What happens when a rocket ship accelerating in outer space runs out of fuel?

Answer 1

Unless a projectile is launched at escape velocity, it cannot leave the earth's gravitational pull. For Earth this means the initial velocity must be about 11.2 km/s (ignoring drag and the launch location and direction relative to the planet's rotation). A projectile is something launched from a slingshot, bow, cannon, rifle, arm, etc... An object with its own propulsion, such as a rocket, is not subject to earth's 11.2 km/s escape velocity. A rocket can leave the earth at a much slower "speed" by simply overcoming the force of gravity at the location and moment of its climb. If you had a ladder tall enough (and a ridiculous supply chain) you could very slowly climb away from the earth under your own power. There is no set or calculable speed for a rocket, or any self-propelled object to "escape" the earth's gravity. So, your question, if changed from rocket to unpowered projectile, could be answered as follows: it will fall back toward earth (as satellites do in orbit). Or, if your question is unchanged, the answer is this: it will continue to move up and away from earth at any velocity it has so long as it maintains a thrust sufficient to overcome the diminishing gravitational attraction between it and the earth--eventually escaping our planet. But remember, earth's attraction is not the only gravitational pull out there!

Answer 2

It uses large engines and a huge amount of fuel to accelerate the rocket away from earth. The fuel burn pushes out huge amounts of gas, forced out in the opposite direction to the rockets direction of travel.

Answer 3

It continues on at its terminal velocity forever unless it hits something.

Answer 4

Then it will escape Earth's gravitational field, and go farther and farther away.