Escape velocity

Main Question or Discussion Point

I don't understand why we need an escape velocity, couldn't we escape the planet by accelerating an object above 9.81 m/s^2?

Also, say you've got an object one meter off the ground and you apply a constant 9.81 m/s^2 acceleration upwards to it so the object is hovering, where is the energy going? Kinetic energy should be zero since there is no velocity (its not moving anywhere) and there would be no gain in potential energy either since again its not ascending or descending gravity.

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Nono, im not talking about any animal skeletal structure holding up the object, just say its a 100% efficient rocket or something there providing acceleration.

gabbagabbahey
Homework Helper
Gold Member
Well, what is the potential energy of the object when it is at a height of 1 meter? What would it be if it were allowed to fall to the ground?

Danger
Gold Member
Denton, with any constant acceleration whatsoever, you will escape a gravitational well. As Assclown (who is probably less inebriated than me) pointed out, you could easily walk your way up as long as you had something to climb upon. Escape speed (not velocity, which implies a direction) refers to ballistic, rather than powered, flight.

russ_watters
Mentor
Note, however, that in order to escape you need to reach escape velocity. If you accelerate upwards at 9.8 m/s, you will eventually reach a velocity and altitude where your velocity exceeds escape velocity at that altitude. Turn off your engines too soon and you'll fall back to earth. You just don't ever need to be going faster than the escape velocity at the surface of the earth -- but none of our rockets do that anyway.

Now the second part of the OP is the answer to the question of why the space shuttle accelerates at 3g instead of 1g: it is actually accelerating at 4g instead of 2 g: applying twice the force and achieving 3x the acceleration. Where does the extra energy go? It is dissipated as heat. Lost. The answer is the same whether a rocket holds an object 1m off the ground or you do with your muscles.