It'll be a very gentle affair at stellar scales, highly unlikely to have any noticeable effect, so sparse are the stars spread. Also, movement on human time spans won't be apparent. While still extremely unlikely, a possible close pass of a star could perturb the Oort cloud, sending comets/asteroids inward (and outward).

Also, the Earth will likely not be habitable at that time due to the Sun's changes.

I'm great fun at parties.