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This may seem silly a lot but I really need some clarification on the necessity of escape velocity for a rocket leaving the Earth's gravity. A stone thrown vertically upwards reaches to a certain height before falling to the ground. The height at which the total potential energy gained by the stone is equal to the sum of the kinetic energy at the ground and the work done on it during launch. Since, after throwing it upwards, no external work is added, the stone WILL return to the ground in accordance with the law of energy conservation (velocity < escape velocity). But in a rocket, continuous work is being added from its booster motors. Then why is it necessary for it to acquire escape velocity in order to leave the Earth? What will make it stop from leaving? Consider the following hypothetical case:

A hypothetical situation:

Suppose we build a long vertical shaft on the Earth's surface, reaching into deep space and a person starts climbing on it (just like Jack on a bean stalk). Will he also require escape velocity to leave the Earth's gravity? If no, then how is it any different from a conventional rocket launch?

Please answer!

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No, I believe you're right. Escape velocity is the velocity such that if you achieve it, you will escape. If you weigh 500N, and you strap a rocket to your back that provides 501N of force (let's ignore the engineering issues here...) you start accelerating upwards and you keep accelerating upwards until the rocket turns off. You will get to space that way if you want. Escape velocity is meaningful however if you are building a device that's going to burn nearly all of its fuel relatively quickly and you want to be sure the velocity it gets to is high enough to get away--which is a lot like an actual rocket in some respects.

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  • $\begingroup$ Does it imply that we only need escape velocity to leave the Earth's gravity in order to keep the fuel consumption to a minimum? And if, the rocket fuel is not a concern, we can "crawl" all our way into deep space beyond Earth's gravity? $\endgroup$ – Vinit Shandilya Mar 6 '15 at 6:32
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    $\begingroup$ I'm not sure if it's more efficient fuel-wise per se, but it might just be more practical rather than trying to start and stop the combustion. I really have no idea though. But, yes, if you had an engine that could provide a thrust only slightly above its own weight but do so continuously, conceivably you could "crawl" to space. In real life, many spacecraft use ion thrusters which are very very slow but allow them to make long-term course corrections. You could never use one to escape a gravity well, though. $\endgroup$ – zeldredge Mar 6 '15 at 6:38

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