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Question
This is not a homework question.
If you watch journey into a black hole before reading this
question on YouTube, you will understand better what I am describing in
graph trajectory zones.
There are four graph trajectory zones, when orbiting a black hole.
The green zone is a safe zone, the yellow zone is a risky zone, the orange zone is danger zone where there are no orbits stable, or unstable, and then there is the red zone, the Event Horizon.
So if you had a space shuttle and wanted to slow yourself down with
gravity from the black hole, so that you could visit earth in the future in
your lifetime.
I heard from this show you can orbit a black hole for a year
and four years will have passed on earth from your perspective.
How much would time slow down if a shuttle orbited in the color coded regions.
Orbiting in the photon sphere area, or the orange zone like in the you tube video, where light can orbit a black hole before falling in.
If you were in a space shuttle, the shuttle would have to travel around or at the speed of light, in the area.
So rather than orbiting in a space shuttle, if you just
had two space shuttles, with a larger space shuttle outside of the black
hole, with the most powerful rocket thrusts technologically possible.
Then
there would be a long chain, or steel pole, whatever is best to use for
strength, to hold, and keep in place the smaller shuttle.
So the long chain, or pole would be coming out the back of the big
shuttle that the smaller space shuttle would be attached to.
The chain, or pole attached to the smaller shuttle, would be attached to
it from the side.
So the larger shuttle would reverse slowly let the smaller
shuttle go into the black hole, and when the black hole started to pull on
the smaller shuttle the larger ship would use its powerful boosters, to
keep the smaller shuttle from falling in the black hole.
Remember the smaller shuttle is attached to the larger ship by the strong chain, or pole.
So could the smaller ship stay in the orange region of the black
hole, the photon sphere area where light can orbit, before falling in.
I want to see if the smaller ship can sit in the orange zone for a long time
to get the best time dilation in that orange region.
So if you can imagine a big space shuttle with a long chain, or pole, the
chain, or pole can be any size it need to be to be strong enough to hold
the smaller shuttle.
The big shuttle has this chain, or pole attached to the smaller shuttle,
and the big shuttle slowly reverses itself backwards into the black hole
with the smaller shuttle going in first.
So when the black hole starts to pull on the smaller shuttle, the bigger
shuttle turns on its powerful boosters, the most powerful boosters technologically possible, to stop the smaller shuttle from falling past the event horizon.
So the bigger shuttle is keeping the smaller shuttle in a stable place in
the orange zone, and is keeping it perfectly still in that photon sphere, orange region area.
So would this idea work, is this a better way to keep a shuttle stable in
the orange zone, rather than orbiting.
would it take more powerful boosters to keep the second ship stable in that area.
Also the second shuttle is going into the black hole first, the chain or pole attached to it is behind it.
So any spaghettification that happens to the second shuttle has to happen  first before the chain or pole gets spaghettified.
So the pole or chain getting affected cannot be a problem.
So can this way be better than orbiting a black hole to get better time dilation.

Thank you for your time and help with these questions.

Answer
Nicholas - There is not much aerodynamics in your question, so I suggest asking an expert in physics. If I had to answer, I would say that the gravitational forces are so strong near a black hole that no chain would be strong enough to hold the second shuttle, nor would the boosters be strong enough. A better answer would be to calculate the gravitational forces near a black hole. But I don't know how to do that. Maybe you can figure it out.

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