# Essay/Term paper: Newton's law of universal gravitation

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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 proved that the force on an object was

proportional to an object's mass and its acceleration. And the equation that he

had formulated so far did not include anything that would resemble the

acceleration. Thus he knew that a gravitational constant must be present and

that it should be the same throughout all of the universe. However, due to

scientific limitations he was never able to figure out the exact value of this

constant (Zitzewitz 161).

One hundred years later, though, an young engineer by the name of

Cavendish devised a complex apparatus that was able to measure this

gravitational constant. Basically by using very sensitive telescopes and known

angles he was able to determine the distance one ball moved another ball. This

is often known as "weighing the earth" (Zitzewitz 162-163).

The effects of Newton's Law of Universal Gravitation were varied; but

the most common use for his law was the prediction of several planets beyond

Jupiter and Saturn. In 1830, it appeared that Newton's Law of Universal

Gravitation had not been correct because the orbit of Saturn did not follow his

law. Some astronomers thought that the force of an undiscovered planet may be

changing its course and in 1845 a couple of scientists at the Berlin Observatory

began searching for this hidden planet. It did not take very long. The massive

planet now known as Neptune was found on the first night of searching (Zitzewitz

164).

Perhaps one of the most key things about any theory of gravity prior to

Einstein was the fact that none of them proposed the origin of gravity.

Newton's law always proved to be true in the common world but did not explain

the source of the force (Eddington 95). Albert Einstein proposed his Theory of

Gravity in his General Theory of Relativity. In this he said that space was a

three dimensional plane and that masses curved this plane in one way or another

(Eddington 95). Thus a massive object would cause a large "hole" and smaller

objects would "orbit" it. It is interesting to note that in either case,

Newton's or Einstein's law, both prove to be true in the common world. Massive

universal objects, such as black holes, are an exception but that's another

story in itself (Edwards 498).

Works Cited

Zitzewitz, Paul W., Robert F. Neff, and Mark Davids. (1992). Physics:

Principles and Problems. Peoria, Illinois: Glencoe.

Gamow, George. (1962). Gravity: Classic and Modern Views. Garden City, New

York: Anchor Books.

Eddington, Sir Arthur. (1987). Space, Time, & Gravitation: An Outline of the

General Relativity Theory. Cambridge: Cambridge University Press.

Edwards, Paul. (Ed.) (1967). The Encyclopedia of Philosophy. New York, New

York: MacMillan.

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