Assume the following hypothetical situation: an enormous body, 20,000 ly in diameter (I recognise that 'asteroids' per se tend to be smaller), approaches the Milky Way, perpendicular to its equatorial plane, and headed straight for planet Earth, or at least on a trajectory where it will definitely collide with the Earth at some point. Assume that the body (the 'evil space rock', from now on) is a perfectly spherical, homgenous body of density 3000 kg m^-3, that magically appeared 25,000 ly from the Milky Way (i.e. its gravitational waves have only just begun propagating towards the Earth). At what distance would it begin to have any effect on the Earth? At what distance would it upset the Earth's orbit enough to cause destructive climate change and a consequent extinction event? At what distance would it extract the Earth from orbit entirely and begin pulling it towards itself? And, as a side-query, what would happen if the evil space rock were to impact (or rather, get sucked into) Sagittarius A*? What if it was aimed there instead of at Earth?