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Can a rocket use just enough fuel to reach an area wherein it has escaped a planet's gravitational pull and then turn its engine off?

Supposing there is nothing else with a gravitational pull that the rocket would get caught in, would the rocket keep on moving since there is nothing to slow it down?

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    $\begingroup$ Why would it keep accelerating? Where's the force accelerating it coming from? What exactly do you mean by "escaping" a planet's gravitational pull - reaching escape velocity? $\endgroup$
    – ACuriousMind
    Commented Aug 11, 2021 at 23:35
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    $\begingroup$ It would not keep accelerating because that would take force or fuel, but it would keep moving at a constant speed. This is how NASA is able to send satellites into far distant space, even outside of our solar system. They just keep moving at a constant speed. $\endgroup$ Commented Aug 11, 2021 at 23:37
  • $\begingroup$ @foolishmuse oh ok, thanks. Sorry for saying accelarating i meant moving. $\endgroup$ Commented Aug 11, 2021 at 23:41
  • $\begingroup$ @mohamedelgamal, I've edited your question in accord with your comment above mine. Please feel free to revert or re-edit if you're not happy with my edit. $\endgroup$ Commented Aug 11, 2021 at 23:46
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    $\begingroup$ "an area wherein it has escaped a planet's gravitational pull" The gravitational field of any massive object is technically infinite, so the area you mention does not exist (barring GR theories). $\endgroup$ Commented Aug 12, 2021 at 3:17

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As pointed out in the comments, the rocket would continue at a constant velocity (given that gravity is nearly non-existent in the proximity of the rocket). However, gravity is present everywhere in the universe. Granted, in some areas of space you can find nearly flat spacetime, but would the rocket continue on forever at a constant velocity? Probably not. As the rocket continues on it journey it will at some future point interact with space-time that is more significantly curved (gravitation) and that will result in a change in the rocket's velocity.

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    $\begingroup$ and there are gas particles and light bombarding the rocket from all sides, which over time will also have an effect. $\endgroup$ Commented Aug 12, 2021 at 10:29
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    $\begingroup$ "it will at some future point interact with space-time that is more significantly curved (gravitation) and that will result in a change in the rocket's velocity" Yes, but the odds are good that it will keep moving (which is the question), even if not in a straight line with constant velocity. $\endgroup$
    – Flater
    Commented Aug 12, 2021 at 11:01
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If there is nothing else with a gravitational pull, then yes, it would go on forever.

However, this will not work in practice because the galaxy is full of "something else". You could leave Earth's orbit with a velocity of $11.186 km/s$ (that's Earth's escape velocity), but you cannot leave the Solar System, because the Solar System's escape velocity for a spacecraft launched from Earth is $16.6 km/s$. For a faster object, you could leave the Solar System, but the Milky Way's escape velocity is about $317 km/s$. Therefore your spacecraft will eventually turn around (i.e. accelerate).

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    $\begingroup$ As an example, the Voyager 1 spacecraft, launched from earth almost 44 years ago is currently traveling at about 38K mph. That translates, if my calculations are correct, into a velocity of about 16.9 km/s. So it has enough velocity to escape the solar system (which is has now done) but not enough (by a wide margin) to escape the Milky Way. $\endgroup$
    – jwh20
    Commented Aug 12, 2021 at 13:18
  • $\begingroup$ That's interesting. I'd never heard of these other escape velocities before. I assume all escape velocities are relative to the system's barycenter (since there's no such thing as absolute velocity)? $\endgroup$
    – T.E.D.
    Commented Aug 12, 2021 at 13:20
  • $\begingroup$ At least the 11.186km/s are when launched from Earth’s surface. $\endgroup$
    – Michael
    Commented Aug 12, 2021 at 13:29
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    $\begingroup$ @T.E.D. The Sun's escape velocity at the distance of the Earth is 42.1 km/s. Earth's orbiting at about 29.8 km/s relative to the Sun The value of 16.6 km/s is the minimum Earth-relative velocity you need in low earth orbit, to depart Earth in a hyperbolic trajectory that, if pointed in the correct direction, will put you at 42.1 km/s relative to the Sun once you leave the Earth's sphere of influence, and on a solar escape trajectory. $\endgroup$
    – notovny
    Commented Aug 14, 2021 at 9:58
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    $\begingroup$ @T.E.D. Which velocity that I mentioned are you asking about? If it's the 42.1km/s, as mentioned, that's the Solar escape velocity (that is, relative to the Sun) at a distance of 1 AU from the Sun. $\endgroup$
    – notovny
    Commented Aug 14, 2021 at 23:16
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If your question was, "would it keep moving if it doesn't encounter any gravitational field" Yes it would.

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Space is not empty. The gaps between the planets in our solar system are relatively empty, but once outside this cosmic carpet sweeper, there is interstellar matter that has mass.

Momentum would wash off, motion might continue but velocity would continually be reduced at a diminishing rate, over time. Forever is a long time.

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