In 1685, Issac Newton proposed his Law of Universal Gravitation as a “center-to-center attraction between all forms of matter” (Hecht 147).  The discovery of this breakthrough in physics has a rustic origin. The story goes that while sitting in an orchard, Newton saw an apple fall to the ground which sent him into meditation for the cause of its drop.  Newton determined that the reason it fell was because a force from the Earth attracted the apple (Narlikar 23).  A more precise definition of gravity cannot be found other than the result of an attraction between masses.  Upon questioning for a better cause of gravity, Professor David Newman from the University of Alaska Fairbanks states that “Gravity simply is”.  There is a current movement to quantify the forces of gravity, magnetism, and electricity into one force called the Grand Unification Scheme (Narlikar 187), but until the discovery of The Theory of Everything, the statement that “Gravity simply is” will have to do for now (Hecht 1114).         

The moon is held in orbit by Earth's gravitational force.  As a natural satellite, the Moon is in constant freefall about the Earth, falling towards the Earth's center of gravity.  The reason that the moon doesn’t fall down to the surface of the Earth is because the curvature of the Earth makes the surface fall away at the same rate (Hecht 158).  First proposed by Newton, the Law of Universal Gravitation denotes the gravitational force between any two bodies as:
                                                          F = GmM/R² 
where F is the force of gravity, G is the universal gravitational constant, m and M are the masses of the two bodies, and R is the distance between the centers of the two masses.  For the Earth-Moon system, the force of gravity between the two bodies is:
                  F = (6.67E-11 N·m²/kg²)(7.35E+22 kg)(5.98E+24 kg)/(3.84E+8m)²
                                                       F = 1.99E+20 N
To find the acceleration due to gravity of the Earth and Moon, you simply manipulate the equation F = ma
                                         Since F = m GM/R², g = GM/R²
For the Earth with a mass of  5.98E+24 kg and a radius of 6.37E+6 m, the acceleration due to gravity is:
                         g = (6.67E-11 N·m²/kg²)(5.98E+24 kg)/(6.37E+6 m)²
                                                       g = 9.81 m/s²
For the Moon with a mass of  7.35E+22 kg and a radius of 1.74E+6 m, the acceleration due to gravity is:
                        g = (6.67E-11 N·m²/kg²)(7.35E+22 kg)/ (1.74E+6 m)²
                                                       g =  1.62 m/s²

The acceleration due to gravity of the Moon is 1.62 m/s², which is only about a sixth of the Earths g of 9.81 m/s².  This difference in gravitational force between the two bodies is due to their difference in mass (Hecht 152).