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v$_r$ and μ are radial velocities and proper motion as seen from the Sun (ie heliocentric) and the equations in the appendix convert to v in the $S_o$ frame which is the center of the Galaxy. So, the motion of the MW is (0,0,0). If you want to, you can solve for v$_r$ and μ for the MW by plugging v=(0,0,0) into the equation, and find the heliocentric ...


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The main factor is the velocity of the encounter. The higher the relative velocity between the two galaxies, the easier it is for them to pass through each other without being slowed down enough for a proper merger to take place, and without being strongly distorted by the encounter. (In a very high speed encounter, the two galaxies will spend almost no time ...



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