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Isaac Newton was a great English mathematician, physicist, and astronomer. He was endowed with a powerful, original and tenacious mind. He used logic and deduction to investigate the workings of mathematics and physics.

Isaac Newton was the first to explain that the force that makes objects fall with constant acceleration on the Earth (terrestrial gravity) is the same that keeps planets and stars in motion.

From an early age he was interested in questions relating to nature, studying them and conducting experiments.

**Among his great achievements are**:

- the infinitesimal calculus,
- the colors of light and
- the law of universal gravitation.

**Newton’s predecessor astronomers**

Furthermore, of the Mayan, Chaldean, and Greek astronomers, Isaac Newton’s immediate predecessors were:

- Nicolaus Copernicus, Poland 1473-1543
- Tycho Brahe, Sweden 1546-1601
- Galileo Galilei, Italy 1564-1642
- Johannes Kepler, Germany 1571-1630

**Newton’s Contemporary Astronomers**

- Giovanni Cassini, Italy 1625-1712
- Christiaan Huygens, Holland 1629-1695
- Edmond Halley (1656-1742)

### Childhood and education

Isaac Newton was born on January 4, 1643, in the small village of Woolsthorpe, in the Lincolnshire district, England.

His father was a small landowner who died in early October 1642, shortly before Newton’s birth.

Newton’s mother enrolled him at King’s School in nearby Grantham.

There in Grantham, Newton stayed with a pharmacist until he was sixteen, in 1659.

In those years of childhood, he developed his great mechanical ability, which he exercised in the construction of various mechanisms (the most cited is a water clock) and toys (especially kites, to whose tails he tied lanterns that, at night, frightened children). his neighbors).

When he was sixteen years old, his mother made him return to Woolsthorpe, so that he could start taking care of the lands inherited by the family.

However, young Isaac was not at all interested in assuming his responsibilities as a landowner.

### Newton entered Cambridge

His mother, advised by Newton’s teacher, and by that of his own brother, agreed to have him return to school, to prepare for his admission to Cambridge University.

In June 1661, Newton was admitted to Trinity College, Cambridge.

Not having sufficient financial resources, he enrolled as a family. In this way, he earned his support, in exchange for providing domestic services to the wealthiest students.

There in Cambridge, Isaac Newton began to receive a solid education based on the principles of Aristotelian philosophy.

In December 1663, at the University of Cambridge, the Reverend Henry Lucas, Member of the English Parliament, bequeathed in his will a library of 4,000 volumes, and commissioned the purchase of land that would give an annual yield of 100 pounds to found a Chair of mathematics.

The intense scientific and intellectual activity that reigned at the University of Cambridge stimulated Newton’s prodigious mind and aroused his interest in mathematics and questions relating to the investigation of nature.

### Newton’s contribution to mathematics

In 1664, Newton invented the famous formula for the development of the power of a binomial with any exponent, integer or fractional, although it took him several years to communicate it to the secretary of the Royal Society.

But it was the beginning of his great contribution to the development of mathematics as a necessary tool for the study of nature.

The first complete exposition of his method of mathematical analysis by means of infinite series was written by Newton in 1669.

The procedure followed by Newton to establish the binomial formula had the virtue of making him see the importance of infinite series for infinitesimal calculus.

Around this time, Newton drew up his first ideas about the infinitesimal calculus; ideas that he did not publish until later.

The infinitesimal calculus is a mathematical tool that Newton invented. In later years, the infinitesimal calculus was indispensable for the study of celestial mechanics and many other scientific activities.

Newton was not the first to use that kind of calculus; In fact, the first edition of his work, contained the recognition that Leibniz was in possession of an analogous method.

The infinitesimal calculus is one of the most basic and important conceptual and analytical tools invented by humans. Without him, the history of science would have been different.

It is now recognized that the inventors of the infinitesimal calculus were two giants of science: Isaac Newton and Wilhelm Leibniz.

