## Thursday, 9 July 2009

### Newton's Law of Universal Gravitation

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 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.