Author: admin | at 17.05.2014 |
Categories: Real Life Miracles Of God

In 1687, Isaac Newton combined his observations with theories from other scientists about gravity and gravitation into a scientific law: the Law of Universal Gravitation.

The force of attraction between two masses is defined by the Universal Gravitation Equation. Scientists and philosophers from ancient times have made observations about gravity on Earth. In studying the orbits of planets around the Sun, Kepler determined that gravitational attraction varied with separation, while formulating his Laws of Planetary Motion. In 1687, Isaac Newton's observations on planetary motion and empirical measurements, allowed him to establish the Law of Universal Gravitation, which was explained in the publication of Philosophiæ Naturalis Principia Mathematica (or simply Principia) set of three books that stated his Laws of Motion, the Law of Universal Gravitation and a derivation of Kepler's Laws of Planetary Motion.

The story that Newton was sitting under a tree when he was hit in the head by a falling apple, thus causing him to discover gravity, is a fable. The Law of Universal Gravitation states that every object of mass in the Universe attracts every other object of mass with a force which is directly proportional to the product of their masses and inversely proportional to the square of the separation between their centers.

Note: Newton's Law of Universal Gravitation is sometimes incorrectly called the Theory of Universal Gravitation.

Note: Also, the Law of Universal Gravitation is sometimes called the Universal Law of Gravitation.

Newton could not explain the mechanism of how and why gravitation occurred, except that it was some sort of force at a distance.

From the Law of Universal Gravitation, Newton formulated the Universal Gravitation Equation, which defines the gravitational force between two objects. Application of this equation is especially useful in determining the orbits of celestial objects, such as that of the planets around the Sun.

However, in most cases there are more than two objects involved, which can result in some complicated mathematics. For example, the motion of the planet Mars around the Sun is not only determined by the masses of Mars and the Sun but also by the influence of the gravitation from Mar's moons, the Earth and other planets. Predictions of the orbit of the planet Mercury proved to be slightly inaccurate using the Law of Universal Gravitation. Electromagnetic waves or light rays are deflected by gravitation, especially when they pass by a large mass, such as the Sun. The Law of Universal Gravitation requires that the gravitational force is transmitted instantaneously over large distances to maintain stability in planetary and stellar orbits. This implies that what is called the speed of gravitation (also carelessly called the speed of gravity) is infinite.

Solutions to these problems were finally found in Einstein's Theory of General Relativity that he published in 1915. Since ancient times, scientists and philosophers studied gravity and then later gravitation.

Please include it as a link on your website or as a reference in your report, document, or thesis. Every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them.

The gravitational constant is defined as the force of attraction between two bodies of unit mass separated by unit distance. Where 'W' is the weight, 'm' is the mass of the body and 'g' is the acceleration due to gravity. According to Newton's law of universal gravitation, a point mass, m1, exerts a gravitational force, , on another point mass, m2. In modern language, the law states: Every point mass attracts every single other point mass by a force pointing along the line intersecting both points.

Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies. Newton's law has since been superseded by Einstein's theory of general relativity, but it continues to be used as an excellent approximation of the effects of gravity in most applications. A recent assessment (by Ofer Gal) about the early history of the inverse square law is "by the late 1660s", the assumption of an "inverse proportion between gravity and the square of distance was rather common and had been advanced by a number of different people for different reasons". In 1686, when the first book of Newton's Principia was presented to the Royal Society, Robert Hooke accused Newton of plagiarism by claiming that he had taken from him the "notion" of "the rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center".

