Newton's Law of Gravitation and Applications
Sir Isaac Newton discovered many laws dealing with math and physics. One particular law, the law of gravitation, dealt with the heavens and planets. This law was derived and at first though that it could only apply to outer space, but is shown that we can use it elsewhere also. Newton's law of gravitation is applied to many circumstances, and helps us derive other very useful equations. His law is very versatile and powerful because it opens gateways to other laws and equations. In 1666, 45 years after Johannes Kepler discovered his laws about planetary motion; Isaac Newton discovered an interesting fact about planets. (Zitzewitz p160) Newton discovered that the net force on a planet must vary inversely with the square of the distance between two planets from the centers. (Zitzewitz p160) This is expressed in algebraic form as F~1/d2. (Zitzewitz p160) ~ is substituting for the symbol of "is proportional to". Also, Newton discovered that the force acted in the direction of a line connecting the centers. (Zitzewitz p160) But Newton was unable at this time to measure the magnitude of the force. (Zitzewitz p160) The falling apple made Newton think of the problem of the motion of the planets. (Zitzewitz p161) Newton r
(Zitzewitz p161) If they wer!e twice the distance from the sun, the force would be only a quarter as strong. (Zitzewitz p165) it's centripetal acceleration is ac=v2/r. By using G the universal gravitation constant, along with h, Planck's constant and C, the velocity of light, we obtain Planck's length l=(Gh/C3)~10-33cm. (Vondeling, p185)With the gravitational force law, it is possible to find an approximate value for the mass of the earth. Volume 7, p2490) If the shell were simply rolled from the barrel of the gun, it would fall to the ground at once because the force of gravity would pull it down. (Vondeling, p186) Thus gives us the mass of the Earth. (Zitzewitz p165) There are many different ways to apply Newton's law of universal gravitation, and also many ways to extrapolate the equation and information to lead to other equations, laws, and situations. Westerville, Ohio: Glencoe/McGraw-Hill, 1995. Volume 7, p2490) When the shell is fired it leaves the gun in a certain direction with a certain amount of force. (Prigogine, p178) This gravitational constant used in Newton's law of gravitation gives Planck a lot of base to build the "Planck era" on. (Vondeling, p186) Deriving this for ME=gRE2/G.
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