technically it wouldn't rise for 2 earth days on saturn and that happens all the time so does that mean proto gets kicked every 2 days?

also if you were to fly around the world in the fastest jet in the same rotation you might be able to hide behind the side of the earth facing away from the sun, as long as you're out of orbit enough you should be able to stay there or counteract the small amount of velocity caused by the earths rotation.