered by
many to be the greatest scientific book ever written. It is the fundamental
work for all of modern science.
5. Newton was the integrator, the
unifier, the organizer, of all the scientific knowledge available at the time.
He established a solid platform on which all modern science could be built. 

Galileo's laws of Motion:
Aside from his numerous inventions, Galileo also laid down the first
accurate laws of motion for masses. Galileo measured that all bodies
accelerate at the same rate regardless of their size or mass.
Key among his investigations are:
 developed the concept of motion in terms of velocity (speed
and direction) through the use of inclined planes.
 developed the idea of force, as a cause for motion.
 determined that the natural state of an object is rest or uniform
motion, i.e. objects always have a velocity, sometimes that velocity has
a magnitude of zero = rest.
 objects resist change in motion, which is called inertia.
Kepler's laws of Planetary Motion:
Kepler developed, using Tycho Brahe's observations , the first kinematic description of
orbits, Newton will develop a dynamic description that
involves the underlying influence (gravity)
 1st law (law of elliptic orbits): Each planet moves in an
elliptical orbit with the Sun at one focus.
Ellipses that are highly flattened have high eccentricity. Ellipses
that are close to a circle have low eccentricity.
 2nd law (law of equal areas): a line connection the Sun and a
planet (called the radius vector) sweeps out equal areas in equal times
Objects travel fastest at the low point of their orbit, and travel
slowest at the high point of their orbit.
 3rd law (law of harmonics): The square of a planet's orbital period
is proportional to its mean distance from the Sun cubed.
The 3rd law is used to
develop a ``yardstick'' for the Solar System, expressing the distance to
all the planets relative to Earth's orbit by just knowing their period
(timing how long it takes for them to go around the Sun).
Although successful, Kepler's laws remained a set of empirical rules without a dynamical basis. The link between these laws and the physical world would be established about 50 years later by Isaac Newton (16421727).
Newton:
Newton's Explanation of Kepler's Laws
Newton expanded on the work
of Galileo to better define the relationship between energy and
motion. In particular, he developed the following concepts:
 change in velocity = acceleration caused by force
 inertia = resistance
to change in velocity and is proportional to the mass of the
object
 momentum = quantity
of motion energy and is equal to mass times velocity
 law of conservation of momentum = total momentum (mass x velocity)
of an interaction is conserved is the same before and after
Example: Cars and Trucks on Ice!
A corollary to Newton's ideas was the so called Clockwork Universe
model. A concept that states that the total momentum of the Universe
is conserved, interactions redistribute the momentum, but the total never
changes. In this model, God only starts the clock (initial cause),
then it runs by itself for the rest of time.
Newton's laws of motion:
 1st law: a body remains at rest or moves in a straight line of
constant velocity as long as no external forces acts on it
 2nd law: a body acted on by a force will accelerate such that force
equals mass times acceleration (F=ma)
 3rd law: for every action there is an equal and opposite
reaction
Well fine, if gravity is an attractive force, then how come the
moon doesn't come crashing into the earth, or the earth into
the sun. What causes an orbit to be stable?
An orbit is the balance between inertial and gravitational forces. That is,
the earth is continually falling toward the sun, but inertia also wants the
earth to keep moving in a straight line. When these two forces are in
balance a stable orbit results:
Newton's Law of Universal Gravitation:
Galileo was the first to notice that objects are ``pulled'' towards
the center of the Earth, but Newton showed that this same force
(gravity) was responsible for the orbits of the planets in the Solar
System.
Objects in the Universe attract each other with a force that varies
directly as the product of their masses and inversely as the square of
their distances
But how can you show this from first principles?
Well only an R^{2} force law can reproduce Kepler's Third Law:
and for something really cool
All masses, regardless of size, attract other masses with gravity. You
don't notice the force from nearby objects because their mass is so
small compared to the mass of the Earth. Consider the following
example:
Newton's development of the underlying cause of planetary motion,
gravity, completed the solar system model
begun by the Babylonians and early Greeks. The mathematical
formulation of Newton's dynamic model of the solar system became the
science of celestial mechanics, the greatest of the deterministic
sciences.
Although Newtonian mechanics was the grand achievement of the 1700's,
it was by no means the final answer. For example, the equations of
orbits could be solved for two bodies, but could not be solved
for three or more bodies. The three body problem
puzzled astronomers for years until it was learned that some
mathematical problems suffer from deterministic chaos, where
dynamical systems have apparently random or unpredictable behavior.
Synposis of the Principia