One of the problems would be to find as much information as possible about every star. Are all 300 Billion stars in the Milky Way classified by mass, velocity, direction, etc? Are they all even distinguishable as discrete independent stars?

Doing even a single n^{2} calculation on 300 billion stars would be problematic.

One, might be able, however, to do the calculation around various exemplars. Say, one wished to calcuilate our sun's trajectory and mass interactions in relation to the other 300 billion stars. This might be able to be reduced to an order-n calculation, and something one could calculate given the availability of the data. Designed generally, one could pick other exemplars too, such as VY Canis Majoris, and then repeat the calculations around it (again an order-n calculation).

One could always choose some kind of a simplification such as choosing a smaller galaxy, or to consider imposing symmetry, so rather than calculating on 300 billion stars, perhaps choose a 1 degree sector, and do the calculation on 1 billion stars. It still may be a n^{2} calculation, but on much fewer stars. Also, doing the calculations on a certain sector of the Milky Way would help reduce the number of hidden stars.

If data errors are random, then they might average out to a large extent. However, if there is a specific bias in the data errors, then the outcome could be off significantly.