Timing Argument take on the Milky Way and Andromeda past-encounter

Understand

The two-body problem of $M31$ and the Milky Way (MW) galaxies with a Cosmological Constant background is studied, with emphasis on the possibility that they experienced Past Encounter (PE).

• PE are possible only for non-zero transverse velocity and their viability is subject to observations of the imprints of such near collisions.
• By implementing the Timing Argument (TA) for two isolated point bodies, it is shown that if $M{31}$ and the MW have had PE, then the predicted mass of the Local Group (LG) should be twice larger.
• Since the predicted mass is too large, the MW and $M31$ galaxies should have collided at $\sim 8 Gys$.