Effect of time dilation on a satellite

[some bloke]

I've got the start of a plot forming in my mind, and I'm wondering if it's likely to be supported by physics at all.

My basic understanding:
when astronauts go to the International Space Station, due to the speed at which it is travelling, time passes ever-so-slightly slower for them. This effect also must be compensated for in satellites for GPS, or their clocks go wrong.
This effect becomes more notable at higher speeds, approaching light speed.

So, if a satellite was orbiting Earth fast enough (with whatever thrusters needed to prevent it slingshotting into space) then time would go much slower on the satellite compared to on earth, am I correct?

The second part of my design is that this satellite is occupied by an upper class caste of people, who use drugs to "overclock" their minds and then remote control avatars on the planet, using a system which works significantly faster than any human brain could, so has sufficiently fast responses for the avatars. In this method, the upper caste can live for hundreds of years as avatars on the planet.

My questions are:
1: Would time dilation produce a sufficient effect to allow this?
2: would it have any effect if the satellite was itself spinning at a high speed, with the axis perpendicular to the direction of travel, resulting in a uniform higher speed on the outside of the satellite without the satellite itself moving unrealistically fast around the planet?
3: Would it be possible to relay information back and forth between two objects which operate at different time speeds? are there limitations on this? I understand that they have contact with the ISS so it must be possible. Would the waves be blue- or red-shifted by the difference in the speed of time at the source and destination?

General premise is that this is a terraforming company, with skilled engineers overseeing the hundreds-year long terraforming projects, without sacrificing their lifetimes.

 

[PeroK]

I've got the start of a plot forming in my mind, and I'm wondering if it's likely to be supported by physics at all.

My basic understanding:
when astronauts go to the International Space Station, due to the speed at which it is travelling, time passes ever-so-slightly slower for them. This effect also must be compensated for in satellites for GPS, or their clocks go wrong.
This effect becomes more notable at higher speeds, approaching light speed.

So, if a satellite was orbiting Earth fast enough (with whatever thrusters needed to prevent it slingshotting into space) then time would go much slower on the satellite compared to on earth, am I correct?

The second part of my design is that this satellite is occupied by an upper class caste of people, who use drugs to "overclock" their minds and then remote control avatars on the planet, using a system which works significantly faster than any human brain could, so has sufficiently fast responses for the avatars. In this method, the upper caste can live for hundreds of years as avatars on the planet.

My questions are:
1: Would time dilation produce a sufficient effect to allow this?
2: would it have any effect if the satellite was itself spinning at a high speed, with the axis perpendicular to the direction of travel, resulting in a uniform higher speed on the outside of the satellite without the satellite itself moving unrealistically fast around the planet?
3: Would it be possible to relay information back and forth between two objects which operate at different time speeds? are there limitations on this? I understand that they have contact with the ISS so it must be possible. Would the waves be blue- or red-shifted by the difference in the speed of time at the source and destination?

General premise is that this is a terraforming company, with skilled engineers overseeing the hundreds-year long terraforming projects, without sacrificing their lifetimes.

Actually, the astronauts in the ISS age slightly faster than those of us on Earth, owing to the gravitational time dilation being slightly greater than the velocity-based time dilation. In any case, both effects are insignificant.

The main problem with your scheme is the energy requirements. The gravity of the planet would contribute very little to a high-speed orbit, so you'd essentially be accelerating towards the planet all the time. And, also, you'd need to be far enough away that this acceleration is about 1g (Earth). I suspect that would be a long way away.

Other than that, the basic idea is correct. Any high speed flight would allow a time differential between those on the flight and those on the planet. There would essentially be no problem exchanging information, although it would not be real time, because the ship would be too far away.

That said, the thing that almost all sci-fi overlooks is the fact that if you had interstellar space flight and terraforming technologies, then you'd almost cetainly have the robotic technology to do the job. Plus, even with the differential ageing, if you went on an interstellar space flight and came back to Earth, you'd have to allow 10-20 years of your life in any case. You might come back to Earth 200 years later only 20 years older (having supervised a 100-year terraforming project)!

 

[some bloke]

Hi PeroK,

Thankyou for the response!

The g-force on the passengers of the sattelite is not something which I'm concerned with, as they will be unconscious throughout and I have already come up with a theory to compensate for it.