### The plague epidemic in England

When the great plague epidemic of 1665 broke out in London, Cambridge closed its doors and Newton returned to Woolsthorpe.

In March 1666, he returned to Cambridge, but in June the plague reappeared and the College discontinued its activities.

In a posthumous letter, Newton described the years 1665 and 1666 as the most fruitful time of his invention, during which he thought about mathematics and philosophy more than ever since.

Many of the ideas of mathematics, the theory of colors and the first ideas about gravitational attraction, related to the permanence of the Moon in its orbit around the Earth, were the achievements that Newton achieved in those years.

### Theory of universal gravitation

Until the middle of the 17th century, astronomers had managed to describe in great detail the trajectories of the Earth, the Moon, and the planets. But no one had been able to find out the cause of these precise displacements.

It was Isaac Newton who discovered that “*everything happens as if matter attracts matter*.” But he did much more: he discovered that there is a quantitative relationship for the force of attraction between two objects with mass.

The force of gravity of the Earth, causes an acceleration of the Moon towards the Earth. The force of gravity of the Moon, causes an acceleration of the Earth towards the Moon. Both forces have the same intensity.

From his reflections and calculations, he deduced that every object in the universe that has mass exerts an attraction on every other object with mass, even if they are separated by a great distance. He called this attractive force *“gravity.”*

Newton’s first calculations to find out something about the mutual attraction of the Earth and the Moon, hit an obstacle: show that the force of attraction between two spheres is equal to that which would exist if the masses of each of them, were concentrated in the respective centers.

He solved this problem in February 1685, after checking the validity of his law of gravitational attraction, by applying it to the case of the Moon. The idea, born twenty years earlier, was then confirmed thanks to the precise measurement of the Earth’s radius carried out by the French astronomer Jean Picard.

In the gravitation formula, it is very important to enter a value that serves to obtain the exact value of the gravitational attractive forces. It is the famous “constant G”, the universal constant of gravitation.

The constant G is approximately 6.674 * 10 ^{-11}

Newton did not know the cause of this constant and neither did he know its exact value. He could only indicate that it was a universal constant, and that its value was a fairly small number.

Only a long time later, the techniques necessary to improve the calculation of its value were developed.

### Characteristics of the force of gravity, according to Newton:

- is always attractive, never repulsive.
- always produces attraction between bodies, whatever their composition.
- each body exerts a force on the other, the two forces are equal in intensity and direction, but opposite in sense.
- It is produced by attracting the center of gravity of one object with the center of gravity of the other.
- It is universal, and all material particles are subject to it, without exception.
- It has infinite scope, no matter how far two bodies are from each other, they continue to experience this force.
- It loses intensity, in proportion to the square of the distance that separates the bodies. For example, if one object is moved three times as far away from another, then the force of gravity is reduced to one-ninth.
- the transmission is instantaneous and does not need a transmission medium

However, Newton could never find a satisfactory explanation for how gravitational force is transmitted.

He always humbly affirmed that he did not know what was the cause of all this. Well into the 21st century, nobody knows yet.

Inside the atoms, the force of gravity does not play an important role, due to the very small magnitude of the masses of the elementary particles.

The mathematician and astronomer Edmond Halley had the merit of overcoming Newton’s reluctance to publish his work.

He personally arranged for the manuscript to be presented in April 1686 to the Royal Society. In addition, he took care of the expenses of the printing, completed in July 1687.

Isaac Newton enunciated the *Law of Universal Gravitation* in his book, entitled “*The Mathematical Principles of Natural Philosophy*,” which are known as “*The Principia*.” It is one of the most important books in all of history.

*The Principia* contained the first printed exposition of the infinitesimal calculus created by Newton, although Newton preferred that, in general, the work present the fundamentals of physics and astronomy, formulated in the synthetic language of geometry.

Newton himself was in charge of propagating, towards the end of his life, the anecdote that relates his first thoughts on the law of gravity, with the casual observation of an apple that fell from one of the fruit trees of the his garden.

