Escape Velocity

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lukman

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Hi all, sorry, i dont understand escape velocity very well, all i know that on earth, a rocket must speed up faster that escape velocity to get in to orbit. My question is, in space elevator, does the cargo need to travel at high velocity as rocket does? Imagine there is an object, maybe a building, ladder&nbsp;or a mountain, very high into orbit, can a person climb at a snail pace&nbsp;reach the mountain peak? <div class="Discussion_UserSignature"> </div>

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drwayne

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Hi all, sorry, i dont understand escape velocity very well, all i know that on earth, a rocket must speed up faster that escape velocity to get in to orbit. My question is, in space elevator, does the cargo need to travel at high velocity as rocket does? Imagine there is an object, maybe a building, ladder&nbsp;or a mountain, very high into orbit, can a person climb at a snail pace&nbsp;reach the mountain peak? <br />Posted by lukman</DIV></p><p>Actually, an object moving at "escape velocity" does not go into orbit, it escapes Earth entirely.&nbsp; I assume you meant orbital velocity?</p><p>Assuming so, realize that being at orbital altitude does not mean one is in orbit.&nbsp; In your ladder example, stepping off the ladder leads to a fall back to Earth.&nbsp; </p><p>One falls in one is in orbit as well, but you are moving around the Earth as a speed such that the Earth is curving away from you at the same rate as you are falling.</p><p>Wayne</p><p><br /><br />&nbsp;</p> <div class="Discussion_UserSignature"> <p>"1) Give no quarter; 2) Take no prisoners; 3) Sink everything."  Admiral Jackie Fisher</p> </div>

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DrRocket

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Hi all, sorry, i dont understand escape velocity very well, all i know that on earth, a rocket must speed up faster that escape velocity to get in to orbit. My question is, in space elevator, does the cargo need to travel at high velocity as rocket does? Imagine there is an object, maybe a building, ladder&nbsp;or a mountain, very high into orbit, can a person climb at a snail pace&nbsp;reach the mountain peak? <br />Posted by lukman</DIV></p><p>Escape velocity can be understood in terms of energy and conservation of energy.&nbsp; When you raise an object against the force of gravity that object gains potential energy.&nbsp; When you drop it that potential energy is turned into kinetic energy as it falls.&nbsp; Similarly if you throw an object upwards the velocity and hence kinetic energy decrease as the object nears the top of its trajectory, and then increased again as it falls.&nbsp; At the very top of the trajectory the object is stopped and the original kinetic energy has become potential energy.</p><p>Now gravity decreases as the square of the distance from the source.&nbsp; Because of that relatinship one can show, using calculus, that if the object is moved an infinite distance from the source (the Earth for instance) that the amount of potential energy is a finite number.&nbsp; So if you give the object an velocity that imparts a kinetic energy greater than the potential energy of an infinite displacement that object will never fall back down.&nbsp; That level of velocity is called the escape velocity.</p><p>In the case of an elevator or a rope climb, one is applying a force throughout the climb.&nbsp; So the energy is imparted at each stage in whch force is applied over a distance.&nbsp; Therefore you get the necessary energy from the continual application of force and not from just an initial velocity.&nbsp; Hence you can climb the rope slowly, or go up the elevator slowly, &nbsp;and still progress upward indefinitely.&nbsp; <br /></p> <div class="Discussion_UserSignature"> </div>

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lukman

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Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Escape velocity can be understood in terms of energy and conservation of energy.&nbsp; When you raise an object against the force of gravity that object gains potential energy.&nbsp; When you drop it that potential energy is turned into kinetic energy as it falls.&nbsp; Similarly if you throw an object upwards the velocity and hence kinetic energy decrease as the object nears the top of its trajectory, and then increased again as it falls.&nbsp; At the very top of the trajectory the object is stopped and the original kinetic energy has become potential energy.Now gravity decreases as the square of the distance from the source.&nbsp; Because of that relatinship one can show, using calculus, that if the object is moved an infinite distance from the source (the Earth for instance) that the amount of potential energy is a finite number.&nbsp; So if you give the object an velocity that imparts a kinetic energy greater than the potential energy of an infinite displacement that object will never fall back down.&nbsp; That level of velocity is called the escape velocity.In the case of an elevator or a rope climb, one is applying a force throughout the climb.&nbsp; So the energy is imparted at each stage in whch force is applied over a distance.&nbsp; Therefore you get the necessary energy from the continual application of force and not from just an initial velocity.&nbsp; Hence you can climb the rope slowly, or go up the elevator slowly, &nbsp;and still progress upward indefinitely.&nbsp; <br />Posted by DrRocket</DIV><br /><br />Thanks for the explanation <div class="Discussion_UserSignature"> </div>

