# Isaac Newton and the law of universal gravitation

Gravitation is the force of mutual attraction that bodies experience due to having a certain mass.

The existence of this force was established by the English mathematician and physicist Isaac Newton in the seventeenth century. In addition, this brilliant scientist developed for its formulation the so-called fluxion calculation (what is now known as integral calculus).

Isaac Newton was born on December 25, 1642, in Woolsthorpe, Lincolnshire. When he was three years old, his widowed mother remarried and left him in the care of his grandmother. When he was a widower for the second time, he decided to send him to an elementary school in Grantham. In the summer of 1661 he entered Trinity College at the University of Cambridge, where he received his teaching degree.

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. It also resolved issues related to light and optics, formulated the laws of motion and deduced, from them, what we know as Law of universal gravitation.

Newton's law, which is 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 inversely proportional to the square of the distance that separates them ( law of the inverse of the square of the distance). The law includes a constant of proportionality (G) that is called the constant of universal gravitation and whose value, determined by precise experiments, is:
G = 6,67384*10-11 N * m² / kg².

To determine the intensity of the gravitational field associated with a body with a certain radius and mass, the acceleration with which a test body (of radius and unit mass) falls within said field is established. By applying Newton's second law by taking the values ​​of the force of gravity and a known mass, the acceleration of gravity can be obtained.

This acceleration has different values ​​depending on the body on which it is measured; Thus, for the Earth a value of 9.8 m / s² (equivalent to 9.8 N / kg) is considered, while the value obtained for the surface of the Moon is only 1.6 m / s², that is, about six times smaller than that corresponding to our planet, and on one of the giant planets of the solar system, Jupiter, this value would be about 24.9 m / s².

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

From considerations like this it is possible to deduce one of Kepler's laws (the third), which relates the radius of the orbit that describes a body around another central, with the time it takes to sweep the area that said orbit contains, and that affirms that the time is proportional to 3/2 of the radius.

This result is universally applicable and is also true for elliptical orbits, of which the circular orbit is a particular case in which the major and minor semi-axes are equal.

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