**Newton’s universal law of gravitation –**

Newton’s law of universal gravitation usually states that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centres. The publication of the law is known as the “First Great Unification”, as it marked the unification of the first described phenomena of gravity on Earth with known astronomical behaviours.

It is a general physical law derived from empirical observations that Isaac Newton called inductive reasoning. It is a part of classical mechanics and was formulated in Newton’s work Philosophiae Naturalis Principia Mathematica (“The Principia”), which was first published on 5 July 1687. When Newton presented Book 1 of the unpublished text to the Royal Society in April 1686, Robert Hooke claimed that Newton had derived the inverse square law from him.

Newton’s law was later superseded by Albert Einstein’s theory of general relativity. However, the universality of the gravitational constant remains intact and the law is still used in most applications as an excellent approximation to the effects of gravity. Relativity is needed only when extreme accuracy is required, or when dealing with very strong gravitational fields, such as those found near extremely massive and dense objects, or at short distances (such as the orbit of Mercury around the Sun).

**History – early history – **

In 1604, Galileo Galilei correctly predicted that the distance covered by a falling object is proportional to the square of the elapsed time. The relation to the distances of objects in free fall was confirmed by the Italian Jesuits Grimaldi and Riccioli between 1640 and 1650. He also calculated Earth’s gravity by recording the oscillations of a pendulum.

A modern assessment of the early history of the inverse square law is that “by the late 1670s”, the notion of “the inverse proportion between gravity and the square of the distance” was common and applied in different ways by many other people. Was upgraded from Reason”. The same author credits Robert Hooke with an important and significant contribution but considers Hooke’s claim of priority on the inverse square point to be irrelevant, as suggested by many individuals other than Newton and Hooke. He points instead to the idea of “combining celestial motions” and to Newton’s thinking away from “centrifugal” and toward “centrifugal”.

**Plagiarism Controversy – **

In 1686, when the first book of Newton’s Principia was presented to the Royal Society, Robert Hooke accused Newton of plagiarism, claiming that he had taken from him the “notion” of the “law of gravitation”, which reciprocally the square of the distances from the centre”. At the same time (according to a contemporary report by Edmond Halley) Hooke agreed that “the demonstration of the curves resulting from it” was entirely Newton’s.

**Hooke’s work and claims –**

Robert Hooke published his ideas about the “system of the world” in the 1660s, when he read to the Royal Society on March 21, 1666, “Concerning the turning of direct motion into a curve by an observable attracting principle” a Letter. And he published them again in 1674 in a somewhat developed form, with the addition of “An Attempt to Prove the Motion of the Earth by Observation”. Hooke announced in 1674 that he planned to explain “a system of the world which differs in many particulars from that hitherto known”, on the basis of three postulates: that “all celestial bodies have their own centres; There is a force of attraction or gravity towards.

**Newton’s work and claims –**

Newton countered Hooke’s claim on the inverse square law in May 1686, denying that Hooke should be credited as the author of the idea. In the Reasons, Newton recalled that the idea had been discussed with Sir Christopher Wren prior to Hooke’s 1679 letter. Newton also pointed to and acknowledged the earlier work of others, including Bullialdus, (who suggested, but without demonstration, that there was an attractive force from the Sun in inverse square proportion to the distance), and Borelli (who suggested, also without demonstration, that there was a centrifugal tendency in counterbalance with a gravitational attraction towards the Sun to cause the planets to move in ellipses) could). DT Whiteside describes the contributions to Newton’s thinking that came from Borelli’s book, a copy of which was in Newton’s library at the time of his death.

**Modern Priority Controversy –**

Since the time of Newton and Hooke, scholarly discussion has also touched on the question of whether Hooke’s mention of ‘combining motion’ in 1679 provided anything new and valuable to Newton, even if Hooke’s claim at the time actually had not been. As mentioned above, Newton’s manuscripts from the 1660s show him actually combining tangential motion with the effects of a radially directed force or effort, For example in the derivation of the inverse square relation for the circular case. They show Newton clearly articulating the concept of linear inertia – for which he was indebted (as was Hooke probably) to Descartes’ work published in 1644. Newton does not seem to have learned these matters from Hooke.

**Newton’s reservation –**

Newton was able to formulate his law of gravitation in his monumental work, he was very uncomfortable with the notion of “action at a distance” that was implicit in his equations. In 1692, in his third letter to Bentley, he wrote: “That one body may act upon another at a distance through a vacuum without the mediation of any other object, by and through which their action and force may be communicated to one another, it is to me such a great absurdity, that I believe that any man who has a competent capacity to think in philosophical matters can ever fall into this.

**Gravitational Field – **

The gravitational field is a vector field that describes the gravitational force that would apply to an object per unit of mass, at a given point in space. It is actually equal to the acceleration due to gravity at that point.

It Is a generalization of the vector form, which becomes especially useful when more than two objects are involved (such as a rocket between the Earth and the Moon).

**Observations conflicting with Newton’s formula **

• Newton’s theory did not fully explain the precession of the perihelion of the planetary orbits, especially that of Mercury, which was discovered long after Newton’s life. There is a 43-arcsecond discrepancy per century between the Newtonian calculation, which results only from gravitational attraction from other planets, and the precession observed with advanced telescopes during the 19th century.

• The estimated angular deflection of light rays (considered as particles travelling at the expected speed) by gravity which is calculated using Newton’s theory is only half of the deflection observed by astronomers. Calculations using general relativity are very close to astronomical observations.

• In spiral galaxies, the orbits of stars around their centres strongly disobey both Newton’s laws of universal gravitation and general relativity. However, astrophysicists explain this marked phenomenon by assuming the presence of a large amount of dark matter.

**Einstein’s solution –**

The first two conflict with the observations above that were explained by Einstein’s theory of general relativity, in which gravity is an expression of curved space-time due to the force propagated between bodies. In Einstein’s theory, energy and momentum distort the spacetime around them, and other particles move in trajectories determined by the geometry of spacetime. It gave a description of the motions of light and mass that was consistent with all available observations. In general relativity, the force of gravity is a fictitious force that arises from the curvature of space-time, because the gravitational acceleration of a body in free fall is due to it. The world line is a geodesic of space-time.

**The Solution to Newton’s law of universal gravitation –**

The n-body problem is an ancient, classical problem, which predicts different speeds of a group of celestial bodies interacting gravitationally with each other. The solution to this problem has been driven – since the time of the Greeks – by a desire to understand the motion of the Sun, planets and visible stars.

By Chanchal Sailani | January 1st, 2023 | Editor at Gurugrah_Blogs.

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