I recently saw something by Randall Munroe about this, the guy who makes xkcd. Something in there where the moon would partially restart the rotation of earth.
Staying in space is hard. After getting up above the atmosphere, you then need to get thrown sideways so fast that the curve of the arc you've been thrown on is equal to the curvature of the planet's surface.
Earth's rotational speed will only get you about 1/15th of the way to reaching orbital velocity.