Hooke's statements up to 1674 made no mention, however, that an inverse square law applies or might apply to these attractions. Newton, faced in May 1686 with Hooke's claim on the inverse square law, denied that Hooke was to be credited as author of the idea. Newton further defended his work by saying that had he first heard of the inverse square proportion from Hooke, he would still have some rights to it in view of his demonstrations of its accuracy. This remark refers among other things to Newton's finding, supported by mathematical demonstration, that if the inverse square law applies to tiny particles, then even a large spherically symmetrical mass also attracts masses external to its surface, even close up, exactly as if all its own mass were concentrated at its center. In regard to evidence that still survives of the earlier history, manuscripts written by Newton in the 1660s show that Newton himself had, by 1669, arrived at proofs that in a circular case of planetary motion, "endeavour to recede" (what was later called centrifugal force) had an inverse-square relation with distance from the center.[20] After his 1679-1680 correspondence with Hooke, Newton adopted the language of inward or centripetal force. On the other hand, Newton did accept and acknowledge, in all editions of the 'Principia', that Hooke (but not exclusively Hooke) had separately appreciated the inverse square law in the solar system. Since the time of Newton and Hooke, scholarly discussion has also touched on the question of whether Hooke's 1679 mention of 'compounding the motions' provided Newton with something new and valuable, even though that was not a claim actually voiced by Hooke at the time. Nevertheless, a number of authors have had more to say about what Newton gained from Hooke and some aspects remain controversial.[24] The fact that most of Hooke's private papers had been destroyed or have disappeared does not help to establish the truth. Newton's role in relation to the inverse square law was not as it has sometimes been represented.

If the bodies in question have spatial extent (rather than being theoretical point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses which constitute the bodies. For points inside a spherically-symmetric distribution of matter, Newton's Shell theorem can be used to find the gravitational force.

The portion of the mass that is located at radii r < r0 causes the same force at r0 as if all of the mass enclosed within a sphere of radius r0 was concentrated at the center of the mass distribution (as noted above).

The portion of the mass that is located at radii r > r0 exerts no net gravitational force at the distance r0 from the center. As a consequence, for example, within a shell of uniform thickness and density there is no net gravitational acceleration anywhere within the hollow sphere.

Newton's law of universal gravitation can be written as a vector equation to account for the direction of the gravitational force as well as its magnitude. It can be seen that the vector form of the equation is the same as the scalar form given earlier, except that F is now a vector quantity, and the right hand side is multiplied by the appropriate unit vector. The gravitational field is a vector field that describes the gravitational force which would be applied on an object in any given point in space, per unit mass. It is a generalisation of the vector form, which becomes particularly useful if more than 2 objects are involved (such as a rocket between the Earth and the Moon). Gravitational fields are also conservative; that is, the work done by gravity from one position to another is path-independent. Newton's description of gravity is sufficiently accurate for many practical purposes and is therefore widely used. In situations where either dimensionless parameter is large, then general relativity must be used to describe the system. Newton's theory of gravitation requires that the gravitational force be transmitted instantaneously. Newton's Theory does not fully explain the precession of the perihelion of the orbits of the planets, especially of planet Mercury, which was detected long after the life of Newton.[32] There is a 43 arcsecond per century discrepancy between the Newtonian calculation, which arises only from the gravitational attractions from the other planets, and the observed precession, made with advanced telescopes during the 19th Century. The predicted angular deflection of light rays by gravity that is calculated by using Newton's Theory is only one-half of the deflection that is actually observed by astronomers.

In spiral galaxies, the orbiting of stars around their centers seems to strongly disobey Newton's law of universal gravitation.

The observed fact that the gravitational mass and the inertial mass is not the same for all objects is unexplained within Newton's Theories. Substituting the inertial mass dilation expression from Special relativity yields the following expression. While Newton was able to formulate his law of gravity in his monumental work, he was deeply uncomfortable with the notion of "action at a distance" that his equations implied.

These objections were explained by Einstein's theory of general relativity, in which gravitation is an attribute of curved spacetime instead of being due to a force propagated between bodies.

The n-body problem is an ancient, classical problem[36] of predicting the individual motions of a group of celestial objects interacting with each other gravitationally. This law states that the mass of an object is attracted toward the mass of other objects by a force called gravitation. Although the law and its equation were effective in predicting many phenomena, several discrepancies later arose in astronomical measurements. Although he may have been inspired by seeing an apple fall from a tree, his studies and correspondence with other scientists who were studying gravitation probably influenced him more than seeing an apple fall. However, it was shown that the gravitation from a large uniform sphere is approximately the same as if all the mass was concentrated at its center. Critics said that this explanation was bringing the occult or mysticism into science, which Newton denied. The result is that orbit of Mars includes perturbations or deviations caused by the other planets.

However, calculations from Newton's law result in only one-half of the deflection that is actually observed by astronomers. Although light from the Sun may take eight minutes to reach the Earth, gravitational changes would have to occur immediately to maintain orbital stability between the two objects. Isaac Newton formalized the observations into a scientific law: the Law of Universal Gravitation, which states that states that all objects of mass are attracted toward other objects of mass, due to a force called gravitation.

