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Modified Newtonian dynamics (MOND) is a variant on Newton's laws developed in 1983 by Mordehai Milgrom, offering an explanation for the same observations that motivate the concept of dark matter. MOND is not widely accepted in physics, but often gets consideration in studies if they might provide evidence for or against it.
MOND affects gravity by modifying the law, "F=ma", its modification being insignificant within daily life and throughout the solar system, but significant when forces are extremely small, such as that of gravity over the distances between stars, galaxies, etc. MOND represents a radical change to physics (as was general relativity), but because the evidence for dark matter is so restricted, nearly all of it consisting of large-scale dynamics, science demands that alternatives (such as MOND) should be explored. MOND does not offer a fully-defined law, but a template that fits laws which could produce the effects attributed to dark matter. In place of the law, F=ma, MOND has:
F = m μ(a/a0) a
μ( x>>1 ) ≈ 1 μ( x<<1 ) ≈ x
Various functions are tried as a workable μ(x), one example being:
μ(x) = x / (1+x)
Research into MOND has continued and continues: variants consistent with relativity have been produced, as well as studies specifically looking for evidence, and ideas developed of how it might be tested, one such idea being tracking wide binaries, in which the gravitational attraction between the stars and their resulting acceleration is so slight that the difference implied by the MOND equation could be significant.