The "Missing Mass Problem" in Astronomy and the Need for a Modified Law
  of Gravity
  Since the 1930s, astronomical observations have accumulated evidence that our
understanding of the dynamics of galaxies and groups of galaxies is grossly
incomplete: assuming the validity of Newton's law of gravity on astronomical
scales, the observed mass (stored in stars and interstellar gas) of stellar
systems can account only for roughly 10% of the dynamical (gravitating) mass
required to explain the high velocities of stars in those systems. The standard
approach to this "missing mass problem" has been the postulate of "dark
matter", meaning an additional, electromagnetically dark, matter component that
provides the missing mass. However, direct observational evidence for dark
matter has not been found to date. More importantly, astronomical observations
obtained during the last decade indicate that dark matter cannot explain the
kinematics of galaxies. Multiple observations show that the discrepancy between
observed and dynamical mass is a function of gravitational acceleration (or
field strength) but not of other parameters (size, rotation speed, etc.) of a
galaxy; the mass discrepancy appears below a characteristic and universal
acceleration ("Milgrom's constant"). Consequently, the idea of a modified law
of gravity, specifically the ansatz of Modified Newtonian Dynamics (MOND), is
becoming increasingly important in astrophysics. MOND has successfully
predicted various important empirical relations of galaxy dynamics, including
the famous Tully-Fisher and Faber-Jackson relations. MOND is found to be
consistent with stellar dynamics from binary stars to clusters of galaxies,
thus covering stellar systems spanning eight orders of magnitude in size and 14
orders of magnitude in mass. These developments have the potential to initiate
a paradigm shift from dark matter to a modified law of gravity as the physical
mechanism behind the missing mass problem.