The French philosopher, Voltaire, was responsible for propagating this anecdote, which he knew from Newton’s niece.

### Newton returned to Cambridge in 1967

Newton finally returned to Cambridge in April 1667. Shortly thereafter, in October 1667, he was elected a fellow of Trinity College. Two years later he was appointed professor.

In 1672, Newton was made a *Fellow of the Royal Society of London*, in recognition of his contribution to science, having built a telescope.

### Newton and optics

The chapter of science that he chose to teach his classes at Trinity College was *optics,* to which he had been devoting his attention since, in 1666, he had the idea that led to his discovery of the composite nature of the light.

In February 1672, a few days after the Royal Society of London had chosen him as one of its members, he presented his first communiqué on the subject.

In this statement, Newton provided indisputable experimental evidence that white light was a mixture of rays of different colors, each characterized by its different degree of refraction when passing through an optical prism.

Newton considered that his discovery that white light is a mixture of rays of different colors, was the most unique and the most important of the discoveries that had been made until then, related to the knowledge of nature.

The prestigious secretary of the Royal Society, Robert Hooke opposed Newton’s ideas on optics.

Robert Hooke had an enormous influence on the sages of his time and, without a doubt, the discovery and consequences of universal gravitation, is due in large part to the respect that Newton felt for him and for his ideas.

Hooke argued that light is electromagnetic waves; On the other hand, Newton affirmed that light is a phenomenon resulting from the emission of luminous corpuscles by hot bodies.

In 1676, Newton gave up on pursuing the controversy about his theory of colors and for a few years, he again took refuge in almost absolute privacy.

He concentrated on his work on differential and integral calculus. He devoted much of his thoughts to two subjects far removed from the world of his research on nature: *alchemy* and *biblical studies*.

### The movement of the planets

Newton received a letter from Robert Hooke, then secretary of the Royal Society, in which he tried to get Newton to reestablish his contact with the institution; and he suggested the possibility of doing so, commenting on Hooke’s own theories about the motion of the planets.

This letter restored Newton’s interest in dynamic mechanics. He soon found that the trajectory followed by a body moving under the force of gravity with another, would have an elliptical shape. Initially, he had thought that the path followed by those two bodies would be a spiral.

Since then, he postulated that the Earth and all the planets should move in an elliptical orbit around the Sun.

In 1684, the English mathematician and astronomer, Edmond Halley, was Professor of Mathematics at Oxford. He visited Newton in Cambridge, and asked him what the orbit of a planet would be if the force of gravity decreased with the square of distance. Newton’s response was immediate: “*an ellipse*.”

Marveling at how quickly Newton considered resolved an issue that Hooke and Halley himself were competing in clarifying, the latter asked Newton: *how do you know the shape of the curve?* Newton smiled and said, “*I have calculated it*.”

Until Newton found his famous formula for gravity, astronomers observed and recorded each night, for hundreds of nights, the positions of a planet. Mathematical calculus marked the fundamental difference between Newton and all his predecessors.

Einstein’s theory of relativity is said to have improved and replaced Newton’s theory of gravity. It’s true. But, in the calculation and monitoring of the trajectories of planets, comets, asteroids, satellites and spaceships, what is used are Newton’s formulas.

### Last years in Newton’s life

In 1703, after Hooke’s death, Newton was elected President of the Royal Society, a position he held until his death.

In 1705, Anne Stuart, Queen of Great Britain and Ireland, bestowed upon him the title of Sir.

In the first days of March 1727, a stone in his bladder, marked the beginning of his agony: Newton’s life was extinguished in the early morning of March 20, 1727.

He was buried in Westminster Abbey, surrounded by the great men of England.

The University of Cambridge now offers Internet access to more than 4,000 manuscripts by Isaac Newton. It is a spectacular demonstration of the possibility of access that currently has to the best sources of information so that the number of people who are interested in science increases.