Modified Newtonian dynamics: Difference between revisions

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that is, the star's rotation velocity is independent of ''r'', its distance from the centre of the galaxy – the rotation curve is flat, as required. By fitting his law to rotation curve data, Milgrom found <math>a_0 \approx 1.2 \times 10^{-10} \mathrm{ms}^{-2}</math> to be optimal. This simple law is sufficient to make predictions for a broad range of galactic phenomena.

Milgrom's law can be interpreted in two different ways. One possibility is to treat it as a modification to the classical [[law of inertia]] (Newton's second law), so that the force on an object is not proportional to the particle's acceleration ''a'' but rather to ''μ''<math>\mu\left(''\frac{a''/''}{a_0}\right)a''<sub>0</submath>)''a''. In this case, the modified dynamics would apply not only to gravitational phenomena, but also those generated by other [[forces]], for example [[electromagnetism]].<ref>M. Milgrom, "MOND - Particularly as Modified Inertia", {{arxiv|1111.1611}}</ref> Alternatively, Milgrom's law can be viewed as leaving Newton's Second Law intact and instead modifying the inverse-square law of gravity, so that the true gravitational force on an object of mass ''m'' due to another of mass ''M'' is roughly of the form

:<math> \frac{GMm}{\mu \left (\frac{a}{a_0} \right ) r^2}.</math>