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If I understand it correctly, the escape velocity of a body is the velocity I would need to escape that body's gravity if I did not continuously thrust against its gravity. So this question boils down to two things:

  1. Is it possible to escape a body's gravity without reaching escape velocity, and if so will my scheme work?

  2. Presuming instead that I'm not on Earth but am somewhere within the event horizon of a black hole, then everything I've read says that this wouldn't be possible once you cross the event horizon of a black hole, since "nothing can escape". Is that right? If the answer to question 1. is that the scheme would work, why are black holes special?

Qmechanic
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Michael Stachowsky
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2 Answers2

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1: in this scenario, there would be no acceleration, so it depends on what velocity you start out at. If it's non-zero (and directed away from the Earth) then, yes, you would keep going away indefinitely. It's not possible in practice though (you can't generate thrust indefinitely like that). Like you say, escape velocity refers to a ballistic (unpowered) trajectory. It also decreases with altitude.

The escape velocity does however represent the most efficient (energy-wise) way of leaving Earth - i.e. adding all the speed at once instead of continuously thrusting. The energy associated with the escape velocity is the minimum energy needed to escape. Which leads to...

2: A black hole's escape velocity is greater than the speed of light. Therefore, the minimum energy needed to escape it is at least infinity. There are probably better ways of formulating this though...

Kristoffer Sjöö
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Is it possible to escape a body's gravity without reaching escape velocity ?

Yes (although you can never entirely escape from any object's gravitational field, so your wording needs to be tightened up). Escape velocity is simply the minimum velocity required to achieve an open ended trajectory (which is what I assume you mean by "escape a body's gravity") ballistically i.e. without any additional thrust. If you build a rocket (powered by unobtanium, which is almost weightless and releases huge amounts of energy) which first of all accelerates to $1$ km/hr and then reduces its thrust so that it exactly equals the weight of the rocket and any air resistance, then this rocket will travel on an open-ended trajectory as far as you like at a speed of $1$ km/hr.

However, this scheme won't let you escape from inside the event horizon of a black hole because no amount of thrust can take you further away from the centre of the black hole once you have passed its event horizon. Inside the event horizon all trajectories, even powered ones, eventually end up at the singularity or whatever is at the centre of the black hole.

gandalf61
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