Although the law and its equation were effective in predicting many phenomena, several discrepancies arose in measurements that were made. The gravitational force is attractive, proportional to the product of the masses, and inversely proportional to the square of the distance, r, between the masses. Both are inverse-square laws, where force is inversely proportional to the square of the distance between the bodies. Relativity is required only when there is a need for extreme precision, or when dealing with very strong gravitational fields, such as those found near extremely massive and dense objects, or at very close distances (such as Mercury's orbit around the sun). The same author does credit Hooke with a significant and even seminal contribution, but he treats Hooke's claim of priority on the inverse square point as uninteresting since several individuals besides Newton and Hooke had at least suggested it, and he points instead to the idea of "compounding the celestial motions" and the conversion of Newton's thinking away from "centrifugal" and towards "centripetal" force as Hooke's significant contributions. This is a subject extensively discussed since that time and on which some points, outlined below, continue to excite controversy.

Thus Hooke clearly postulated mutual attractions between the Sun and planets, in a way that increased with nearness to the attracting body, together with a principle of linear inertia. Hooke's gravitation was also not yet universal, though it approached universality more closely than previous hypotheses.[7] He also did not provide accompanying evidence or mathematical demonstration. Among the reasons, Newton recalled that the idea had been discussed with Sir Christopher Wren previous to Hooke's 1679 letter.[12] Newton also pointed out and acknowledged prior work of others,[13] including Bullialdus,[14] (who suggested, but without demonstration, that there was an attractive force from the Sun in the inverse square proportion to the distance), and Borelli[15] (who suggested, also without demonstration, that there was a centrifugal tendency in counterbalance with a gravitational attraction towards the Sun so as to make the planets move in ellipses).

Hooke, without evidence in favor of the supposition, could only guess that the inverse square law was approximately valid at great distances from the center. Thus Newton gave a justification, otherwise lacking, for applying the inverse square law to large spherical planetary masses as if they were tiny particles.[18] In addition, Newton had formulated in Propositions 43-45 of Book 1,[19] and associated sections of Book 3, a sensitive test of the accuracy of the inverse square law, in which he showed that only where the law of force is accurately as the inverse square of the distance will the directions of orientation of the planets' orbital ellipses stay constant as they are observed to do apart from small effects attributable to inter-planetary perturbations. As described above, Newton's manuscripts of the 1660s do show him actually combining tangential motion with the effects of radially directed force or endeavour, for example in his derivation of the inverse square relation for the circular case. 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 a force relative to another force. In the limit, as the component point masses become "infinitely small", this entails integrating the force (in vector form, see below) over the extents of the two bodies.

That is, the individual gravitational forces exerted by the elements of the sphere out there, on the point at r0, cancel each other out.

General relativity reduces to Newtonian gravity in the limit of small potential and low velocities, so Newton's law of gravitation is often said to be the low-gravity limit of general relativity. Attempts by physicists to identify the relationship between the gravitational force and other known fundamental forces are not yet resolved, although considerable headway has been made over the last 50 years (See: Theory of everything and Standard Model). Given the classical assumptions of the nature of space and time before the development of General Relativity, a significant propagation delay in gravity leads to unstable planetary and stellar orbits. Calculations using General Relativity are in much closer agreement with the astronomical observations. Astrophysicists, however, explain this spectacular phenomenon in the framework of Newton's laws, with the presence of large amounts of Dark matter. The equations for Newtonian gravitation and Newtonian inertia use the same "mass", while in those of General Relativity they diverge. When it is near to the speed of light, the denominator approaches zero and the momentum explodes because effective inertial mass explodes. 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 unable to experimentally identify the motion that produces the force of gravity (although he invented two mechanical hypotheses in 1675 and 1717). In Einstein's theory, energy and momentum distort spacetime in their vicinity, and other particles move in trajectories determined by the geometry of spacetime. Solving this problem a€” from the time of the Greeks and on a€” has been motivated by the desire to understand the motions of the Sun, planets and the visible stars. It wasn't until 1915 that Einstein's Theory of General Relativity provided a solution to these discrepancies.

