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. [38] For example, Newtonian gravity provides an accurate description of the Earth/Sun system, because some thirty years after Newton`s death in 1727, Alexis Clairaut, a mathematical astronomer who played a leading role in the field of gravitational studies, after reviewing the publications published by Hooke, wrote: “We must not think only this idea. von Hooke diminishes Newton`s fame”; and that “Hooke`s example” serves to “show the distance between a truth that is seen and a truth that is demonstrated.” [32] [33] In situations where one of the dimensionless parameters is large, general relativity must be used to describe the system. General relativity is reduced to Newtonian gravity within the limit of small potentials and low velocities, so Newton`s law of gravity is often called the low gravity limit of general relativity. Gravitational fields are also conservative; That is, the work of gravity from one position to another is independent of the orbit. As a result, there is a gravitational potential field V(r), so 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 the masses and vice versa as the square of the distance between them. In symbols, the magnitude of the gravitational force F is equal to G (the gravitational constant, whose size depends on the system of units used and which is a universal constant), multiplied by the product of the masses (m1 and m2) and divided by the square of the distance R: F = G (m1m2)/R2. Isaac Newton introduced the law in 1687 and used it to explain the observed motions of planets and their moons, which had been reduced to a mathematical form by Johannes Kepler in the early 17th century. Newton`s law of universal gravity can be written as a vector equation to account for the direction of gravitational force as well as its magnitude. In this formula, the amounts in bold represent vectors. Assuming SI units, F is measured in newtons (N), m1 and m2 in kilograms (kg), r in meters (m), and the constant G is 6.67430(15)×10−11 m3⋅kg−1⋅s−2.

[35] The value of the constant G was first accurately determined from the results of the Cavendish experiment by British scientist Henry Cavendish in 1798, although Cavendish himself did not calculate a numerical value for G. [6] This experiment was also the first laboratory test of Newton`s theory of gravity between masses. It took place 111 years after the publication of Newton`s Principia and 71 years after Newton`s death, so none of Newton`s calculations could use the value of G; Instead, he could only calculate one force in relation to another force. Newton`s conclusion on the amplitude of gravitational force is summed up symbolically, since Hooke`s statements up to 1674 did not mention that an inverse-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. [16] 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”). [14] It was later, written to Newton on January 6, 1679|80[17] 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. [18] (The conclusion on speed was wrong.) [19] In Newton`s law of gravitation, we stated that mass is a decisive quantity. We consider that mass and weight are identical, but in reality they are different. Weight is the gravitational force exerted on an object of a certain mass. The weight of the object can be obtained by multiplying the mass of the object m by the acceleration due to gravity g on the surface of the Earth. The measured acceleration due to gravity at the Earth`s surface is about 980 cm/second/second. The force acting between the Sun and the Earth is an example of a gravitational force. As shown in the figure, the masses m and me are attached to both ends of the beam. The beam is attached to a solid support with a string. The cord is attached to the center of the beam so that it can achieve balance. Now two large masses M`et M are lowered next to them. The gravitational force between the two pairs of masses causes the string to twist in such a way that the amount of torsion is compensated by the gravitational force.

The gravitational force can be measured by appropriate calibration. Since we know the value of the masses and the distances between them, the only unknown quantity is G in the universal law of gravity. Thus, the value of G is calculated from the measured quantities. The universal law of gravity can explain almost everything from how an apple falls from a tree to why the moon revolves around the earth. Watch the video and understand the beauty of the law of universal gravity. 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. The gravitational field is located on, inside and outside symmetrical masses. 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. 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. [21] Newton also pointed to earlier work by others,[22] including Bullialdus,[10] (who proposed, but without demonstration, that there was a gravitational pull of the Sun in inverse square relationship to distance) and Borelli[11] (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).