On earth, I know that if I throw a tennis ball straight up while in a car, it comes straight back down thanks to Newton's first law. The ball, the air in the car, and myself are all moving at a speed, and when I throw the ball up, I'm actually throwing it forward relative to someone standing on the street.

What I don't understand is that once I leave the atmosphere of earth and reach the vacuum of deep space, where the earth's gravity is no longer keeping me in orbit (right?), why do I not behave like a tennis ball that was thrown too high in a convertible? Is it really that simple that I'm continuing along within the solar system as it orbits the galaxy center simply because I was already going the same speed? Is the barycenter of the solar system dragging me along through the galaxy?

Unfortunately I'm ignorant as to what effect I should Google to understand how, if I turn off rockets and coast, I'm coasting at enough speed to keep up with the solar system. Please someone help me.