In the 1600s, Galileo Galilei, Robert Hooke and Johannes Kepler formulated laws of gravity near the Earth. On the other hand, universal gravitation implies that gravitation is throughout the universe, which is slightly different than a universal law. Einstein's Theory of General Relativity provided a solution to the Universal Gravitation problems. Coulomb's law has the product of two charges in place of the product of the masses, and the electrostatic constant in place of the gravitational constant. Bruce Brackenridge, although much has been made of the change in language and difference of point of view, as between centrifugal or centripetal forces, the actual computations and proofs remained the same either way. They also show Newton clearly expressing the concept of linear inertiaa€”for which he was indebted to Descartes' work, published in 1644 (as Hooke probably was).[23] These matters do not appear to have been learned by Newton from Hooke. Newton himself felt that the concept of an inexplicable action at a distance was unsatisfactory (see "Newton's reservations" below), but that there was nothing more that he could do at the time.

Moreover, he refused to even offer a hypothesis as to the cause of this force on grounds that to do so was contrary to sound science. This allowed a description of the motions of light and mass that was consistent with all available observations. In the 20th century, understanding the dynamics of globular cluster star systems became an important n-body problem too.[37] The n-body problem in general relativity is considerably more difficult to solve.

The Law of Universal Gravitation only makes predictions of how bodies are attracted and does not explain why it happens.

They also involved the combination of tangential and radial displacements, which Newton was making in the 1660s.

Examples of this include: the experiments of Galileo Galilei that, decades before Newton, established that objects that have the same air or fluid resistance are accelerated by the force of the Earth's gravity equally, regardless of their different inertial masses. He lamented that "philosophers have hitherto attempted the search of nature in vain" for the source of the gravitational force, as he was convinced "by many reasons" that there were "causes hitherto unknown" that were fundamental to all the "phenomena of nature".

In general relativity, the gravitational force is a fictitious force due to the curvature of spacetime, because the gravitational acceleration of a body in free fall is due to its world line being a geodesic of spacetime.

The lesson offered by Hooke to Newton here, although significant, was one of perspective and did not change the analysis.[21] This background shows there was basis for Newton to deny deriving the inverse square law from Hooke.

In these cases, the forces and energies that are required to accelerate various masses is completely dependent upon their different inertial masses, as can be seen from Newton's Second Law of Motion, F = ma. These fundamental phenomena are still under investigation and, though hypotheses abound, the definitive answer has yet to be found.

The force of attraction between two masses is defined by the Universal Gravitation Equation. Scientists and philosophers from ancient times have made observations about gravity on Earth. In studying the orbits of planets around the Sun, Kepler determined that gravitational attraction varied with separation, while formulating his Laws of Planetary Motion. In 1687, Isaac Newton's observations on planetary motion and empirical measurements, allowed him to establish the Law of Universal Gravitation, which was explained in the publication of Philosophiæ Naturalis Principia Mathematica (or simply Principia) set of three books that stated his Laws of Motion, the Law of Universal Gravitation and a derivation of Kepler's Laws of Planetary Motion.

The story that Newton was sitting under a tree when he was hit in the head by a falling apple, thus causing him to discover gravity, is a fable. The Law of Universal Gravitation states that every object of mass in the Universe attracts every other object of mass with a force which is directly proportional to the product of their masses and inversely proportional to the square of the separation between their centers.

Note: Newton's Law of Universal Gravitation is sometimes incorrectly called the Theory of Universal Gravitation.

Note: Also, the Law of Universal Gravitation is sometimes called the Universal Law of Gravitation.

Newton could not explain the mechanism of how and why gravitation occurred, except that it was some sort of force at a distance.

From the Law of Universal Gravitation, Newton formulated the Universal Gravitation Equation, which defines the gravitational force between two objects. Application of this equation is especially useful in determining the orbits of celestial objects, such as that of the planets around the Sun.

However, in most cases there are more than two objects involved, which can result in some complicated mathematics. For example, the motion of the planet Mars around the Sun is not only determined by the masses of Mars and the Sun but also by the influence of the gravitation from Mar's moons, the Earth and other planets. Predictions of the orbit of the planet Mercury proved to be slightly inaccurate using the Law of Universal Gravitation. Electromagnetic waves or light rays are deflected by gravitation, especially when they pass by a large mass, such as the Sun. The Law of Universal Gravitation requires that the gravitational force is transmitted instantaneously over large distances to maintain stability in planetary and stellar orbits. This implies that what is called the speed of gravitation (also carelessly called the speed of gravity) is infinite.

