Huh. I would have thought that once they break orbit that the sun’s gravity well would do the heavy lifting pulling.
If you care to learn orbital mechanics, Kerbal Space Program is a great teacher.
That one’s been sitting unplayed in my library for a very long time. I guess it’s time to give it a shot.
Imagine that you’re standing on a train and have a baseball. If you throw the ball off the train, the ball will still have momentum in the direction of the train’s movement.
If you want to throw the ball to a friend the train just passed, you have to be able to throw the ball faster than the train is moving or it will never reach them.
Mythbusters did this! (Well, the ball fell to the ground, but for a split second it looked like it was hovering after being shot out of a cannon.)
“Breaking orbit” still leaves you in almost the same orbit around the sun as the earth. You need to slow down a lot to bring the periapsis of the orbit within the suns surface.