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I had a recent conversation with my girlfriend, who is a physics grad student. She was kind enough to listen to me rant about an idea concerning escape velocity. Unfortunately, I am still thinking about this question, but don't want to bother her with it.

My thought is that we shouldn't actually need to reach 11km/sec to leave the earth's gravity. Instead of this, can we simply apply enough force to overcome earth's gravity without reaching that speed? How we would do this is not a part of my question.

Orbital altitude is $99$ miles. Travelling $60$ mph straight up should get you there in $1.65$ hours, granted you have enough force to push. I know some of the simpler math like $F=ma$, but that didn't help me understand.

I browsed some articles about space elevators and couldn't find my answer.

Then I thought about a regular elevator and the fact that it has enough force to move it away from the earth successfully. Even if the elevator moved at $1$ nanometer/sec, it would still move away from the Earth, overcoming the minute pull of gravity at that altitude.

If you missed it, my question was: can we simply apply enough force to overcome Earth's gravity without reaching that speed?

Edit: In another example, let's say we could drive a car from here to low Earth orbit. As long as we had enough torque, we should be able to overcome gravity, much like a pickup truck pulling a bunch of lumber. Is that correct?

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  • $\begingroup$ The issue is how much total energy it takes, since there is no "elevator" at hand, so a fixed amount of force/power is needed just to hold a launch vehicle at a given altitude (against gravity), and one must exceed that to accelerate. In terms of overall energy used it's much more efficient to accelerate as rapidly as possible for the technology (and payload). $\endgroup$ – Hot Licks Jan 10 '15 at 14:18
  • $\begingroup$ I can't believe no-one has mentioned the obligatory xkcd that explains exactly this question: what-if.xkcd.com/58 $\endgroup$ – Oscar Bravo Jan 31 '18 at 8:32
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Escape velocity is how fast an object must be moving to escape another object's gravity without needing any additional force/acceleration. The examples you've proposed are perfectly valid ways for objects to escape earth's gravity without attaining escape velocity but only work because some kind of force is continually pushing/pulling the object ever upwards. So in short, yes, if we had enough torque, and an engine that had enough fuel to run long enough to reach the desired altitude, then escape velocity need never be attained.

I believe what you are trying to get at specifically is whether an object moving at constant speed could escape the earth's gravity. The answer is yes, as long as you had a force to counteract gravity and allow the object to continue to move upwards.

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You've missed a little appreciated point about orbital velocities.

A satellite has to travel round the Earth fast enough to prevent it falling back. The velocity depends on the altitude. If we take a GPS satellite as an example, the altitude is about 20,000 km from the ground and the orbital speed is about 14,000 km/hour. But assuming you launch from the equator your velocity due to the rotation of the Earth is 1700 km/h. So your rocket needs to accelerate the satellite by a shade over 12,000 km/hour.

If you're just trying to escape the Earth then yes you can do it as slowly as you want, because you just have to do an amount of work equal to the gravitational potential at the surface and you can do this as slowly as you want. However if you're trying to get into orbit it is not enough to just ascend (slowly) to the orbital altitude. You must also increase your orbital velocity enough to stay in orbit.

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  • $\begingroup$ +1 for mentioning the issue with the orbital velocity. This is what most laymen are confused about. $\endgroup$ – pfnuesel Jan 10 '15 at 14:33
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Yes we can, and in fact this is exactly what rockets do. They build up speed and altitude slowly, getting them to orbit or beyond without necessarily ever reaching the surface escape velocity of 11km/s.

The technology required to do this is much easier than what would be required to make a sudden jump to escape velocity and then coast up. (Air resistance makes that yet again far more difficult.)

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  • $\begingroup$ I think I understand you. See my edit with an additional analogy. $\endgroup$ – Rick Scolaro Jan 21 '14 at 3:52
  • $\begingroup$ Rockets do not do this 'exactly'. They indeed do not apply an instantaneous changes in velocity, since this would require infinite force/acceleration. But the time in which they do propel themselves, for example for a Hohmann transfer, is much shorter than the period of their orbit. $\endgroup$ – fibonatic Jan 21 '14 at 11:10
  • $\begingroup$ Yes, but the question never asked whether it was necessary to have constant propulsion, only whether it could be done slower than instantly. And that is 'exactly' what rockets do. $\endgroup$ – David Z Jan 21 '14 at 11:16
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You're right in your assumption that it's possible, else how would we climb stairs?

The usual figure given for escape velocity concerns only gravitational field strength at the mean surface distance from the center of mass of the planet - at the equator - and completely neglects atmospheric friction, and has no practical bearing on our everyday lives. It is taken into account with regarding Intercontinental Missiles, but they can travel quite into the thin atmosphere where parabolic and hyperbolic calculations based on escape velocity become more relevant. I've a feeling 1950's,1960's and '70s TV programs has much to answer for regarding misconceptions of this, and also regarding public curiosity about such matters.

I may be censured for saying this, but maybe it is possible to build a stairway to heaven. (Geostationary orbit) But do remember to take your own atmospheric envelope.

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  • $\begingroup$ Joshua (comment beneath), important point about definitions that I missed. $\endgroup$ – Duckisaduckisaduck Jan 21 '14 at 4:13
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There is no minimum speed necessary to overcome gravity. All you require is some source of support to oppose the gravitational force on your payload/space vehicle.

But bear in mind:

If you were to raise an object up from the surface of the Earth at say, 60 miles per hour, and kept moving it away from the Earth until it arrived at some point where the pull of the Earth's gravity became insignificant, and allowed your object to come to rest at that point, you would find: the work you put into lifting that object would essentially equal the kinetic energy the object would have if travelling at Earth's escape velocity. The fact that the object never attained significant speed does not lessen the amount of work which has to be done on it to lift it to some given altitude. You could accelerate that same object to Earth's escape velocity while it is at (or very near) Earth's surface and (ignoring air resistance and the effects of other objects) it will ascend, gradually slowing down due to Earth's gravity, until it comes to a stop at a point where Earth's gravity will no longer affect it.

Also:

If you could lift a payload straight up from the Earth's surface into space, then what? The only way to keep it from falling back is to place it into an orbit, which means accelerating it to some significant velocity. And if it's a low orbit, it will be a significant fraction of the Earth's escape velocity anyway.

The reason space rockets go fast is partly to achieve an orbital velocity and partly efficiency. With nothing much to push "against" in air or space, you can only get push from engine thrust, which consumes propellant all the while it is operating. The more vigorously it pushes (higher exhaust velocity), the more efficiently it can do work on the vehicle. If your rocket produces only as much thrust as your vehicle weighs, you burn fuel and get nowhere. If your rocket produces twice as much thrust as your vehicle weighs, half the thrust balances gravity and the other half accelerates you at 1G. If your rocket produces 3 times as much thrust as your vehicle weighs, only 1/3 of its thrust balances gravity and the other 2/3 accelerates you at 2G.

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protected by Qmechanic Jul 20 '15 at 23:52

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