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. F_{12}= -F_{21}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. F_{grav}= G m_{1}m_{2}/ r^{2}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 swormley1@gmail.com