I was considering a ring around the planet, which is then spun up (essentially forming a single, continuous satellite). This would also allow for the signals to be transmitted to fixed points, which would be counter-rotating, forming geostationary points. This would also mechanically prevent the satellite from exiting orbit in either direction. I realize the forces involved would be colossal, but such things can be waived by phrases like nanostructures and superalloys - assuming a nigh-on indestructible construction, this should be possible, no?

The timeline is also unimportant - the selling point of the scheme I was theorising was to "build your own world", where the terraforming team will be the first inhabitants of the new world, so hypersleep to get there, spun up to ridiculous speeds to build it, then make planetfall to live there for the rest of their lives.

The robotics argument is a strong one, I am considering using some waffle about the human mind being faster than a computer when on the drugs, and the unreliability of the computing systems, how easily people are taught vs computers, having "the human touch", that sort of thing.

The further idea is that the different floors of the satellite will be moving at different speeds to one another, so depending on how high up the ranks / how much you paid, the slower time travels for you (and so the longer you will live on the planet as an avatar).

 

[PeroK]

It sounds interesting.

Of course, the boring idea is you just sleep through it all and it doesn't matter whether 500 years have passed.

 

[some bloke]

Of course, the boring idea is you just sleep through it all and it doesn't matter whether 500 years have passed.

That's one I'm aiming to avoid, as you say, it's quite a boring plotline!

A further curiosity;

If you were in a spinning satellite, of sufficient size that the outer sections of it were moving significantly faster than the inner ones, what would you observe as you moved outwards? the people further out would be experiencing time slower, so would they be observed to be moving slower than those further in? Assuming that there was some force in play which eliminated the centripetal force, so you wouldn't be thrown outwards. And, if you fired a sniper rifle in either direction, how would it affect the trajectory of the bullet? I'm assuming that the bullet wouldn't go straight outwards as this would need it to speed up, so gain energy, which it can't do, so it must "curve" in the opposite direction of the movement of the satellite, right? but, if it is passing through a steadily decreasing speed of time, it will be observed to travel slower the further it goes - would this compensate for the energy needed to continue traveling in a straight line?

I'm starting to make my brain hurt!

 

[Janus]

Hi PeroK,

Thankyou for the response!

The g-force on the passengers of the sattelite is not something which I'm concerned with, as they will be unconscious throughout and I have already come up with a theory to compensate for it.

I was considering a ring around the planet, which is then spun up (essentially forming a single, continuous satellite). This would also allow for the signals to be transmitted to fixed points, which would be counter-rotating, forming geostationary points. This would also mechanically prevent the satellite from exiting orbit in either direction. I realize the forces involved would be colossal, but such things can be waived by phrases like nanostructures and superalloys - assuming a nigh-on indestructible construction, this should be possible, no?

The timeline is also unimportant - the selling point of the scheme I was theorising was to "build your own world", where the terraforming team will be the first inhabitants of the new world, so hypersleep to get there, spun up to ridiculous speeds to build it, then make planetfall to live there for the rest of their lives.

The robotics argument is a strong one, I am considering using some waffle about the human mind being faster than a computer when on the drugs, and the unreliability of the computing systems, how easily people are taught vs computers, having "the human touch", that sort of thing.

The further idea is that the different floors of the satellite will be moving at different speeds to one another, so depending on how high up the ranks / how much you paid, the slower time travels for you (and so the longer you will live on the planet as an avatar).

Such a continuous ring satellite could not maintain an orbit on its own without some active system making corrections to hold it there. Basically, such a structure is inherently unstable. The slightest disturbance in position will set up a situation where it then falls further and further out of balance until the ring brushes the planet.
This was proved by James Clark Maxwell, back in the 19th century, while working on the structure of Saturn's rings. His proof showed that the rings could not be solid structures and therefore must be made up of individual particles.

Also, I don't think you quite grasp the magnitude of the g forces involved. At just 0.866 c, which only gives you a time dilation of 2, even if your ring had a radius equal to that of the Earth's orbit around the Sun, the ring would experience ~46,000g.

 

[PeroK]

That's one I'm aiming to avoid, as you say, it's quite a boring plotline!

A further curiosity;

If you were in a spinning satellite, of sufficient size that the outer sections of it were moving significantly faster than the inner ones, what would you observe as you moved outwards? the people further out would be experiencing time slower, so would they be observed to be moving slower than those further in? Assuming that there was some force in play which eliminated the centripetal force, so you wouldn't be thrown outwards. And, if you fired a sniper rifle in either direction, how would it affect the trajectory of the bullet? I'm assuming that the bullet wouldn't go straight outwards as this would need it to speed up, so gain energy, which it can't do, so it must "curve" in the opposite direction of the movement of the satellite, right? but, if it is passing through a steadily decreasing speed of time, it will be observed to travel slower the further it goes - would this compensate for the energy needed to continue traveling in a straight line?

