# What happens after a rocket is fired with velocity equal to or greater than escape velocity? [closed]

When a rocket is fired a speed greater than or equal to escape velocity, then it does not have any gravity effect of the earth.

So, suppose if a rocket is having that much energy which will only last for 1 sec. Then it will move with 11.2km/s and it escapes from the earth.

My question is what happens after that?

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• It escapes! Just like the voyager probes it keeps heading out into deep space. – user22079 Jul 19 '13 at 6:45
• Escape velocity. If you have exactly the escape velocity you will be on a parabolic orbit, and if you have any excess energy you will be on a hyperbolic orbit. You escape to infinity, slowing down under gravity the whole time. – Michael Brown Jul 19 '13 at 7:10
• It takes a lot of fuel to launch a payload plus the fuel to launch a payload, plus the fuel for that, and that etc. The equation is exponential such that there is a practical limit to how much you can lift. – user22079 Jul 19 '13 at 7:14
• It hasn't escaped Sun yet! – Ali Jul 19 '13 at 7:14
• Presuming it's outside the atmosphere (so it doesn't get slowed down by that and burn up) it will escape the Earth and slow down as it does so. Once it has escape velocity there is no need to keep pushing. Extra fuel is used for making course corrections. After going to Pluto the New Horizons probe will keep travelling outward and the extra fuel will be used to divert it to any suitable Kuiper belt objects which are near enough. – Michael Brown Jul 19 '13 at 8:09

From a comment by the OP.

If you have gravitational pull even if your speed is greater than or equal to escape velocity then what is the use of 11.2 km/s for a rocket

javaprogrammer, to think that gravity somehow no longer affects the rocket after it attains escape velocity is to seriously misunderstand the nature of gravity.

The equation of motion that governs the rocket does not depend on the speed of the rocket.

For simplicity, consider the idealized case of just the Earth and the rocket.

The equation of motion tells us that the rocket, once the engine is shut down, will always have an acceleration towards the Earth no matter how fast the rocket may be travelling away from the Earth.

However, the equation of motion tells us something else, it tells us that, given a particular speed when the engine shuts off, there are three possible outcomes:

(1) the rocket will eventually slow, stop, and start travelling towards the Earth. This is the case that the rocket does not have escape velocity when the engine stops.

(2) the rocket will slow with its speed approaching zero but never quite getting there. This is the case that the rocket has exactly the escape velocity when the engine stops.

(3) the rocket will slow with its speed approaching some non-zero value but never quite getting there. This is the case that the rocket has greater than escape velocity when the engine stops.

i saw in Discovery science in which they have said that NASA has sent a spacecraft to move into outer solar system and it is run by slow degradation of some radioactive element. And the fuel is little sufficient till 2030. My question why does it require fuel at all

To produce electrical power to run the spacecraft systems.

In simple terms, once the rocket has escape velocity it will keep flying away from the earth. And, once the rocket has that energy, even if only for 1 second, it will keep it and gradually convert that kinetic (movement) energy into potential energy (the energy it has by being higher in the earth's "gravitational potential well". The sum of kinetic and potential energy will always stay the same.

When a rocket is fired a speed greater than or equal to escape velocity then it does not have any gravity effect of the earth.

That is wrong. No matter how fast you go, or how far away you are, you always feel the gravitational pull of the earth. That means that you will slow down gradually. If you start with exactly escape velocity, then earth's gravity will reduce your speed to zero (relative to the earth) when you reach infinity, after an infinite time. If your initial speed is greater, then you will always have some speed, even at infinity

All the above assumes there is only the earth and the rocket. In reality, there are other bodies in the universe. At 11.2 km/s the rocket does not have enough velocity to escape from the solar system, so it will fly around the sun and may eventually even come back to the earth because of that. To escape from the sun itself, you need a speed of 617.5 km/s relative to the sun, not to the earth. However, as the earth already moves around the sun at a distance of 15,000,000 km, you don't need all of that speed to escape the sun from the earth. As Pulsar pointed out a mere 42 km/s will do.

• The value 617.5 km/s is the escape velocity on the surface of the Sun. Instead, you need to use the escape velocity at the Earth-Sun distance, which is ~42 km/s. If you correct that, I'll give you a +1. – Pulsar Jul 19 '13 at 11:06
• @hdhondt If you have gravitational pull even if your speed is greater than or equal to escape velocity then what is the use of 11.2 km/s for a rocket.Even if your speed is 1km/s then also you can move – java programmer Jul 19 '13 at 11:37
• @Pulsar yeah, I realised that too, shortly after posting the answer, but did not get around to correcting it. – hdhondt Jul 19 '13 at 11:59
• @java I'm not sure what you're trying to say. At less than 11.2 km/s the earth will eventually pull you back. At a greater speed you will continue to move away from the earth, forever. – hdhondt Jul 19 '13 at 12:01
• @hdhonhdt see when you throw a stone upwards,it does not have a speed of 11.2km/s but it goes upwards – java programmer Jul 20 '13 at 4:27

Only considering earth (no sun, no Milky Way galaxy, no Andromeda galaxy - to each of which you are more strongly bound to than to Earth), and ignoring friction due to Earth's atmosphere, what would happen if you reach a velocity away from Earth slightly faster than the escape velocity: $v = v_{esc} + \delta v$?

Effectively you would be trading kinetic energy for potential energy, until you effectively escape earth's gravitational attraction and reach a final velocity that takes you ever farther away from Earth. Doing the math it follows that this final velocity equals $v_{final} = \sqrt{2 v_{esc} \delta v}$.

So if - after burning all your rocket fuel - you reach a speed of 11,201 m/s at a position where your local escape velocity is 11,200 m/s, you will start noticing a gradual drop in speed, until after some time you move away from earth at a speed of about 150 m/s. From that moment onward, you keep cruising at this speed.

Note that in the absence of friction you don't need any propulsion to maintain a given speed. You do need propulsion, however, if you wish to accelerate.

• you stay in india? I got to know this from your profile. Me to stay in india. – java programmer Jul 20 '13 at 4:30
• my doubt is something else and i am getting some else still its useful to me so +1 – java programmer Jul 20 '13 at 4:33
• @javeprog - yes, already a year in Bangalore. Time flies. – Johannes Jul 20 '13 at 4:57