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author | bnewbold <bnewbold@robocracy.org> | 2017-01-16 16:01:24 -0800 |
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committer | bnewbold <bnewbold@robocracy.org> | 2017-01-16 16:01:24 -0800 |
commit | 6ab08f6b19734ac925ab9cafd567cb2f7735af6b (patch) | |
tree | 0e7a5cc7251bce880cf8f8055a915121742a58c2 /examples/newtonian_gravity/page.md | |
parent | c08fefa5e30e680e348acf7817201193b1a9634f (diff) | |
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update newtonian gravity page
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diff --git a/examples/newtonian_gravity/page.md b/examples/newtonian_gravity/page.md new file mode 100644 index 0000000..5678435 --- /dev/null +++ b/examples/newtonian_gravity/page.md @@ -0,0 +1,83 @@ + +Newton's law of universal gravitation states that a particle attracts every +other particle in the universe using a force that is directly proportional to +the product of their masses and inversely proportional to the square of the +distance between them. This is a general physical law derived from empirical +observations by what Isaac Newton called inductive reasoning. It is a part of +classical mechanics and was formulated in Newton's work Philosophiæ Naturalis +Principia Mathematica ("the Principia"), first published on 5 July 1687. (When +Newton's book was presented in 1686 to the Royal Society, Robert Hooke made a +claim that Newton had obtained the inverse square law from him; see the History +section below.) + +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. +The force is proportional to the product of the two masses and inversely +proportional to the square of the distance between them. The first test of +Newton's theory of gravitation between masses in the laboratory was the +Cavendish experiment conducted by the British scientist Henry Cavendish +in 1798. It took place 111 years after the publication of Newton's Principia +and approximately 71 years after his death. + +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. Both are inverse-square laws, where force is inversely +proportional to the square of the distance between the bodies. 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. + + +## Alternatives + +Newton's law has since been superseded by Albert Einstein's theory of general +relativity, but it continues to be used as an excellent approximation of the +effects of gravity in most applications. 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). + +### Observational Foils + +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. 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. Calculations using General Relativity are in much +closer agreement with the astronomical observations. + +In spiral galaxies, the orbiting of stars around their centers seems to +strongly disobey Newton's law of universal gravitation. Astrophysicists, +however, explain this spectacular phenomenon in the framework of Newton's laws, +with the presence of large amounts of Dark matter. + +## Solutions to the equation + +The n-body problem is an ancient, classical problem of predicting the +individual motions of a group of celestial objects interacting with each other +gravitationally. Solving this problem — from the time of the Greeks and on — +has been motivated by the desire to understand the motions of the Sun, planets +and the visible stars. In the 20th century, understanding the dynamics of +globular cluster star systems became an important n-body problem too. The +n-body problem in general relativity is considerably more difficult to solve. + +The classical physical problem can be informally stated as: given the +quasi-steady orbital properties (instantaneous position, velocity and time) of +a group of celestial bodies, predict their interactive forces; and +consequently, predict their true orbital motions for all future times. + +The two-body problem has been completely solved, as has the Restricted 3-Body +Problem. + +## References + +The body of this page originally came from Wikipedia. + +* Wikipedia: [Gravity](https://en.wikipedia.org/wiki/Gravity), + [Newton's law of universal gravitation](https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation), + [Inverse Square Law](https://en.wikipedia.org/wiki/Inverse-square_law) + |