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Astronomy/Four black hole time dilation question for you.

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Dear Astronomer,
Can you please help with these questions, cannot find the answers to these questions Online, or on Yahoo Answers. I am getting lot of different answers from Yahoo Answers.
Question 1. If you watch journey into a black hole before reading this question on YouTube it only takes four minutes to watch, you will understand better what I am describing in graph trajectory zones. Orbiting a black hole dangerous, 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 you orbited in the color coded regions
So Question 1. If you orbited in the green zone for a year how much time would pass on the earth.
Question 2. If you orbited in the yellow risky zone for a year how much time would pass on the earth.
Question 3. If you orbited in the orange zone for a year how much time would pass on the earth.
Question 4. If you orbited in the orange zone, where there are no orbits stable, or unstable, this area is called the photon sphere where light can just stay in orbit.

So the shuttle would be orbiting in the orange zone, as close to the Event Horizon as possible.
Is this orange zone is the best place to be in terms of slowing down a space shuttle in time, to kind of time travel relative to outside observers watching.
Also will the space shuttle get sphagettified in this orange region?
Question 2.  If you watch journey into a black hole before reading this question on YouTube, it only takes four minutes to watch, you will understand better what I am describing in graph trajectory zones.
Orbiting a black hole dangerous, 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 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 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 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.
So would this idea work, is this a better way to keep a shuttle stable in the orange zone, rather than orbiting.
Question 3. If two black holes came together, and their gravity radiuses crossed/overlapped, does the time dilation factor increase?

If two black holes came together and their gravity radius's crossed/overlapped, would the time dilation in the area where the black holes crossed/overlapped be doubled, or not.
If you put a space shuttle in between the crossed/overlapped area, would the space shuttle get twice as much time dilation, from an observers view, looking from far away from the black hole?
I am thinking itís a way to increase time dilation to go slower, without getting spaghettified.
Because four years pass for every year youíre in the black hole.
A simpler way to understand this question, is if you look at the video on you tube called a journey into a black hole where you can see the trajectory of the black hole as the space shuttle enters the black hole.
Think if this question as two color coded trajectories of two black holes crossing/overlapping each other, if they came together slowly.
Question 4. If you watch the video on you tube called journey into a black hole, it only takes four minutes to watch, the video describes the orbits which are stable, and unstable.
Can you please watch the video first, or this questions not going to make sense to you.
So in the video it describes safe, and unsafe orbits.
The green orbit is where orbits are stable, yellow is the risky zone, where you must keep firing the rockets on the shuttle, to stay in orbit.
Then there is the orange zone, then the red zone which is where you would fall into the black hole.
So where exactly in these color coded regions, if you entered in a space shuttle, where would you start to get spaghettified.
And questions 2. Where would the exact point be where the time would become infinite?
If you orbit in the right place four years pass for every year, you orbit the black hole.
But an Astronomer said to me that there is a point when you get close to the black hole where the time dilation factor becomes infinite where is that region on the color coded map where this happens, on the journey into a black hole video.

Thank you for your help with these questions.

Nicholas Lee.

Answer
Hi Nick,

Forgive me if I thought these were "homework" questions. Not many people ask as detailed questions as you do! But I'm glad you're thinking about the subject.

You seem to have two sets of questions. But I'll try and answer each set:

Set 1:
1) I watched the video, and it's a bit misleading. The safe "green zone" can extend very far away from the black hole. If it was a solar-size black hole, it would obviously extend past Pluto's orbit. So the time dilation factor would be VERY small. Nanaseconds. As you get closer to the black hole, two factors come into play. One is your orbital velocity. The faster you go, the more time will be dilated. This is part of Special Relativity - Lorentz Transformations (relative velocity). But then we have to consider General Relativity - time dilation in a gravitational field. Both effects are described in http://en.wikipedia.org/wiki/Time_dilation.

So to answer your question, it depends on where in the green zone we are and our orbital velocity. Based only on gravitational time dilation, I'll use the formula T = T0 / sqrt(1 - r(s) / r ), where r(s) = the Schwarzschild radius and r = our orbital radius. So if we get to 3 Schwarzschild radii from the center, then time is dilated by a factor of 1.22, or for every month passing for you, 1.22 months have passed on earth. If we need to go at half the velocity of light to stay orbit, then there's another factor of 1.15 time dilation.

2) The video mentioned 2 Schwarzschild radii. At that distance, you'd need a velocity of 0.7c, which means time is dilated by a factor of 1.4. There's another factor of 1.4 due to gravitational time dilation. So our total is 1.96 - nearly two months pass on earth for every one of your months.

3) The yellow zone includes the photon sphere (at 1.5 Schwarzschild radii). That should really be the end of the yellow zone. If we reached the photon sphere, we'd need to have a velocity v = c to remain in stable orbit, so that means time is infinitely dilated. No time passes for you (as "seen" from an observer on earth). But if you were now stopped in orbit (which means you'd start accelerating towards the black hole), there would be a factor of 1.7 time dilation just due to gravity.

4) In the orange zone, there are no stable orbits, so it again depends on your speed. If you are just firing thrusters to remain stationary, then your time dilation could be between 1.7 (at the far end of the orange zone / beginning of the yellow zone) to infinite at the close end of the orange zone / beginning of the red zone. As you can see by the formula I used above, when you reach a distance of one Schwarzschild radius, the time dilation due to gravity becomes infinite.

Next Set:

1) The yellow zone - at the photon sphere - is the best best for slowing down time due to velocity. At the event horizon (beginning of red zone) is the best place for slowing down time due to gravity alone. As for sphagettification - I showed you how to compute this last time. But for a 10 solar mass black hole (30 km Schwarzschild radius) and a 100m spacecraft, there'd be a delta force of 9.9 x 10^13 Newtons, so yes - sphagettification. For a much larger black hole, might not be sphagettification.

2) Yes - a ship could stay in the orange region a long time and be stationary, if it had powerful thrusters (or a larger ship pulling it, to counteract gravity). That could happen UNTIL you reach the red zone, where an infinite amount of force would be required to keep the small ship from falling in.  

3) If two black holes came together, there could be a region between them which would experience no gravity! Gravity is a attractive force, and the one black hole would partially (or totally) balance the other. This is just the region between them! Each black hole would still experience the other's strong gravity. They could be in orbit about each other or simply meet and be absorbed into a bigger black hole.

4) As I mentioned before, time dilation becomes infinite when:

a) you travel at v=c to remain in stable orbit at the photon sphere, or
b) at the red zone (event horizon) - due to gravity (General Relativity).

Prof. James Gort  

Astronomy

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James Gort

Expertise

Questions on observational astronomy, optics, and astrophysics. Specializing in the evolution of stars, variable stars, supernovae, neuton stars/pulsars, black holes, quasars, and cosmology.

Experience

I was a professional astronomer (University of Texas, McDonald Observatory), lecturer at the Adler Planetarium, professor of astrophysics, and amateur astronomer for 42 years. I have made numerous telescopes, and I am currently building one of the largest private observatories in Canada.

Publications
StarDate, University of Texas, numerous Journal Publications

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