In physics, the Newtonian limit is a mathematical approximation applicable to physical systems exhibiting (1) weak gravitation, (2) objects moving slowly compared to the speed of light, and (3) slowly changing (or completely static) gravitational fields.[1] Under these conditions, Newton's law of universal gravitation may be used to obtain values that are accurate. In general, and in the presence of significant gravitation, the general theory of relativity must be used.
In the Newtonian limit, spacetime is approximately flat[1] and the Minkowski metric may be used over finite distances. In this case 'approximately flat' is defined as space in which gravitational effect approaches 0, mathematically actual spacetime and Minkowski space are not identical, Minkowski space is an idealized model.
^ abCarroll, Sean M (1997). "Lecture Notes on General Relativity". arXiv:gr-qc/9712019.
In physics, the Newtonianlimit is a mathematical approximation applicable to physical systems exhibiting (1) weak gravitation, (2) objects moving slowly...
emitted at an infinitely large distance, there is no redshift. In the Newtonianlimit, i.e. when R e {\displaystyle R_{\text{e}}} is sufficiently large compared...
of mass, momentum, and energy all of which are important constructs in Newtonian mechanics. SR shows that these concepts are all different aspects of the...
classical Newtonian theory of gravity is recovered in the limit as the ratio r s r {\textstyle {\frac {r_{\text{s}}}{r}}} goes to zero. In that limit, the...
Modified Newtonian dynamics (MOND) is a theory that proposes a modification of Newton's second law to account for observed properties of galaxies. Its...
can easily be checked using the explicit expression for H. In the Newtonianlimit, for quasi-static systems in nearly flat space-times, one can approximate...
: 16 This includes Newtonian gravitation. A standard demonstration in general relativity is to show how, in the "Newtonianlimit" (i.e. the particles...
deformation of classical Newtonian into relativistic mechanics (special relativity), with deformation parameter v/c; the classical limit involves small speeds...
orbits or, equivalently, assuring that the weak-gravity, low-speed limit is Newtonian mechanics, the proportionality constant κ {\displaystyle \kappa }...
theorem Gravitational binding energy Speed of gravity Newtonianlimit Hill sphere Roche lobe Roche limit Phase space Symplectic manifold Liouville's theorem...
The earliest formulation of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on the 17th century...
(or non-relativistic, or the Newtonian approximation) that all speeds are much less than the speed of light. This limit is associated with the Galilean...
with the inclusion of a one-graviton process, and yield the correct Newtonianlimit in d dimensions, but only with a dilaton. Furthermore, some speculate...
analogous to an ergosphere. Since (2+1)-dimensional gravity has no Newtonianlimit, one might fear[why?] that the BTZ black hole is not the final state...
invariant, satisfies the conservation laws, correctly reduces to the Newtonianlimit and satisfies the weak equivalence principle. This theory is Einstein's...
standard definitions of Newtonian kinetic energy and momentum. This is as it should be, for special relativity must agree with Newtonian mechanics at low velocities...
rates (Newtonian fluids). The fluids without a constant viscosity (non-Newtonian fluids) cannot be described by a single number. Non-Newtonian fluids...
symmetries of pp waves, spacetime view of gravitational lensing, Newtonianlimit), Albert Einstein (creator of general relativity, principle of equivalence...
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