[brey]

yes - my question is whether escape velocity is necessary to leave a gravity well.

and if it's not, taking that to its logical conclusion - why do we NEED to go faster than the speed of light to escape from inside the schwarzschild radius of a black hole? can't we leave under constant thrust at 1 m/s?

[PeterWhittaker]

There are a few things to tease apart in this. First, maintaining a constant speed of 1 m/s requires constant application of force to overcome the forces working against you. On a road surface, these are air resistance, rolling resistance, etc. It takes very little force to oppose these at this speed (wind resistance increases with the square of speed, so the faster you go, the more force you need to keep going that fast, which is why gas mileage drops as you move above your engine's optimum operating range).

Heading up from Earth, you are facing a deceleration of 9.8 m/s/s, so you need to apply enough force to counter that. The amount of force depends on payload, e.g., a little plastic drone don't need so much, a Saturn V carrying something to high orbit needs a whole lot.

Escape velocity is the velocity at which no further thrust is required. That's the key point: The object is travelling away from the well so fast that it is already going fast enough to overcome all of the rest of the gravitational drag it will experience until it hits micro/zero-G.

Rockets need constant thrust (constant force and acceleration) to overcome the constant force and acceleration of gravity).

If you accelerated a human being to escape velocity at the surface of the Earth, you would concuss them to death (and likely organ damage them to death).

A photon starts life at C, whatever C is in its current medium.

[brey]

Understood - I appreciate why light, or any unaccelerated object, cannot leave a black hole.

But does that same restriction prevent a rocket which wants to coast at 1m/s - under constant acceleration - from the surface to infinity?

I.e.: is the schwartzchild radius only a point of no return to light, not rockets?

And if not a hard limit to rockets - oh, I guess that's fun to know :-)

(Yes clearly utterly impractical - trying to understand if there's any fundamental reasons at play here)