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Blazing goIITian

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19 May 2007 23:35:15 IST

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517

escape velocity

None

sir ,
i know that it is a very weird query to ask at this stage .. but somehow i tend to think abt it ...

regarding what we call as escape velocity " the min velocity required by a body to escape another body's gravitational field " for earth it is 11.1 km/s .

my question is that if we project a body with a much lesser speed than this limit say even 10 m/s wont it be able to escape ... in howsoever long time or what ... as the grabitational pull will anyways decrease with height ... but conservation of energy may not hold good in that case ... so i m not able to see the paradox of the situation .. pls tell me a missing point in this arguement ... and also clarify what will indeed happen ifthe body is projected with a velocity lesser than the escape velocity ... i mean willit get hung up in the air or what ?

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Aditya Arora

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19 May 2007 23:51:56 IST

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Look,

Earth's gravitational pull becomes negligible after a particular height.

Now, the escape velocity is defined as the velocity needed to take the body to that height and take it just a negligible distance beyond so that the gravitational force does not act on it anymore.

Now, that value is 11.1 km/s . If you give it a velocity less than this, than gravitational force would act on it and would not let it escape. And would certainly bring it back to the surface.

Hope you have got it !!!!

aman

Blazing goIITian

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20 May 2007 12:14:36 IST

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can u ls elaborate .... it is perfect physically to think in ur terms ... but other ways it is difficult to visalize

Ananth Patri

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20 May 2007 12:26:27 IST

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we get the value 11.1 km/s from the derivation of escape velocity.....now tht must be provided and noting less than tht vel for body to cross earth pull.....if some less velocity is provided the body will simply go to some height and fall off back to earth....i dont see any Paradox in this situation.....Hope u r satisfied.....

karthik

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20 May 2007 12:53:18 IST

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my question is that if we project a body with a much lesser speed than this limit say even 10 m/s wont it be able to escape ... in howsoever long time or what ... as the gravitational pull will anyways decrease with height ... and also clarify what will indeed happen ifthe body is projected with a velocity lesser than the escape velocity '

ANSWER:-

It wont escape.Itz becoz due to gravitational pull the speed, wat u considered say 10 m/s will start decreasing......and at a particular time the velocity will be reduced to 0m/s.

.and at that time it will reach the maximum height and then fell back into the earth due to gravitational pull..........and also remember that the projected velocity wont be maintained throughout...........but when it is projected at 11.1km/s it will escape the gravitational force even though the 11.1km/s velocity will be decreased it will certain have some velocity with it when it escapes the gravitational force.

.......

hope u got it

.....

CHEERS!

Aditya Arora

Blazing goIITian

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20 May 2007 13:05:47 IST

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Hi,

Look,

Try to understand it in this way. There is an imaginary line around the earth. If we want a body to escape the earth's gravitational pull, we need to take the body a negligible distance beyond the line. Now, escape velocity is the velocity to take the body to that height plus that negligible distance beyond.

If you give it a lesser velocity, it will not be able to cross that line and would return to the earth's surface.

Now, is it okay ?????

smriti.mathur

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20 May 2007 14:02:41 IST

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With a velocity lesser than 11.1 km/s, the object would be pulled by the gravitational pull of the earth.

Aditya Sahay

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20 May 2007 20:49:38 IST

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If a body is projected VERTICALLY with escape velocity, it will keep moving far & far but never return. In other words, it will always have the necessary kinetic energy to do work against gravity & to make it keep moving forward to infinity. A velocity less than this would bring it back to earth, no matter how far away it is from earth.

Yes, if you project the body at some angle(not vertical) such that its horizontal component is at least 8 km/s, then adequate centrifugal force will be provided to fix it in an orbit above earth(but its vertical component should not be = escape velocity). In the absence of such a force the body must return to the earth.

I think this will help u. If it does, please rate me.

Ananth Patri

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20 May 2007 21:38:50 IST

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I think escape velocity...and all doesnt depend on the angle of projection ...so there is no chance of a parabolic path and all tht centrifugal force actionn.........as much as i know....sorry if i am wrong............

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