where F is the gravitational force acting between two objects, m1 and m2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant. Newton`s law of gravity is similar to Coulomb`s law of electric forces, which is used to calculate the amplitude of the electric force between two charged bodies. Both are inverse square laws where the force is inversely proportional to the square of the distance between bodies. Coulomb`s law has the product of two charges instead of the product of masses and Coulomb`s constant instead of the gravitational constant. This is how Galileo would arrive at the law of universal gravity. Why did he not do it? However, Hooke`s statements up to 1674 did not mention that an inverted square law applies or could apply to these attractions. Hooke`s gravity was also not yet universal, although it came closer to the universality of previous hypotheses.  Nor did he provide accompanying evidence or mathematical demonstrations. On these last two aspects, Hooke himself said in 1674: “Well, what are these different degrees [of attraction], I have not yet tested them experimentally”; and to all his suggestion: “I am only alluding to it for the moment”, “with myself many other things in my hands, which I would complete first and therefore cannot participate as well” (i.e. “follow this investigation”).  It was later, written to Newton on January 6, 1679|80 that Hooke had “conjectures .

that attraction is always in a double relation to the distance from the center, and consequently that velocity is in a subduplicated relation to attraction and therefore, as Kepler supposes, is reciprocal to distance.  (The conclusion on speed was wrong.)  The first laboratory test of the theory of gravity between Newton`s masses was the Cavendish experiment, conducted in 1798 by British scientist Henry Cavendish.  It took place 111 years after the publication of Newton`s Principia and about 71 years after his death. Thus, the equation of universal gravity takes the form: Newton`s description of gravity is sufficiently accurate for many practical purposes and therefore widely used. The deviations from this are small if the dimensionless quantities φ / c 2 {displaystyle phi /c^{2}} and ( v / c ) 2 {displaystyle (v/c)^{2}} are both much smaller than one, where φ {displaystyle phi } is the gravitational potential, v {displaystyle v} is the speed of the objects studied, and c {displaystyle c} is the speed of light in vacuum.  For example, Newtonian gravity provides an accurate description of the Earth/Sun system, as scientists and philosophers have studied gravity and later gravity since ancient times. Isaac Newton formalized the observations in a scientific law: the law of universal gravity, which states that all objects of mass are attracted to other objects of mass due to a force called gravity. This law was originally intended for one-off measures.

However, it has been shown that the gravity of a large uniform sphere is about the same as if all the mass were concentrated in its center. Gravitational fields are also conservative; That is, the work of gravity from one position to another is independent of the orbit. As a result, a gravitational potential field V(r) exists, so the many-body problem is an old classical problem for predicting the individual motions of a group of celestial objects that gravitationally interact with each other. The solution to this problem – since the time of the Greeks – was motivated by the desire to understand the movements of the sun, planets and visible stars. In the 20th century, understanding the dynamics of globular cluster systems also became an important many-body problem.  The many-body problem in general relativity is much more difficult to solve. Newton, confronted in May 1686 with Hooke`s claim on the law of the inverted square, denied that Hooke could be credited as the author of the idea. Newton recalled that the idea had been discussed with Sir Christopher Wren prior to Hooke`s letter of 1679.  Newton also pointed to earlier work by others, including Bullialdus, (who proposed, but without demonstration, that there was a gravitational pull of the Sun in inverse square relationship to distance) and Borelli (who also indicated without demonstration that there was a centrifugal tendency as a counterweight to a gravitational pull toward the Sun to move the planets in ellipses). D T Whiteside described the contribution to Newton`s thought, which came from Borelli`s book, a copy of which was in Newton`s library at his death.

 Newton`s law of gravity, states that every particle of matter in the universe attracts all others with a force that varies directly as the product of masses and vice versa as the square of the distance between them.