Escape the black hole-Oberth maneuver

See the Video link.

There is this black hole called gargantua which is located in interstellar space.It is non-moving and non-rotating.You are at a distance of 1000 km from the black hole. Your initial velocity is zero, you have to escape this black hole, but you don't have the fuel to gain that speed (escape velocity).So here you are going to do the Oberth maneuver where you are going to fire your engines at high speeds to get the most out of your fuel. So you go towards the hole not into it, but at a tangent where the nearest point to the point to the blackhole will be 100km to fire your engines.What should be the minimum change in velocity of the spaceship at the nearest point to escape the black hole? By how much you should gain velocity at the nearest point to escape it? Don't stay too near the hole because it slows down time for you with respect to others. This effect is counter-intuitive and it seems to violate the conservation of energy but it's not. Schrawzchild radius is about an inch dont worry about it! Here you are not detaching anything as in the video.

Assume the mass of blackhole to be \(10^{24} \text{ kg} \) and the gravitational constants as \(10^{-11} \) for easier calculation.

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