I'm starting to make my brain hurt!

A bullet, boringly, would obey Newton's laws and move in a straight line!

You can't ignore centripetal acceleration. You might as well just "switch on" time dilation!

 

[some bloke]

Such a continuous ring satellite could not maintain an orbit on its own without some active system making corrections to hold it there. Basically, such a structure is inherently unstable. The slightest disturbance in position will set up a situation where it then falls further and further out of balance until the ring brushes the planet.
This was proved by James Clark Maxwell, back in the 19th century, while working on the structure of Saturn's rings. His proof showed that the rings could not be solid structures and therefore must be made up of individual particles.

Also, I don't think you quite grasp the magnitude of the g forces involved. At just 0.866 c, which only gives you a time dilation of 2, even if your ring had a radius equal to that of the Earth's orbit around the Sun, the ring would experience ~46,000g.

Thanks, I can't see any reason why this ring wouldn't have some form of correctional thrusters to maintain it's positions.

As for the huge forces involved, I can easily use the power of fiction to waive the fact that no material could hold such a structure together! As for the effect on the people inside, my fictitious approach to cancel out this force is to use the principles of diamagnetic levitation, which has been demonstrated as working on frogs and crickets (it's quite a cool video) to apply a countering force to each atom in the body of the people inside the station using an immensely powerful magnetic field (obviously there could be no magnetic materials in the satellite). My theory is that g-force is not so much the issue, as each part of the human body being affected by it differently - when accelerating in a car, the seat pushes the skin on your back, which pushes your muscles, which pushes your bones, which pushes your organs, which push your blood, etc., meaning all parts of your body are exerting a force on each other - which to my mind is the issue with g-force. The problem is not that the acceleration if exerting a force on you, it is that the chair is only pushing against your back to stop you from moving within the car.
If the force from the chair was instead a field of force which applied sufficient force to directly counter the g-force on each atom in your body independently, then the net force on your body as a whole would be 0, and the force between the parts of your body would also be 0, so you would not feel any exerted g-force.

This would require some poetic license I think, but in my eyes the principle is there for diamagnetic levitation to exert the necessary forces on any non-magnetic objects in the satellite.

A bullet, boringly, would obey Newton's laws and move in a straight line!

You can't ignore centripetal acceleration. You might as well just "switch on" time dilation!

Not ignore, cancel out - acceleration is caused by a force, so by applying a force (as above) to bring the net force to 0 would remove the effects of it - the same way as tying a rock to a string and swinging it stops it from moving away from your hand.

My confusion about the bullet is what constitutes a straight line in a system where everything you're shooting at stays right in front of you, but is moving sideways faster than you are, and has a slower "time zone" than you due to it's speed! or, vice versa, shooting the other way!

IE if you stand on the north pole (the Earth's axis of rotation) and shoot at a target, will your shot be thrown off by the Earth's spin in any way? what if the Earth was spinning reeeeeally fast? because your target will be moving, but you won't be... and my brain hurts again!

 

[PeroK]

Not ignore, cancel out - acceleration is caused by a force, so by applying a force (as above) to bring the net force to 0 would remove the effects of it - the same way as tying a rock to a string and swinging it stops it from moving away from your hand.

If you cancel out the force then there's no acceleration and the object fails to stay in its circular orbit. In the example of the rock, there is only one force on the rock - a centripetal force from the string pulling it towards you.

The problem is that essentially you want to stick to some perceived rules of "time dilation" while playing fast and loose with the laws of physics. There's then no purpose to trying to make your time dilation "realistic".

In any case, trying to create time dilation by spinning your spaceship has considerable disadvantages over having your spaceship in a high-speed powered orbit. You arrive at the distant solar system; the ship with the passengers and engineers orbits the solar system at its insterstellar speed. That achieves your purpose with more than a semblance of genuine science.

 

[DaveC426913]

In Joe Haldeman's The Forever War, battles happened at relativistic speeds, and so were spread out over decades and centuries.

As the war wound down, returning soldiers had few friends left, and they were spread across time. So they made a "waiting room" by putting a shuttle in a highly elliptical orbit around a nearby neutron star or BH. It orbited at relativistic velocities (or was it relativistic mass dilation?), and so its passengers aged slowly. They could let their returning friends "catch up" the years.

