Newton\'s Law of Universal Gravitation

Gravity if one of the four fundamental forces in the universe. Though
the fundamental principles of it eluded scientists until Sir Isaac Newton was
able to mathematically describe it in 1687 (Eddington 93). Gravity plays a
serious part in everyday actions as it keeps everything on the ground; without
gravity everything would be immobile unless a force was applied (then it would
move infinitely because there would be no force to stop it).
Perhaps, the best place to start then would be with such a simple item
as an apple (after all it is what "sparked" Newton\'s creativity). The apple is
one of the two curiosities (the other being the moon) that led Newton to
discover The Law of Universal Gravitation in 1666 (Eddington 93). As Newton
later wrote, it is the story of the sight of an apple falling to the ground (he
was resting at Woolsthorpe because of the plague at Cambridge) that caused
Newton to wonder if this same force was what held the moon in place (Gamow 41).
Newton knew that an object fell to the earth at a rate of about 9.8
meters (32 feet) per second second as pointed out by Galileo. Thus "the apple
that fell from the tree" fell to Earth at about this rate. For the first basic
explanation of this we will assume a linear plane, one in which all forces act
in only one direction. Therefore when the apple fell it went straight towards
the center of the earth (accelerating at about 9.8 meters per second second).
Newton then figured that the same force that pulled the apple to Earth also
pulls the moon to the earth. But what force keeps the moon from flying into the
earth or the earth flying into the sun (Edwards 493)?
To better understand this, one other aspect must first be understood.
Galileo showed that all objects fall to the earth at the same rate (the classic
cannonball and feather proved this). But why? If a piano and a saxophone were
both dropped from the top of the Empire State Building then they would both slam
into the ground at the same rate. Newton realized then that the moon and the
apple were both being pulled towards Earth at the same rate but yet the moon was
the only one who resisted the force and stayed in its elliptical orbit
(Eddington 94). Newton\'s Third Law of Motion says that every force exerted by
one object on another is equal to a force, but opposite in direction, exerted be
the second object on the first (every reaction has an equal but opposite
reaction). So the force of the earth pulling the apple to the ground is
proportionally the same as the force the apple exerts back on the earth.
Now Johannes Kepler lived some forty-five years before Isaac Newton.
And he showed that the orbits of the planets in our solar system were elliptical.
When the time of Newton came around he mathematically proved that, if Kepler\'s
First Law was true, then the force on a planet varied inversely with the square
of the distance between the planet and the sun. He did this using Kepler\'s
Third Law (Zitzewitz 160). The distance in this formula is from the center of
the masses and is the average distance over their entire period. It is also
important to note that the force acted in the direction of this line (an
important factor when dealing with vectors) (Zitzewitz 160).
Newton, confident that his idea of all objects exerting a force back on
Earth, devised a formula for Universal Gravitation. It is important to note
that Newton was not the first to think of Universal Gravitation, he was just the
first one to make considerable and remarkable proofs for it based on
mathematical explanations. He said that if force is relative to the mass of an
object and it\'s acceleration then the force between two objects must also be the
same. Thus he came up with the first part of the equation. Also, as he had
proved earlier using Kepler\'s Third Law of Motion, that the force between two
objects is inversely proportional to their distances squared (an inverse square
law), then that must also be part of the Universal Gravitation equation. Thus
we know that the two masses and the distance are related to the force; and
because the distance is inversely proportional then the product of the masses
divided by the distance between their centers squared must equal the force
between the two objects (Zitzewitz 161).
Now earlier, Newton had