Voyages of Discovery: Copernicus to the Big Bang


  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

  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


  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

  Newton's Gift: How Sir Isaac Newton Unlocked the System of the World
  by David Berlinski
  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)
  "Newton's Principia for the Common Reader" by S. Chandrasekhar
  (1995) Clarendon Press, Oxford ISBN 0 19 851744 0

  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)
  The Mechanical Universe - MU-4  "The Law of Inertia" 28:30

  On the Shoulders of Giants by Steven Hawking