Tuesday, 3 March 2015

Newtons Law Of Gravitation


Gravitation is the force of mutual attraction experienced bodies by having a certain mass. The existence of this force was established by the English mathematician and physicist Isaac Newton in s. XVII, who also developed to its formulation called calculus of fluxions (what today is known as integral calculus).

Isaac Newton was born on December 25, 1642, in Woolsthorpe, Lincolnshire. When he was three, his widowed mother remarried and left him in the care of his grandmother. The widowed a second time, he decided to send him to a primary school in Grantham. In the summer of 1661 he entered Trinity College, University of Cambridge, where he received his title of professor.

During that time he devoted himself to the study and research of the latest advances in mathematics and natural philosophy. Almost immediately, he made fundamental discoveries that were very useful in his scientific career. He also discovered the theory of light and optics, formulated the laws of motion and deduced from them the law of universal gravitation.

The law formulated by Newton and called the law of universal gravitation states that the force of attraction experienced by two bodies endowed with mass is directly proportional to the product of their masses and opposite to the square of the distance between them ( law of inverse square of the distance). The law includes a proportionality constant (G) is called the constant of gravitation and whose value, determined by very precise experiments, is:

6,670. 10-11 Nm² / kg².

To determine the gravitational field associated with a body with a radius and a certain mass, the acceleration with which a body falls Test (radio and mass unit) within this field is set. By applying Newton's second law taking the values of the force of gravity and a known mass, one can obtain the acceleration of gravity.
Such acceleration has different values depending on the body on which it is measured; so, for the earth is considered a value of 9.8 m / s (equivalent to 9.8 N / kg), while the value obtained for the surface of the moon is only 1.6 m / s², ie about six times lower than that for our planet, and one of the giant planets of the solar system, Jupiter, this value would be about 24.9 m / s².

In an isolated system consisting of two bodies, one of which rotates around the other, with the former having a much smaller than the second mass and describing a stable circular orbit around the body that occupies the center, centrifugal force has a value equal to the centripetal due to the existence of universal gravitation.

From considerations such as this one can deduce Kepler's laws (the third), which relates the radius of the orbit described a body around another center, with the time it takes to sweep the area that encloses this orbit, and states that time is proportional to 3/2 of the radius. This result is of universal application and is also true for the elliptical orbits, of which circular orbit is a special case in which the major and minor semiaxes are equal.