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The n-body problem is an ancient, classical problem [19] 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.
A common misconception occurs between centre of mass and centre of gravity.They are defined in similar ways but are not exactly the same quantity. Centre of mass is the mathematical description of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts.
Earth's gravity measured by NASA GRACE mission, showing deviations from the theoretical gravity of an idealized, smooth Earth, the so-called Earth ellipsoid.Red shows the areas where gravity is stronger than the smooth, standard value, and blue reveals areas where gravity is weaker (Animated version).
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
The Watt–Misner theory (1999) is a recent example of a scalar theory of gravitation. It is not intended as a viable theory of gravitation (since, as Watt and Misner point out, it is not consistent with observation), but as a toy theory which can be useful in testing numerical relativity schemes. It also has pedagogical value. [10]
Isaac Newton's law of Universal Gravitation (1687) was a good approximation of the behaviour of gravitation. Present-day understanding of gravitation stems from Einstein's General Theory of Relativity of 1915, a more accurate (especially for cosmological masses and distances) description of gravitation in terms of the geometry of spacetime .
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%.
Le Sage's theory of gravitation is a kinetic theory of gravity originally proposed by Nicolas Fatio de Duillier in 1690 and later by Georges-Louis Le Sage in 1748. The theory proposed a mechanical explanation for Newton's gravitational force in terms of streams of tiny unseen particles (which Le Sage called ultra-mundane corpuscles) impacting all material objects from all directions.