/sci/ - Science & Math

What if you accelerate a rocket out in space from a planet. You give it some speed and turn of the engines. Then it just goes by its kinetic energy further and further into space.

Does the rocket ever fall back down to the planet? Assumimg mathematically idealized situation, no other planets or variables.

Supposedly the gravity of that planet, although becoming weaker farther away, still extends infinitely into space. So no matter how far the rocket is, the gravitational field of the planet is always eating away the kinetic energy of the rocket. So my theory is that at some point given enough time the rocket slows down, starts moving to the opposite direction and goes back to the planet where it started.

Is this right and why or why not?