Newton's Laws
 Law of Inertia 
 An object moves in a straight line
at constant speed unless acted upon by an outside force.
 ``Inertia" is an object's resistance to changing its speed and/or direction.
 Because friction dominates here on the surface of the Earth,
deriving this law required tremendous insight. In our everyday
experience, moving objects inevitably come to rest.
 Since the ancients believed that rest was the natural state
of any object, and since they saw that planets moved continuously,
they had to appeal to some divine "prime mover" that keep pushing
the planets (or their spheres) along.
 Given the law of inertia, once a planet was set in motion
it would continue in motion in the absence of friction/forces.
 Since the planets do not move in straight lines, however,
Newton realized that an "outside force" must be acting  Gravity.

Force = (mass) x (acceleration) F = ma
 For the first time, here is a quantitative mathematical expression of the behavior of nature relating motion, mass, and force. Read in sentence form this equation says:
 Mass measures the resistance of an object to
acceleration when a force is applied.
 It is difficult to accelerate a massive object.
 Given the same mass, larger forces cause greater acceleration.
 Action and Reaction 
 Forces don't act in isolation. When you pull on a rope you
feel the rope pull back on you. When you sit on a chair the chair
pushes up on you with equal and opposite force. You can't push on
something without being pushed back upon by that object.
 A force exerted by one object on another implies an equal
and opposite force exerted by the second object upon the first.
 Rockets propel themselves through the vacuum of space by
pushing out material (the fuel) at high speed in the opposite direction.
Newton's Law of Universal Gravitation
 Since the Moon travels in an orbit around the Earth
(and thus not in a straight line), Newton's First Law requires
that some force must act upon the Moon.
 Newton's insight: This force is the same one that pulls
objects to the ground on the Earth.
 Put another way, objects in orbit are simply falling.
 Newton determined a quantitative relationship for the
gravitational force between two masses (m_{a} and
m_{b}) separated by a distance d_{ab}.
 G is just a number  the gravitational constant. If
you measure mass in kilograms, separation in meters, and force in newtons(!),
then G=6.67 x 10^{11}.
 Any two masses attract one another gravitationally, each one  according to the Third Law  exerting an equal attractive force on the other.
 The greater the masses, the greater the force.
 The second law states that the less massive object
of the two will experience the most acceleration (the
apple falls down much more than the Earth falls up).
 The smaller the separation, the greater the force.
 This law, when you work through the math,
 requires orbital paths to be conic sections (ellipses, parabolas, hyperbolas) and thus provides the physical/quantitative
explanation for Kepler's observations.
Notes
Updated September 30, 2009