The point is, orbiting a hyper-massive body would solve your problem.

 

[some bloke]

I think that i have failed to explain my theory properly.

The centripetal force is the diamagnetic levitation. The difference is that instead of the force transferring across your body, it is affected the whole body in the first place.

Think of it like this: if you have a rope tied around your wrist and are spun, you will have a lot of force on your arm and shoulder due to the g-force. If you are instead hung by a harness and spun at the same rate, you get the same force but less discomfort. Now say that you are being repelled from an exceptionally powerful magnet at an atomic level - this force is the centripetal force, it is what accelerates you towards the centre of rotation. However, because the net force between your separate body parts is 0, it would not tear you apart or crush you, like a wall pressing on your back would, or a rope around your wrist. The force will affect you in a similar manner to gravity.

 

[Janus]

That's one I'm aiming to avoid, as you say, it's quite a boring plotline!

A further curiosity;

If you were in a spinning satellite, of sufficient size that the outer sections of it were moving significantly faster than the inner ones, what would you observe as you moved outwards? the people further out would be experiencing time slower, so would they be observed to be moving slower than those further in? Assuming that there was some force in play which eliminated the centripetal force, so you wouldn't be thrown outwards. And, if you fired a sniper rifle in either direction, how would it affect the trajectory of the bullet? I'm assuming that the bullet wouldn't go straight outwards as this would need it to speed up, so gain energy, which it can't do, so it must "curve" in the opposite direction of the movement of the satellite, right? but, if it is passing through a steadily decreasing speed of time, it will be observed to travel slower the further it goes - would this compensate for the energy needed to continue traveling in a straight line?

I'm starting to make my brain hurt!

While still in the gun, the bullet is forced to travel in a circle. Once fired, it is free to travel in a straight line. What the spinning satellite is doing no longer matters to it. So just because clocks further out and traveling with the satellite are ticking slower than those closer in does not mean that the bullet is passing through regions of slower time as far as it is concerned.
Put another way. Assume the bullet passes a number of clocks attached to the station along its path. For the bullet or any other inertial frame, it will be traveling in a straight line and encountering these clocks, each clock intersecting following a circular path and intersecting with with the bullets straight line path at the time of arrival of the bullet. Relative to the satellite, these clocks will follow a curved line.

As for the effect on the people inside, my fictitious approach to cancel out this force is to use the principles of diamagnetic levitation, which has been demonstrated as working on frogs and crickets (it's quite a cool video) to apply a countering force to each atom in the body of the people inside the station using an immensely powerful magnetic field (obviously there could be no magnetic materials in the satellite).

Here's the problem with that solution, Such diamagnetic levitation doesn't work equally on all materials in the body, at the level you would need to counter the g forces involved, the difference in how the levitation acted on different components of the human body would rip it apart.

Then there are the power requirements to achieve this.

Now I realize that with any SF story you have to rely on a some willing suspension of disbelief on the part of the reader, However, is is also important not to take it too far. If you stretch the credibility too far, you risk losing them.

Oddly enough, sometimes is is better to just invent some new science and technology to do what you want then to try and shoehorn known science in.

If the reader sees that you are trying to support your plot devices with real science, it can be an invitation for them to poke holes in your explanations.

If it is vital to your story for the characters to live at some slowed down time factor during the terraforming process, it just might be better to just say that some new theory allows this without needing the high speeds required by Relativity. Maybe you could combine this with your "hypersleep" concept. That the same process that allows your crew to travel long distances in zero subjective time, can be "tuned down" to allow them to experience some subjective time while long periods of time pass for the planet.

 

[DaveC426913]

As Janus points out, magnetism doesn't affect all materials in the body equally.

Additionally, your assumption that

the net force between your separate body parts is 0, it would not tear you apart or crush you,

is not true.

Magnetism, just like gravity, falls off as the inverse square of the distance, so you will get tidal forces - just like a strong gravitational source.

 

[some bloke]

Hi guys,

Thankyou for the responses on this. I recently uncovered some notes on this idea and I'm looking to breathe some life back into them.

To counter the massive G-forces involved in the orbiting satellite ring (which I am set on keeping), I am considering using artificial gravity, ramped up to the maximum.

So the ring, as a whole, will remain structurally integral and balanced by handwavium supermaterials and thrusters, so that's sorted now.
The crushing g-force on all occupants of the ring will be countered by "Gravity Enhancers", which will amplify the gravity from the planet to the point where it counteracts the g-force. This will take place only inside the ring, so it will rely on its own integrity to hold itself together, whilst using the GE technology to keep the population alive.