Solutions to these problems were finally found in Einstein's Theory of General Relativity that he published in 1915. Since ancient times, scientists and philosophers studied gravity and then later gravitation.

Please include it as a link on your website or as a reference in your report, document, or thesis. Every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them.

The gravitational constant is defined as the force of attraction between two bodies of unit mass separated by unit distance. Where 'W' is the weight, 'm' is the mass of the body and 'g' is the acceleration due to gravity. According to Newton's law of universal gravitation, a point mass, m1, exerts a gravitational force, , on another point mass, m2. In modern language, the law states: Every point mass attracts every single other point mass by a force pointing along the line intersecting both points.

Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies. Newton's law has since been superseded by Einstein's theory of general relativity, but it continues to be used as an excellent approximation of the effects of gravity in most applications. A recent assessment (by Ofer Gal) about the early history of the inverse square law is "by the late 1660s", the assumption of an "inverse proportion between gravity and the square of distance was rather common and had been advanced by a number of different people for different reasons". In 1686, when the first book of Newton's Principia was presented to the Royal Society, Robert Hooke accused Newton of plagiarism by claiming that he had taken from him the "notion" of "the rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center".

Hooke's statements up to 1674 made no mention, however, that an inverse square law applies or might apply to these attractions. Newton, faced in May 1686 with Hooke's claim on the inverse square law, denied that Hooke was to be credited as author of the idea. Newton further defended his work by saying that had he first heard of the inverse square proportion from Hooke, he would still have some rights to it in view of his demonstrations of its accuracy. This remark refers among other things to Newton's finding, supported by mathematical demonstration, that if the inverse square law applies to tiny particles, then even a large spherically symmetrical mass also attracts masses external to its surface, even close up, exactly as if all its own mass were concentrated at its center. In regard to evidence that still survives of the earlier history, manuscripts written by Newton in the 1660s show that Newton himself had, by 1669, arrived at proofs that in a circular case of planetary motion, "endeavour to recede" (what was later called centrifugal force) had an inverse-square relation with distance from the center.[20] After his 1679-1680 correspondence with Hooke, Newton adopted the language of inward or centripetal force. On the other hand, Newton did accept and acknowledge, in all editions of the 'Principia', that Hooke (but not exclusively Hooke) had separately appreciated the inverse square law in the solar system. Since the time of Newton and Hooke, scholarly discussion has also touched on the question of whether Hooke's 1679 mention of 'compounding the motions' provided Newton with something new and valuable, even though that was not a claim actually voiced by Hooke at the time. Nevertheless, a number of authors have had more to say about what Newton gained from Hooke and some aspects remain controversial.[24] The fact that most of Hooke's private papers had been destroyed or have disappeared does not help to establish the truth. Newton's role in relation to the inverse square law was not as it has sometimes been represented.

If the bodies in question have spatial extent (rather than being theoretical point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses which constitute the bodies. For points inside a spherically-symmetric distribution of matter, Newton's Shell theorem can be used to find the gravitational force.

The portion of the mass that is located at radii r < r0 causes the same force at r0 as if all of the mass enclosed within a sphere of radius r0 was concentrated at the center of the mass distribution (as noted above).

The portion of the mass that is located at radii r > r0 exerts no net gravitational force at the distance r0 from the center. As a consequence, for example, within a shell of uniform thickness and density there is no net gravitational acceleration anywhere within the hollow sphere.

Newton's law of universal gravitation can be written as a vector equation to account for the direction of the gravitational force as well as its magnitude. It can be seen that the vector form of the equation is the same as the scalar form given earlier, except that F is now a vector quantity, and the right hand side is multiplied by the appropriate unit vector. The gravitational field is a vector field that describes the gravitational force which would be applied on an object in any given point in space, per unit mass. It is a generalisation of the vector form, which becomes particularly useful if more than 2 objects are involved (such as a rocket between the Earth and the Moon). Gravitational fields are also conservative; that is, the work done by gravity from one position to another is path-independent. Newton's description of gravity is sufficiently accurate for many practical purposes and is therefore widely used. In situations where either dimensionless parameter is large, then general relativity must be used to describe the system. Newton's theory of gravitation requires that the gravitational force be transmitted instantaneously. Newton's Theory does not fully explain the precession of the perihelion of the orbits of the planets, especially of planet Mercury, which was detected long after the life of Newton.[32] There is a 43 arcsecond per century discrepancy between the Newtonian calculation, which arises only from the gravitational attractions from the other planets, and the observed precession, made with advanced telescopes during the 19th Century. The predicted angular deflection of light rays by gravity that is calculated by using Newton's Theory is only one-half of the deflection that is actually observed by astronomers.

