What is escape velocity, and why can I climb away from Earth?

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Offline thedoc

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Dave Morris  asked the Naked Scientists:
   Hello naked scientists, I love your show. My name is David, I'm from Vancouver.

What does escape velocity refer to exactly. It seems that if I have a tall enough ladder, i could climb up at any velocity and escape earths gravitation field, kind of like the space elevator concept. I would never need to reach that escape velocity. please clarify.

thanks naked scientists, keep up the great work


What do you think?
« Last Edit: 04/10/2012 00:30:01 by _system »


Offline damocles

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Escape velocity is the velocity which must be given to an object at the Earth's surface to enable it to make a free flight trajectory that would escape from the Earth's gravitational field. If you are continually applying more force, as with fuel burn on a rocket or muscular contraction on a stepladder, it is quite possible to escape from Earth's gravity without ever getting to a velocity anywhere near that.

A very simple calculation can be based on equating the magnitude of gravitational potential energy at the Earth's surface (= –mgRearth) to the kinetic energy needed to escape this potential well (= 0.5*m*vesc2).

Small corrections should be included to account for the additional kinetic energy that a body might have because of the Earth's rotation. For a slingshot attempt to escape the gravitational field a horizontal Eastward flight from a point on the equator (as in Jules Verne's "Journey to the Moon") would be optimal on an airless planet, but air resistance would make that trajectory both sub-optimal and quite impractical on Earth. For rockets which will fire continuously during the ascent quite different considerations define the optimal trajectory, and not the least of them is minimising energy loss and heat damage from air resistance.
« Last Edit: 04/10/2012 06:34:58 by damocles »
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