Non-Keplerian MW–M31 dynamics under Hyperspherical Expansion Acceleration: a bound solution without Dark Matter

This paper revisits the dynamical status of the Milky Way–Andromeda system in light of recent mass estimates. Observations indicate that M31 contains a total mass of about 4.5 x 10^11 solar masses within 137 kpc, of which roughly 1.5 x 10^11 solar masses (32 percent) are baryonic. Assuming a comparable baryonic fraction for the Milky Way, the combined baryonic mass of the pair amounts to only 2-3 x 10^11 solar masses, far below the value required for a bound Keplerian orbit at the present separation of approximately 780 kpc and the observed blueshift of about –110 km/s. Even including the dark matter inferred from rotation curves, the total mass of the system reaches at most 7-8 x 10^11 solar masses, still well below the 3-5 x 10^11 solar masses demanded by the classical timing argument. In this sense, the apparent “missing mass” reflects the inadequacy of the Keplerian paradigm on group scales rather than the need for an extended dark matter halo.