In spiral galaxies, the orbiting of stars around their centers seems to strongly disobey Newton's law of universal gravitation.

The observed fact that the gravitational mass and the inertial mass is not the same for all objects is unexplained within Newton's Theories. Substituting the inertial mass dilation expression from Special relativity yields the following expression. While Newton was able to formulate his law of gravity in his monumental work, he was deeply uncomfortable with the notion of "action at a distance" that his equations implied.

These objections were explained by Einstein's theory of general relativity, in which gravitation is an attribute of curved spacetime instead of being due to a force propagated between bodies.

The n-body problem is an ancient, classical problem[36] of predicting the individual motions of a group of celestial objects interacting with each other gravitationally. This law states that the mass of an object is attracted toward the mass of other objects by a force called gravitation. Although the law and its equation were effective in predicting many phenomena, several discrepancies later arose in astronomical measurements. Although he may have been inspired by seeing an apple fall from a tree, his studies and correspondence with other scientists who were studying gravitation probably influenced him more than seeing an apple fall. However, it was shown that the gravitation from a large uniform sphere is approximately the same as if all the mass was concentrated at its center. Critics said that this explanation was bringing the occult or mysticism into science, which Newton denied. The result is that orbit of Mars includes perturbations or deviations caused by the other planets.

However, calculations from Newton's law result in only one-half of the deflection that is actually observed by astronomers. Although light from the Sun may take eight minutes to reach the Earth, gravitational changes would have to occur immediately to maintain orbital stability between the two objects. Isaac Newton formalized the observations into a scientific law: the Law of Universal Gravitation, which states that states that all objects of mass are attracted toward other objects of mass, due to a force called gravitation.

Although the law and its equation were effective in predicting many phenomena, several discrepancies arose in measurements that were made. The gravitational force is attractive, proportional to the product of the masses, and inversely proportional to the square of the distance, r, between the masses. Both are inverse-square laws, where force is inversely proportional to the square of the distance between the bodies. Relativity is required only when there is a need for extreme precision, or when dealing with very strong gravitational fields, such as those found near extremely massive and dense objects, or at very close distances (such as Mercury's orbit around the sun). The same author does credit Hooke with a significant and even seminal contribution, but he treats Hooke's claim of priority on the inverse square point as uninteresting since several individuals besides Newton and Hooke had at least suggested it, and he points instead to the idea of "compounding the celestial motions" and the conversion of Newton's thinking away from "centrifugal" and towards "centripetal" force as Hooke's significant contributions. This is a subject extensively discussed since that time and on which some points, outlined below, continue to excite controversy.

Thus Hooke clearly postulated mutual attractions between the Sun and planets, in a way that increased with nearness to the attracting body, together with a principle of linear inertia. Hooke's gravitation was also not yet universal, though it approached universality more closely than previous hypotheses.[7] He also did not provide accompanying evidence or mathematical demonstration. Among the reasons, Newton recalled that the idea had been discussed with Sir Christopher Wren previous to Hooke's 1679 letter.[12] Newton also pointed out and acknowledged prior work of others,[13] including Bullialdus,[14] (who suggested, but without demonstration, that there was an attractive force from the Sun in the inverse square proportion to the distance), and Borelli[15] (who suggested, also without demonstration, that there was a centrifugal tendency in counterbalance with a gravitational attraction towards the Sun so as to make the planets move in ellipses).

Hooke, without evidence in favor of the supposition, could only guess that the inverse square law was approximately valid at great distances from the center. Thus Newton gave a justification, otherwise lacking, for applying the inverse square law to large spherical planetary masses as if they were tiny particles.[18] In addition, Newton had formulated in Propositions 43-45 of Book 1,[19] and associated sections of Book 3, a sensitive test of the accuracy of the inverse square law, in which he showed that only where the law of force is accurately as the inverse square of the distance will the directions of orientation of the planets' orbital ellipses stay constant as they are observed to do apart from small effects attributable to inter-planetary perturbations. As described above, Newton's manuscripts of the 1660s do show him actually combining tangential motion with the effects of radially directed force or endeavour, for example in his derivation of the inverse square relation for the circular case. 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 a force relative to another force. In the limit, as the component point masses become "infinitely small", this entails integrating the force (in vector form, see below) over the extents of the two bodies.

