We are on a spaceship.

The Solar System is traveling at 828,000 km/hr (514,495 mph) through the Milky Way. When you look at night sky the stars you see are the large, close stars less than 5000 light years away.

Do you notice stars whipping past?

Traveling on human-made spaceships would look similar, especially if the ship rotated around its axis to create artificial gravity.