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| -rw-r--r-- | examples/newtonian_gravity/examples.toml | 12 | ||||
| -rw-r--r-- | examples/newtonian_gravity/model.modelica | 10 | ||||
| -rw-r--r-- | examples/newtonian_gravity/page.md | 83 |
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diff --git a/examples/newtonian_gravity/examples.toml b/examples/newtonian_gravity/examples.toml new file mode 100644 index 0000000..516b16c --- /dev/null +++ b/examples/newtonian_gravity/examples.toml @@ -0,0 +1,12 @@ + +[examples] + + [examples.earth_surface] + r = 6.371e6 # radius of earth + m1 = 5.972e24 # mass of earth + + [examples.earth_moon] + r = 385000 # radius of earth + m1 = 5.972e24 # mass of earth + m2 = 7.348e22 # mass of moon + diff --git a/examples/newtonian_gravity/model.modelica b/examples/newtonian_gravity/model.modelica new file mode 100644 index 0000000..6ad0f90 --- /dev/null +++ b/examples/newtonian_gravity/model.modelica @@ -0,0 +1,10 @@ +model NewtonianGravitation + "Simple/classical Inverse-square law force" + parameter Real G=6.674e-11 "Gravitational Constant"; + Real m_1(unit="kilogram") "mass #1"; + Real m_2(unit="kilogram") "mass #2"; + Real r(unit="meter") "radius"; + Real F "force"; +equation + F = (G * m_1 * m_2) / (r^2); +end NewtonianGravitation; 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) + |