That is, the individual gravitational forces exerted by the elements of the sphere out there, on the point at r0, cancel each other out.

General relativity reduces to Newtonian gravity in the limit of small potential and low velocities, so Newton's law of gravitation is often said to be the low-gravity limit of general relativity. Attempts by physicists to identify the relationship between the gravitational force and other known fundamental forces are not yet resolved, although considerable headway has been made over the last 50 years (See: Theory of everything and Standard Model). Given the classical assumptions of the nature of space and time before the development of General Relativity, a significant propagation delay in gravity leads to unstable planetary and stellar orbits. Calculations using General Relativity are in much closer agreement with the astronomical observations. Astrophysicists, however, explain this spectacular phenomenon in the framework of Newton's laws, with the presence of large amounts of Dark matter. The equations for Newtonian gravitation and Newtonian inertia use the same "mass", while in those of General Relativity they diverge. When it is near to the speed of light, the denominator approaches zero and the momentum explodes because effective inertial mass explodes. 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 unable to experimentally identify the motion that produces the force of gravity (although he invented two mechanical hypotheses in 1675 and 1717). In Einstein's theory, energy and momentum distort spacetime in their vicinity, and other particles move in trajectories determined by the geometry of spacetime. Solving this problem a€” from the time of the Greeks and on a€” has been motivated by the desire to understand the motions of the Sun, planets and the visible stars. It wasn't until 1915 that Einstein's Theory of General Relativity provided a solution to these discrepancies.

In the 1600s, Galileo Galilei, Robert Hooke and Johannes Kepler formulated laws of gravity near the Earth. On the other hand, universal gravitation implies that gravitation is throughout the universe, which is slightly different than a universal law. Einstein's Theory of General Relativity provided a solution to the Universal Gravitation problems. Coulomb's law has the product of two charges in place of the product of the masses, and the electrostatic constant in place of the gravitational constant. Bruce Brackenridge, although much has been made of the change in language and difference of point of view, as between centrifugal or centripetal forces, the actual computations and proofs remained the same either way. They also show Newton clearly expressing the concept of linear inertiaa€”for which he was indebted to Descartes' work, published in 1644 (as Hooke probably was).[23] These matters do not appear to have been learned by Newton from Hooke. Newton himself felt that the concept of an inexplicable action at a distance was unsatisfactory (see "Newton's reservations" below), but that there was nothing more that he could do at the time.

Moreover, he refused to even offer a hypothesis as to the cause of this force on grounds that to do so was contrary to sound science. This allowed a description of the motions of light and mass that was consistent with all available observations. In the 20th century, understanding the dynamics of globular cluster star systems became an important n-body problem too.[37] The n-body problem in general relativity is considerably more difficult to solve.

The Law of Universal Gravitation only makes predictions of how bodies are attracted and does not explain why it happens.

They also involved the combination of tangential and radial displacements, which Newton was making in the 1660s.

Examples of this include: the experiments of Galileo Galilei that, decades before Newton, established that objects that have the same air or fluid resistance are accelerated by the force of the Earth's gravity equally, regardless of their different inertial masses. He lamented that "philosophers have hitherto attempted the search of nature in vain" for the source of the gravitational force, as he was convinced "by many reasons" that there were "causes hitherto unknown" that were fundamental to all the "phenomena of nature".

In general relativity, the gravitational force is a fictitious force due to the curvature of spacetime, because the gravitational acceleration of a body in free fall is due to its world line being a geodesic of spacetime.

The lesson offered by Hooke to Newton here, although significant, was one of perspective and did not change the analysis.[21] This background shows there was basis for Newton to deny deriving the inverse square law from Hooke.

In these cases, the forces and energies that are required to accelerate various masses is completely dependent upon their different inertial masses, as can be seen from Newton's Second Law of Motion, F = ma. These fundamental phenomena are still under investigation and, though hypotheses abound, the definitive answer has yet to be found.

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