Lets say you're on a spaceship, and the floor of the ship is pulling you and the other objects in your ship toward it. (it might be easier to think of this in terms of a computer simulation)
If you go beneath the floor of your ship, you are not affected by it's artificial gravity.
Now...
It's the old question of "if you're in a spaceship going near the speed of light, and you turn on your headlights..."
Think about this: Earth is spinning around the sun. The sun is spinning through the Milky Way. The Milky Way is moving away from other galaxies. That's a lot of moving around...