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[1] [2] [3] This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. [4] 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.
The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n-body problem for details
Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
Philosophiæ Naturalis Principia Mathematica (English: The Mathematical Principles of Natural Philosophy) [1] often referred to as simply the Principia (/ p r ɪ n ˈ s ɪ p i ə, p r ɪ n ˈ k ɪ p i ə /), is a book by Isaac Newton that expounds Newton's laws of motion and his law of universal gravitation.
Isaac Newton was born (according to the Julian calendar in use in England at the time) on Christmas Day, 25 December 1642 (NS 4 January 1643 [a]) at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in the county of Lincolnshire. [27] His father, also named Isaac Newton, had died three months before.
Arthur Stanley Mackenzie in The Laws of Gravitation (1899) reviews the work done in the 19th century. [28] Poynting is the author of the article "Gravitation" in the Encyclopædia Britannica Eleventh Edition (1911). Here, he cites a value of G = 6.66 × 10 −11 m 3 ⋅kg −1 ⋅s −2 with a relative uncertainty of 0.2%.
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This mathematical expression of the force did not imply a cause. Newton considered action-at-a-distance to be an inadequate model for gravity. [6] Newton, in his words, considered action at a distance to be: so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. [7]