The gravitational constant (G) is a physical constant used in calculating the gravitational attraction between two objects. It is denoted by G and its value is (6.6743 ± 0.00015) × 10−11 m3 kg−1 s−2.
How is the gravitational force between two objects calculated?
The gravitational force (F) is calculated using the formula F = Gm1m2/r2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.
Why is G considered different from other constants of physics?
G is considered different because it doesn’t depend on material properties but is a geometric factor. The combination GM, not the separate value of M, is the meaningful property of celestial objects.
Who first measured the gravitational constant and when?
Henry Cavendish first measured the gravitational constant in 1797–98 using an apparatus built by John Michell.
What was the original purpose of Cavendish’s experiment?
The original purpose of Cavendish’s experiment was to determine Earth’s density, not to measure the gravitational constant G.
planetary orbits: Kepler, Newton, and gravityBrian Greene demonstrates how Newton's law of gravitation determines the trajectories of the planets and explains the patterns in their motion found by Kepler. This video is an episode in his Daily Equation series.
gravitational constant (G), physical constantdenoted by G and used in calculating the gravitational attraction between two objects. In Newton’s law of universal gravitation, the attractive force between two objects (F) is equal to G times the product of their masses (m1m2) divided by the square of the distance between their centers (r2); that is, F = Gm1m2/r2. The value of G is (6.6743 ± 0.00015) × 10−11 m3kg−1 s−2.
It must be pointed out that G occupies a rather anomalous position among the other constants of physics. In the first place, the mass M of any celestial object cannot be determined independently of the gravitational attraction that it exerts. Thus, the combination GM, not the separate value of M, is the only meaningful property of a star, planet, or galaxy. Second, according to general relativity and the principle of equivalence, G does not depend on material properties but is in a sense a geometric factor. Hence, the determination of the constant of gravitation does not seem as essential as the measurement of quantities like the electronic charge or Planck’s constant.
The gravitational constant G was first measured in 1797–98 by the English scientist Henry Cavendish. He followed a method prescribed, and used an apparatus built, by his countryman the geologist and astronomer John Michell, who had died in 1793.
The apparatus featured a torsion balance: a wooden rod was suspended freely from a thin wire, and a lead sphere weighing 0.73 kg (1.6 pounds) hung from each end of the rod. A much larger sphere, weighing 158 kg (348 pounds), was placed at each end of the torsion balance. The gravitational attraction between each larger weight and each smaller one drew the ends of the rod aside along a graduated scale. The attraction between these pairs of weights was counteracted by the restoring force from a twist in the wire, which caused the rod to move from side to side like a horizontal pendulum.
Cavendish and Michell did not conceive of their experiment as an attempt to measure G. The formulation of Newton’s law of gravitation involving the gravitational constant did not occur until the late 19th century. The experiment was originally devised to determine Earth’s density, which Cavendish determined to be 5.48 grams per cubic centimetre—close to the modern value of 5.51 grams per cubic centimetre. This leads to a value for G of about 6.7 × 10−11 m3 kg−1 s−2. Since the late 19th century, refinements of the Cavendish experiment have been used for determining G.
Although Isaac Newton is well known for his discoveries in optics (white light composition) and mathematics (calculus), it is his formulation of the three laws of motion—the basic principles of modern physics—for which he is most famous. His formulation of the laws of motion resulted in the law of universal gravitation.
How was Isaac Newton educated?
After interrupted attendance at the grammar school in Grantham, Lincolnshire, England, Isaac Newton finally settled down to prepare for university, going on to Trinity College, Cambridge, in 1661, somewhat older than his classmates. There he immersed himself in Aristotle’s work and discovered the works of René Descartes before graduating in 1665 with a bachelor’s degree.
What was Isaac Newton’s childhood like?
Isaac Newton was born to a widowed mother (his father died three months prior) and was not expected to survive, being tiny and weak. Shortly thereafter Newton was sent by his stepfather, the well-to-do minister Barnabas Smith, to live with his grandmother and was separated from his mother until Smith’s death in 1653.
What did Isaac Newton write?
Isaac Newton is widely known for his published work Philosophiae Naturalis Principia Mathematica (1687), commonly known as the Principia. His laws of motion first appeared in this work. It is one of the most important single works in the history of modern science.
Understanding Newton's theory of universal gravitationIsaac Newton's formulation of the law of universal gravitation.
Isaac NewtonIsaac Newton, oil on canvas by Sir Godfrey Kneller, 1702; in the National Portrait Gallery, London. Newton's discoveries in physics and mathematics revolutionized science.
Isaac Newton (born December 25, 1642 [January 4, 1643, New Style], Woolsthorpe, Lincolnshire, England—died March 20 [March 31], 1727, London) was an English physicist and mathematician who was the culminating figure of the Scientific Revolution of the 17th century. In optics, his discovery of the composition of white light integrated the phenomena of colours into the science of light and laid the foundation for modern physical optics. In mechanics, his three laws of motion, the basic principles of modern physics, resulted in the formulation of the law of universal gravitation. In mathematics, he was the original discoverer of the infinitesimal calculus. Newton’sPhilosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy, 1687) was one of the most important single works in the history of modern science.