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drwayne

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Thanks for the explanation <br />Posted by lukman</DIV></p><p>Do you understand why this sentence:</p><p>"a rocket must speed up faster that escape velocity to get in to orbit"</p><p>makes no sense?</p><p>Wayne<br /></p> <div class="Discussion_UserSignature"> <p>"1) Give no quarter; 2) Take no prisoners; 3) Sink everything."  Admiral Jackie Fisher</p> </div>

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lukman

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Do you understand why this sentence:"a rocket must speed up faster that escape velocity to get in to orbit"makes no sense?Wayne <br />Posted by drwayne</DIV><br /><br />Ok, make it simple, why it needs a certain escape velocity to escape earth? Cant we just slowly fly away from earth? Is it at certain point, the gravity pull is stronger? it cant be right? An aeroplane doesnt need escape velocity to put a 10km distance away from earth surface right? so why 100km 1000km or 1000000km will be different?</p> <div class="Discussion_UserSignature"> </div>

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DrRocket

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>At what altitude, a rocket must be faster than escape velocity to get into orbit? and what is orbit is so special? A airplane can use the same speed to move from 5000m to 10000m. If we have a mountain or a building so tall, it reaches orbit, we can just&nbsp;use a stair in the building&nbsp;at a very slow speed and we still can reach the orbital altitude right? Somehow it makes me thinks that gravity is much&nbsp;stronger in the orbit border. &nbsp; <br />Posted by lukman</DIV></p><p>Did you read any of the answers to your original post ?&nbsp; Once you hit escape velocity you no longer are in a closed orbit around a single body, like the Earth.&nbsp; You are headed away from the Earth, never to come back.</p><p>Airplanes are not in an orbit.&nbsp; They are under constant powered thrust.&nbsp; If the engine quits, then they are in an orbit, and that orbit intersects the surface of the Earth -- they crash.</p><p>There is no such thing as orbital altitude.&nbsp; There is an orbital speed associated with each orbit.&nbsp; And the closed orbits that do not result in a crash require a fairly high orbital speed, but a speed less than escape velocity.</p><p>There is no such thing as the orbit border.</p><p>All an orbit is is the trajectory that an object takes as it falls.&nbsp; If you are going to slow you crash.&nbsp; If you are going fast enough you fall around the Earth and don't crash.&nbsp; If you are going really fast, above escape velocity, you fly away from the Earth and you don't come back.<br /></p> <div class="Discussion_UserSignature"> </div>

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lukman

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Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>Did you read any of the answers to your original post ?&nbsp; Once you hit escape velocity you no longer are in a closed orbit around a single body, like the Earth.&nbsp; You are headed away from the Earth, never to come back.Airplanes are not in an orbit.&nbsp; They are under constant powered thrust.&nbsp; If the engine quits, then they are in an orbit, and that orbit intersects the surface of the Earth -- they crash.There is no such thing as orbital altitude.&nbsp; There is an orbital speed associated with each orbit.&nbsp; And the closed orbits that do not result in a crash require a fairly high orbital speed, but a speed less than escape velocity.There is no such thing as the orbit border.All an orbit is is the trajectory that an object takes as it falls.&nbsp; If you are going to slow you crash.&nbsp; If you are going fast enough you fall around the Earth and don't crash.&nbsp; If you are going really fast, above escape velocity, you fly away from the Earth and you don't come back. <br />Posted by DrRocket</DIV><br /><br />I assume this also apply for solar system and galaxies escape velocities, same way right? I think i understand, but only difficult to picture it in my head, thanks Doc <div class="Discussion_UserSignature"> </div>

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DrRocket

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>I assume this also apply for solar system and galaxies escape velocities, same way right? I think i understand, but only difficult to picture it in my head, thanks Doc <br />Posted by lukman</DIV></p><p>It applies to any gravity from any source that can be considered to be a point, and starting from a finite radius beyond that point.&nbsp; Spheres and spherical shells fit that description exactly.&nbsp; Other arrangements also fit it approximately.&nbsp; So on a large scale it applies to solar systems and galaxies.</p> <div class="Discussion_UserSignature"> </div>

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kelvinzero

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<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>....In the case of an elevator or a rope climb, one is applying a force throughout the climb.&nbsp; So the energy is imparted at each stage in whch force is applied over a distance.&nbsp; Therefore you get the necessary energy from the continual application of force and not from just an initial velocity.</DIV></p><p>I just noticed something interesting about space elevators. If you ascend one to geostationary orbit, you will also have gained the velocity to stay in that orbit.&nbsp;I knew that, but the interesting thing is that you only put in the energy to raise yourself to that height. The energy for the velocity you get for free, by very slightly slowing down the rotation of the planet.</p><p>If the elevator was a rigid unobtainium tower that extended past geostationary orbit you wouldnt need to put any more energy in to gain more height and better leverage against the planet. The earth would launch it at great speed sort of like a scoop-ball. http://www.amazon.com/US-Games-Fun-Air-Scoop-Ball/dp/B0002C7FRC</p>

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