In 1687, Sir Isaac Newton introduced the universal law of gravity. Newton`s law of universal gravity is usually stated in such a way that each particle attracts all other particles in the universe with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. [Note 1] The publication of the theory became known as the “first great union” because it marked the union of previously described gravity phenomena on Earth with known astronomical behaviors.    Gravitational interactions do not simply exist between the Earth and other objects; And not just between the sun and other planets. Gravitational interactions exist between all objects with an intensity directly proportional to the product of their masses. So when you`re sitting in your seat in physics class, you`re drawn to your lab partner, the office where you work, and even your physics book. Newton`s revolutionary idea was that gravity is universal – ALL objects attract in proportion to the product of their masses. Gravity is universal. Of course, most gravitational forces are so minimal that they can be noticed. Gravitational forces are recognizable only when masses of objects become large. To illustrate this, use Newton`s universal equation of gravity to calculate gravity between the following known objects. Click the buttons to view the answers.
Hooke`s statements up to 1674, however, did not mention that an inverted law of square applied or could apply to these attractions. Hooke`s gravity was not yet universal, although it is closer to universality than previous hypotheses.  Nor did he provide accompanying or mathematical evidence. On these last two aspects, Hooke himself declared in 1674: “Well, what are these different degrees [of attraction], I have not yet verified experimentally”; and to all his suggestion: “I`m just referring to this now”, “having many other things in my hand that I would do first and therefore I can`t participate in it so well” (i.e., “follow this investigation”).  Hooke later informed Newton in writing on January 6|80|80 that Hooke had made his “conjecture.” that attraction will always be in double proportion to the distance from the center of Reciprocall, and therefore that velocity will be in a subduplicated relationship to attraction and therefore, as Kepler supposes, reciprocal to distance.  (The conclusion on speed was false.)  The proportionalities expressed by Newton`s universal law of gravity are represented graphically by the following figure. Observe how gravity is directly proportional to the product of the two masses and inversely proportional to the square of the separation distance. In situations where one of the dimensionless parameters is large, general relativity should be used to describe the system. General relativity is reduced to Newtonian gravity at the limit of small potential and low velocities, so Newton`s law of gravity is often called the low gravitational limit of general relativity. The first two conflicts with the above observations were explained by Einstein`s theory of general relativity, in which gravity is a manifestation of curved space-time rather than being due to a force propagated between bodies.
In Einstein`s theory, energy and momentum distort space-time in their vicinity, and other particles move in trajectories determined by the geometry of space-time. This allowed for a description of the movements of light and mass that was consistent with all available observations. In general relativity, gravitational force is a fictitious force that results from the curvature of space-time, since the gravitational acceleration of a free-falling body is due to the fact that its world line is a geodesy of space-time. The force acting between the Sun and the Earth is an example of a gravitational force. The second conceptual remark about the above calculation examples is that using Newton`s universal gravitational equation to calculate gravity (or weight) gives the same result as when calculating with the equation presented in unit 2: the gravitational field is located on, inside and outside the symmetric masses. The first test of Newton`s theory of gravity between masses in the laboratory 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. Gravitational fields are also conservative; That is, the work done by gravity from one position to another is independent of the path. As a result, a gravitational potential field V(r) exists, so that the force of the gravitational force between the Earth (m = 5.98 x 1024 kg) and a 70 kg physics student is determined when the student stands at sea level, at a distance of 6.38 x 106 m from the center of the Earth. He never, in his words, “attributed the cause to this power.” In all other cases, he used the phenomenon of motion to explain the origin of various forces acting on bodies, but in the case of gravity, he was not able to experimentally identify the motion produced by gravity (although he invented two mechanical hypotheses in 1675 and 1717).
Moreover, he refused to make even a hypothesis about the cause of this force, arguing that it was contrary to good science. He lamented that “philosophers have so far tried in vain to search for nature” for the source of gravitational force, as he was convinced “for many reasons” that there were “previously unknown causes” that were fundamental to all “phenomena of nature.” These fundamental phenomena are still being studied, and although there are many hypotheses, the final answer has not yet been found. And in Newton`s General Scholium of 1713 in the second edition of Principia: “I have not yet been able to discover the cause of these properties of gravity from phenomena, and I do not simulate hypotheses. It is enough that gravity really exists and acts according to the laws I have explained, and that it serves abundantly to explain all the movements of the celestial bodies.  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. For points in a spherical-symmetric distribution of matter, Newton`s shell theorem can be used to find the gravitational force. The theorem tells us how different parts of the mass distribution affect the gravitational force measured at a point at a distance of r0 from the center of the mass distribution: The universal gravitational force acting between objects is called the gravitational force. The solution to the problem is to replace the known values of G (6.673 x 10-11 N m2/kg2), m1 (5.98 x 1024 kg), m2 (70 kg) and d (6.38 x 106 m) in the universal equation of gravity and solve them for Fgrav. The solution is as follows: assuming SI units, F is measured in newtons (N), m1 and m2 in kilograms (kg), r in meters (m) and the constant G 6.67430(15)×10−11 m3⋅kg−1⋅s−2.  The value of the constant G was first accurately determined in 1798 from the results of the Cavendish experiment by British scientist Henry Cavendish, although Cavendish himself did not calculate a numerical value for G.
 This experiment was also the first test of Newton`s theory of gravity between masses in the laboratory. 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 relative to another force. Newton`s conclusion on the magnitude of gravitational force is symbolically summarized as follows: If the bodies in question have a spatial extent (as opposed to point masses), then the gravitational force between them is calculated by adding up the contributions of the fictitious point masses that make up the bodies. In the limit, when the masses of the constituent points become “infinitely small”, it means integrating the force (in vector form, see below) via the expansions of the two bodies. 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 the help of a string. The rope is attached to the center of the beam so that it can achieve balance. Now two great masses M`and M are lowered next to them. The gravitational force between the two pairs of masses causes the rope to twist so that the amount of torsion is compensated only by the gravitational force.