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Thread: How to find escaping velocity of an object in any Planet ?

  1. #1 How to find escaping velocity of an object in any Planet ? 
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    I don't know how to find the escaping velocity of any object in Earth. Not only in earth but also in any Planet.. Plz help me.. :?


    I am reddaiah.
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    Forum Professor river_rat's Avatar
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    Hey there reddaiah

    This isn't as difficult to work out as you think, you just need to remember two important points about gravity. For starters, it is a conservative force so the total energy the system is constant and secondly that the potential energy of a point in a gravitational field GM/r is U = -GMm/r. This means that the total energy of that point is E = 1/2mv<sup>2</sup> - GMm/r and for escape we need this to be positive when the point is infinity far away from the source of the field.

    This implies that 1/2mv<sup>2</sup> - GMm/r > 0 => v > Sqrt(2GM/r) where M is the mass of the planet and r is the radius of the planet. So the escape velocity is v<sub>escape</sub> = Sqrt(2GM/r).

    Interestingly enough this formula (which is all classical newtonian mechanics) gives the correct swartchzchild radius, just plug in c as the escape velocity and you arrive at r<sub>swartchzchild</sub> = 2GM/c<sup>2</sup>


    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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    Forum Freshman Keith's Avatar
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    I don't understand escape velocities...err, how they are used. They aren't really applicable cause we are always adding more energy. Escape velocities are ridiculously high and we cant really get anything to go that fast. Can we?
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    "We make our world significant by the courage of our questions and by the depth of our answers." -Carl Sagan
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  5. #4  
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    From earth it is a problem, atmospheric friction is the knub, and blows the equation out, on earht the escape velocity (if I remember correctly) is around 11Km/second this excludes atmospheric resistance (again to memory so I could be wrong). There have been attempts to put shells into orbit. On an asteroid you could probably 'jump' off it.... Phobos (a moon of mars has an escape velocity of around 11 metres per second! so with a good bow you could launch an arrow into orbit!
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  6. #5  
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    That 11km/s is if you throw something that has no thrust once you threw it. But rocket is different, it can increase or rather sustain its velocity as it goes up.
    where are we? what are we?
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  7. #6  
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    That is escape velocity! - if you want to use a rocket with continuous power thrust it could escape at 1mph!
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  8. #7 Re: How to find escaping velocity of an object in any Planet 
    Universal Mind John Galt's Avatar
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    Quote Originally Posted by reddaiah224
    I don't know how to find the escaping velocity of any object in Earth. Not only in earth but also in any Planet.. Plz help me.. :?
    River Rat has given an excellent exposition on the subject.
    Quote Originally Posted by Keith
    I don't understand escape velocities...err, how they are used.
    Space scientists need to know escape velocities when sending probes to other planets. If the spacecraft cannot achieve escape velocity it will be unable to break free from the Earth's gravity field.
    Quote Originally Posted by Keith
    Escape velocities are ridiculously high and we cant really get anything to go that fast. Can we?
    They aren't that high, and we have frequently achieved them. The Pioneer spacecraft have achieved escape velocity for the solar system, which they are in the process of leaving.
    Quote Originally Posted by Megabrain
    on earht the escape velocity (if I remember correctly) is around 11Km/second this excludes atmospheric resistance
    Atmospheric resistance has nothing to do with it. You need to be travelling at 11.2 km/sec whether you are in a vacuum or in the atmosphere. (Technically, in a vacuum, since you must already be in space, the escape velocity would be a little lower than 11.2.)
    Quote Originally Posted by Megabrain
    if you want to use a rocket with continuous power thrust it could escape at 1mph!
    No you couldn't. Your statement is incorrect.
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  9. #8  
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    Hmm maybe a bit of clarity needed here, the Earth's escape velocity from it's surface is around 11Km/sec if you fired a projectile at this velocity from the surface it would be subject to atmospheric resistance. the further you move from the earth the lower the ecape velocity. - clear now?

    Quote Originally Posted by wiki
    The object is assumed to be influenced by no forces except the gravitational field; in particular there is no propulsion (as by a rocket), there is no friction (as between the object and the Earth's atmosphere; these conditions correspond to freefall), and there is no gravitational radiation.
    Full article at:- http://en.wikipedia.org/wiki/Escape_velocity

    Ophiolite, a continuously powered rocket could escape the earth's gravitational field at any speed, it needs only to burn enough fuel to overcome gravity. then a short burst to gain it's desired speed - think about it.
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  10. #9  
    Universal Mind John Galt's Avatar
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    Quote Originally Posted by Megabrain
    Hmm maybe a bit of clarity needed here, .
    I agree.
    Quote Originally Posted by Megabrain
    Hmm maybe a bit of clarity needed here, the Earth's escape velocity from it's surface is around 11Km/sec if you fired a projectile at this velocity from the surface it would be subject to atmospheric resistance.
    Of course it would. Therefore it would slow down. Therefore it would be travelling at less than the escape velocity. Therefore it would not escape the Earth. It would have to be fired at a speed sufficiently high that despite the air resistance it would have slowed to escape velocity (or faster) by the time it left the atmosphere.
    Quote Originally Posted by Megabrain
    the further you move from the earth the lower the ecape velocity. - clear now?
    Which is exactly the point I made when I said: "(Technically, in a vacuum, since you must already be in space, the escape velocity would be a little lower than 11.2.)"
    It has been clear to me from the outset. It still does not appear to be clear to you.
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  11. #10  
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    Escape velocity is specifically calculated as a value from the surface of the body, not from a point above the atmosphere. -

    Quote Originally Posted by Ophie
    Atmospheric resistance has nothing to do with it. You need to be travelling at 11.2 km/sec whether you are in a vacuum or in the atmosphere. (Technically, in a vacuum, since you must already be in space, the escape velocity would be a little lower than 11.2.)
    That statment is not correct, the 11.2 figure is from the surface (without considering atmospheric intreference). From low earth Orbit I calulate the 'escape velocity' to be around 10.92Km/s. - wiki makes it a little less (unless they rounded it down or, chose a different height.).
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  12. #11  
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    It is true that continuously powered rocket should attain escape velocity at SOME point (infinity included), whether it is near earth surface or not. And this velocity is reduced as you go further from earth. This means you can escape at 1mph. (That is of course if you want to escape the earth gravitational well.)
    where are we? what are we?
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  13. #12  
    Universal Mind John Galt's Avatar
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    Megabrain, read what I wrote, not what you think I wrote. There is nothing in your last clarification that does not mirror exactly what I said.
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  14. #13  
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    You can escape the earth's gravity at 1mph. A balloon demonstrates this within the atmosphere. If you contrived some kind of "balloon" that also worked outside the atmosphere, you could come and go at any velocity you chose. Basically it would be an "antigravity device". Of course, to actually build an antigravity device you'd have to understand gravity inside out.
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