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Is it sure that Milky way and Andromeda will collide or might they just start a rotation around their center of masses?

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I think the most recent work on this is by van der Marel (2019). It has of course never been in question that the Milky Way (MW) and Andromeda (M31) are moving towards each other, but 3D motions are required to map their trajectories.

van der Marel et al. combined proper motion data from the Hubble Space Telescope and Gaia satellite to work out the tangential velocity (correcting for the rotation pattern) of M31 with respect to the MW. The conclusion is that there will be a glancing blow in 5.5 Gyr, with a percenter of 75 kpc (after including the influence of M33 and the Large Magellanic Cloud). Nevertheless this is still close enough that it will result in the merger of the galaxies shortly afterwards.

It has to be said though that there is no detailed exploration of the full error space in the paper, so while I think a merger is pretty certain, the details and timing are still a bit debatable.

The following picture appeared in a press release accompanying the paper.

Evolution if the Local Group

Some investigation of these issues is provided by Schiavi et al. (2020). Altering the tangential velocity of M31 by its error bar does vary the outcome between almost a direct hit and a glancing blow followed by several further, decreasing orbits followed by a merger some tens of Gyr in the future.

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