On the trajectory of the Andromeda-Milky Way collision The Andromeda-Milky Way collision is going to happen in approximately 4 billion years. What trajectory would the Andromeda galaxy follow on its path to collision with the Milky Way? How could this be calculated using General Relativity?
 A: That actually depends on various numbers we still are not sure about


*

*The mass of the Milky Way:
This is a whole subject by itself, including the dark halo, it can range from $0.8\times 10^{12}M_{\odot}$ to $2.0\times 10^{12}M_{\odot}$, depending on the tracer you use to estimate it, e.g. stars in the stellar halo, hypervelocity stars, dwarf satellite galaxies, stellar streams, $\cdots$

*The mass of M31:
This is an even harder question to answer. We believe it is heavier than the Milky Way itself,  but how much more is not very clear. There's, however, a good handle on the sum of these two masses, that comes from something called 'timing argument'. The problem is that this argument is very degenerated and clearly depends on us knowing what is the mass of the MW

*The proper motion of M31:
If measuring the mass of M31 is difficult, measuring its velocity is quite the challenge. Turns out that measuring the radial component of the velocity is not that difficult with good spectroscopic observations (just need to measure the shift of the lines). But measuring the other two components (the ones projected on the sky) are way harder. You basically need to take many pictures for many years and see how it moves ... not a trivial task
In summary, you may get a good handle on all these three numbers, but an accurate representation of the orbit is not knows until you have very precise estimations of the mass and velocity of each body, which we currently do not have. There are a few simulations, but you should be careful how you interpret them
