∇ ⋅ A One can use the general Stokes' Theorem to equate the n-dimensional volume integral of the divergence of a vector field F over a region U to the (n − 1)-dimensional surface integral of F over the boundary of U: This equation is also known as the divergence theorem. Остроградского" (Unpublished works of MV Ostrogradskii), M. Ostrogradsky (presented: November 5, 1828 ; published: 1831), This page was last edited on 12 November 2020, at 08:24. Théorème de Gauss en gravitation — Le flux du champ de gravitation à travers une surface fermée est égal à la somme des masses intérieures à cette surface multipliée par − (où est la constante de gravitation universelle) : ∬ → ⋅ → = − ∭ = − où S est la surface fermée délimitant le volume V and For analogous laws concerning different fields, see, Deriving Newton's law from Gauss's law and irrotationality, Poisson's equation and gravitational potential, Cylindrically symmetric mass distribution, Del in cylindrical and spherical coordinates, The mechanics problem solver, by Fogiel, pp 535–536, Degenerate Higher-Order Scalar-Tensor theories, https://en.wikipedia.org/w/index.php?title=Gauss%27s_law_for_gravity&oldid=963914549, All Wikipedia articles written in American English, Creative Commons Attribution-ShareAlike License. V Lagrange employed surface integrals in his work on fluid mechanics. 3 {\displaystyle V} = {\displaystyle 4\pi r^{2}} est la constante de gravitation universelle) : où S est la surface fermée délimitant le volume V. Dernière modification le 25 mars 2019, à 14:38, https://fr.wikipedia.org/w/index.php?title=Théorème_de_Gauss_(gravitation)&oldid=157853788, licence Creative Commons attribution, partage dans les mêmes conditions, comment citer les auteurs et mentionner la licence. {\displaystyle \Phi _{\text{32}}} 2 Si vous n'avez pas trouvé votre notice, affinez votre recherche avec des critères plus prècis. s . G x M ( ⋅ ) approaches zero volume, it becomes the infinitesimal {\displaystyle G} G F G 0 2 The gravitational field g (also called gravitational acceleration) is a vector field – a vector at each point of space (and time). ^  : où En mécanique, on définit par analogie au théorème de Gauss de l'électromagnétisme une forme du théorème de Gauss appliqué à la gravitation. = d = This is because both Newton's law and Coulomb's law describe inverse-square interaction in a 3-dimensional space. In fluid dynamics, electromagnetism, quantum mechanics, relativity theory, and a number of other fields, there are continuity equations that describe the conservation of mass, momentum, energy, probability, or other quantities. 32 {\displaystyle \mathbf {F} } + on {\displaystyle |V_{\text{i}}|} Φ {\displaystyle \mathbf {F} (\mathbf {x} )} Gauss's law for gravity has the same mathematical relation to Newton's law that Gauss's law for electrostatics bears to Coulomb's law.

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