  The stability of galaxies is either explained by the existence of dark matter
or caused by a modification of Newtonian acceleration (MOND). Here we show that
the modification of the Newtonian dynamics can equally well be obtained by a
modification of Newton's law of universal gravitational attraction (MOGA), by
which an inverse square attraction from a distant object is replaced with an
inverse attraction. This modification is often proposed in the standard model,
and with the modification of the attraction caused by dark matter. The recently
derived algorithm, Eur. Phys. J. Plus 137, 99 (2022); Class. Quantum Grav. 39,
225006 (2022), for classical celestial dynamics is used to simulate models of
the Milky Way in an expanding universe and with either MOND or MOGA. The
simulations show that the galaxies with MOND dynamics are unstable whereas MOGA
stabilizes the galaxies. The rotation velocities for objects in galaxies with
classical Newtonian dynamics decline inversely proportional to the square root
of the distance $r$ to the galaxy's center. However, the rotation velocities
are relatively independent of $r$ for MOGA and qualitatively in agreement with
experimentally determined rotation curves for galaxies in the Universe. The
modification of the attractions may be caused by the masses of the objects in
the central part of the galaxy by the lensing of gravitational waves from
far-away objects in the galaxy.
