```  Voyages of Discovery: Copernicus to the Big Bang
http://edu-observatory.org/olli/VD-C2BB/Week3.html

Isaac Newton (1642-1727) discovered (and showed mathematically)
that objects in free fall (such as planets influenced by a
central force like the Sun's gravity) follow the paths of conic
sections.

The task of deducing all three of Kepler's laws from Newton's
universal law of gravitation is known as the Kepler problem. Its
solution is one of the crowning achievements of Western thought.

Isaac Newton's solution to "the Kepler Problem" is well presented
in episode 22 of "The Mechanical Universe" series, mathematics
and all... and can be viewed online at

The Mechanical Universe - MU-22  "The Kepler Problem" 28:30
http://www.learner.org/resources/series42.html

Newton's Laws

p = mv

This equation says that the momentum of a body is the product of its
mass and its velocity. If this were a calculus based course, I would
be obliged to tell you that this equation involves a time derivative,
where Newton defined velocity v = dr/dt .

Newton's first law, also called the "law of inertia", states that body
at rest remains at rest and a body in motion continues to move at a
constant velocity unless acted upon by an external force.

"Hidden in the law of inertia is that fact the whether an
object is in motion or not depends strictly on the point of
view of the observer".

Conservation of momentum, embodied in Newton's first law, is a
fundamental law of physics which states that the momentum of a system
is constant if there are no external forces acting on the system.

F = dp/dt (Newton wrote)

F = ma    (Euler's version)

Either equation (after all they are equivalent) relates force, mass and
acceleration. Again, if this were a calculus based course, I would be
obliged to tell you that this equation involves a time derivative,
where the velocity a = dv/dt. In Euler's version on Newton's second
law, F is the applied force, m is the mass of the particle, and a is
the particle's acceleration.

F12 = -F21

Whenever a body exerts a force on another body, the latter exerts a
force of equal magnitude and opposite direction on the former. This is
known as the weak law of action and reaction.

Fgrav = G m1 m2 / r2

Gravity is the force exerted by all objects having mass on all other
objects having mass. Newton's Law of Gravitation says that the
gravitational force between to masses is proportional to their masses
and inversely proportional to the square of the distance between them.

Newton's Law of Gravitation incorporates the inverse-square law,
which states that some physical quantity or strength is inversely
proportional to the square of the distance from the source of that
physical quantity. Gravity, light, and sound all obey the
inverse-square law.

"Newton's law completely describe all the phenomena of classical
mechanics...."

Newton's Gift: How Sir Isaac Newton Unlocked the System of the World
by David Berlinski
http://www.amazon.com/dp/0743217764

The Principia: Mathematical Principles of Natural Philosophy, by
Isaac Newton, Trans. I. Bernard Cohen and Anne Whitman, with the
assistance of Julia Budenz (University of California Press:
Berkeley, 1999)
http://www.amazon.com/dp/0520088174

"Newton's Principia for the Common Reader" by S. Chandrasekhar
(1995) Clarendon Press, Oxford ISBN 0 19 851744 0
http://www.amazon.com/dp/019852675X

Quoting from "Great Physicists: The life and times of leading
physicists from Galileo to Hawking: by William H Cropper.

'For his final study, Chandra chose a remarkable subject--Isaac
Newton. Chandra was a student of science history and biography, and
he had a wide acquaintance among his contemporaries in physics and
astrophysics. But for him one scientist stood above all those of
the past and present, and that was Newton. He decided to pay homage
to Newton, and try to fathom his genius, by translating "for the
common reader" the parts of Newton's Principia that led to the
formulation of the gravitational law.

'Newton relied on the geometrical arguments that are all but
incomprehensible to a modern audience. To make them more
accessible, Chandra restated Newton's proofs in the now
conventional mathematical languages of algebra and calculus. His
method was to construct first his own proof for a proposition and
then to compare it with Newton's version. "The experience was a
sobering one," he writes. "Each time, I was left in sheer wonder at
the elegance, the careful arrangement, the imperial style, the
incredible originality, and above all the astonishing lightness of
Newton's proofs, and each time I felt like a schoolboy admonished
by the master."'

Galileo Galilei (1564-1642)
http://galileo.rice.edu/galileo.html
http://en.wikipedia.org/wiki/Galileo_Galilei

The Mechanical Universe - MU-4  "The Law of Inertia" 28:30
http://www.learner.org/resources/series42.html

On the Shoulders of Giants by Steven Hawking
http://www.amazon.com/dp/0762413484

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