Formative influences
Born in the hamlet of Woolsthorpe, Newton was the only son of a local yeoman, also Isaac Newton, who had died three months before, and of Hannah Ayscough. That same year, at Arcetri near Florence, Galileo Galilei had died; Newton would eventually pick up his idea of a mathematical science of motion and bring his work to full fruition. A tiny and weak baby, Newton was not expected to survive his first day of life, much less 84 years. Deprived of a father before birth, he soon lost his mother as well, for within two years she married a second time; her husband, the well-to-do minister Barnabas Smith, left young Isaac with his grandmother and moved to a neighbouring village to raise a son and two daughters. For nine years, until the death of Barnabas Smith in 1653, Isaac was effectively separated from his mother, and his pronounced psychotic tendencies have been ascribed to this traumatic event. That he hated his stepfather we may be sure. When he examined the state of his soul in 1662 and compiled a catalog of sins in shorthand, he remembered “Threatning my father and mother Smith to burne them and the house over them.” The acute sense of insecurity that rendered him obsessively anxious when his work was published and irrationally violent when he defended it accompanied Newton throughout his life and can plausibly be traced to his early years.
After his mother was widowed a second time, she determined that her first-born son should manage her now considerable property. It quickly became apparent, however, that this would be a disaster, both for the estate and for Newton. He could not bring himself to concentrate on rural affairs—set to watch the cattle, he would curl up under a tree with a book. Fortunately, the mistake was recognized, and Newton was sent back to the grammar school in Grantham, where he had already studied, to prepare for the university. As with many of the leading scientists of the age, he left behind in Grantham anecdotes about his mechanical ability and his skill in building models of machines, such as clocks and windmills. At the school he apparently gained a firm command of Latin but probably received no more than a smattering of arithmetic. By June 1661 he was ready to matriculate at Trinity College, Cambridge, somewhat older than the other undergraduates because of his interrupted education.
Influence of the Scientific Revolution
When Newton arrived in Cambridge in 1661, the movement now known as the Scientific Revolution was well advanced, and many of the works basic to modern science had appeared. Astronomers from Nicolaus Copernicus to Johannes Kepler had elaborated the heliocentric system of the universe. Galileo had proposed the foundations of a new mechanics built on the principle of inertia. Led by René Descartes, philosophers had begun to formulate a new conception of nature as an intricate, impersonal, and inert machine. Yet as far as the universities of Europe, including Cambridge, were concerned, all this might well have never happened. They continued to be the strongholds of outmoded Aristotelianism, which rested on a geocentric view of the universe and dealt with nature in qualitative rather than quantitative terms.
Like thousands of other undergraduates, Newton began his higher education by immersing himself in Aristotle’s work. Even though the new philosophy was not in the curriculum, it was in the air. Some time during his undergraduate career, Newton discovered the works of the French natural philosopher Descartes and the other mechanical philosophers, who, in contrast to Aristotle, viewed physical reality as composed entirely of particles of matter in motion and who held that all the phenomena of nature result from their mechanical interaction. A new set of notes, which he entitled “Quaestiones Quaedam Philosophicae” (“Certain Philosophical Questions”), begun sometime in 1664, usurped the unused pages of a notebook intended for traditional scholastic exercises; under the title he entered the slogan “Amicus Plato amicus Aristoteles magis amica veritas” (“Plato is my friend, Aristotle is my friend, but my best friend is truth”). Newton’s scientific career had begun.
The “Quaestiones” reveal that Newton had discovered the new conception of nature that provided the framework of the Scientific Revolution. He had thoroughly mastered the works of Descartes and had also discovered that the French philosopher Pierre Gassendi had revived atomism, an alternativemechanical system to explain nature. The “Quaestiones” also reveal that Newton already was inclined to find the latter a more attractive philosophy than Cartesian natural philosophy, which rejected the existence of ultimate indivisible particles. The works of the 17th-century chemist Robert Boyle provided the foundation for Newton’s considerable work in chemistry. Significantly, he had read Henry More, the Cambridge Platonist, and was thereby introduced to another intellectual world, the magical Hermetic tradition, which sought to explain natural phenomena in terms of alchemical and magical concepts. The two traditions of natural philosophy, the mechanical and the Hermetic, antithetical though they appear, continued to influence his thought and in their tension supplied the fundamental theme of his scientific career.
Although he did not record it in the “Quaestiones,” Newton had also begun his mathematical studies. He again started with Descartes, from whose La Géometrie he branched out into the other literature of modern analysis with its application of algebraic techniques to problems of geometry. He then reached back for the support of classical geometry. Within little more than a year, he had mastered the literature; and, pursuing his own line of analysis, he began to move into new territory. He discovered the binomial theorem, and he developed the calculus, a more powerful form of analysis that employs infinitesimal considerations in finding the slopes of curves and areas under curves.
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By 1669 Newton was ready to write a tract summarizing his progress, De Analysi per Aequationes Numeri Terminorum Infinitas (“On Analysis by Infinite Series”), which circulated in manuscript through a limited circle and made his name known. During the next two years he revised it as De methodis serierum et fluxionum (“On the Methods of Series and Fluxions”). The word fluxions, Newton’s private rubric, indicates that the calculus had been born. Despite the fact that only a handful of savants were even aware of Newton’s existence, he had arrived at the point where he had become the leading mathematician in Europe.
Work during the plague years
Who created the color wheel?For millennia, many believed Aristotle's theory that all colors were a mixture of black and white. How did we learn otherwise?
When Newton received the bachelor’s degree in April 1665, the most remarkable undergraduate career in the history of university education had passed unrecognized. On his own, without formal guidance, he had sought out the new philosophy and the new mathematics and made them his own, but he had confined the progress of his studies to his notebooks. Then, in 1665, the plague closed the university, and for most of the following two years he was forced to stay at his home, contemplating at leisure what he had learned. During the plague years Newton laid the foundations of the calculus and extended an earlier insight into an essay, “Of Colours,” which contains most of the ideas elaborated in his Opticks. It was during this time that he examined the elements of circular motion and, applying his analysis to the Moon and the planets, derived the inverse square relation that the radially directed force acting on a planet decreases with the square of its distance from the Sun—which was later crucial to the law of universal gravitation. The world heard nothing of these discoveries.
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