After unknown amount of years traveling at 14 million MPH, one would think that by now we'd be getting closer to the source of attraction causing the pull to be stronger and increase the speed of travel and SPLAT!
The sun will go supernova and cook all the planets in about 4 billion years. The Andromeda galexy will collide with our Milky Way galexy also in about 4 billion years. The collision with the Great Attractor is farther out than that so why worry?