I smiled when I decided to go for gravity enhancement rather than artificial gravity because:
1: it implies restrictions in the technology - we can't do anything, and creating gravity is not possible, but amplifying it has become so
2: It allows some extra plots for me to choose from - what happens if the planet has a moon which passes over, changing the net gravity? What happens if someone, misguidedly, tries to turn the gravity off so they can float to access something? what happens if the protagonist is trapped in a room whilst the villain tries to deactivate the g-force in there?

Just to confirm - as gravity affects all matter dependant on its mass, it would directly and effectively cancel out g-force, if it could be applied?

Essentially the outer shell of the hollow ring would be experiencing massive g's, but the inside would be in an orbit, as if around a supermassive object.

But then, would that cause gravitational time dilation?

 

[DaveC426913]

2: It allows some extra plots for me to choose from - what happens if the planet has a moon which passes over, changing the net gravity? What happens if someone, misguidedly, tries to turn the gravity off so they can float to access something? what happens if the protagonist is trapped in a room whilst the villain tries to deactivate the g-force in there?

Just to confirm - as gravity affects all matter dependant on its mass, it would directly and effectively cancel out g-force, if it could be applied?

Essentially the outer shell of the hollow ring would be experiencing massive g's, but the inside would be in an orbit, as if around a supermassive object.

But then, would that cause gravitational time dilation?

I can't speak for anyone else, but I don't remember your setup for this and thus have no advice.

A simple diagram would be of great use.

 

[member 656954]

@some bloke, I'm just about finished a novel that has extensive use of orbital mechanics supporting the action, a subject of which I know very little. After struggling to do the math on paper (yes, I'm that insane) I purchased AstroGrav, which did all the heavy lifting for me. What I discovered is that orbits are incredibly fine tuned. Perfectly so, which I doubt would surprise an expert, but to discover that adding even a few km/s to the speed of a body could perturb it into a different orbital plane, or even exit it out of the solar system altogether, was a revelation.

The point of this pre-ramble is that you're going to have to invoke handwavium and unobtanium in massive quantities to make your scenario work, which means you can shape it however you need. With regards time dilation, an alternative to crafting measures to combat it, is to just go FTL.

Reading your thoughts here, you seem to have a number of disparate ideas in play, based on technical ideas, rather than an overall narrative that the technology supports and your 'solutions' are getting increasingly complicated without clarifying your intent. If you can get back to the basics of what you want to say with the story, the scenarios should generally drop out and you'll know which parts to include and which to jettison.

 

[DaveC426913]

What I discovered is that orbits are incredibly fine tuned...

I think you are looking at highly contrived scenarios by using a simulator. It is distorting your idea of the scale and effort involved.

A simulator allows you to add or subtract a huge amount of velocity with the flick of a slider.

but to discover that adding even a few km/s to the speed of a body could perturb it into a different orbital plane, or even exit it out of the solar system altogether, was a revelation.

A few km/s is huge in the real world, and takes a great deal of effort.

The ISS is "only" moving at 7.7k/s - that's single digits. What we are able to do IRL over a reasonable time frame is equivalent to fractions of a km/s.

Even when we add velocity to orbiting objects, it doesn't send them careening out of the system - it simply subtlely causes their orbit to become a little more eccentric.

 

[member 656954]

I think you are looking at highly contrived scenarios by using a simulator. It is distorting your idea of the scale and effort involved.

It's actually an accurate solar system model, I was trying to shift asteroid orbits and I worked out the energies involved to effect the orbital changes I was writing, @DaveC426913, so I've an idea of the scale - HUGE and way beyond anything we can possibly conceive of doing even in the medium term.

Even when we add velocity to orbiting objects, it doesn't send them careening out of the system - it simply subtlely causes their orbit to become a little more eccentric.

It depends on the object and how much you add

But my point was to the OP that working all the science out for the satellite scenario is messy, and probably won't add to the story because what was described was physically difficult and if the author is having trouble describing it, then you can bet the reader will have trouble deciphering it.

 

[some bloke]

The steps of my intended background for my story are:
1: People who want to terraform planets don't want to spend their whole lives doing so, and instead devise this ring system which allows time to pass slower for them than it does on the planet.
2:People on the ring remotely pilot robots/androids on the surface of the planet, from the ring.
3: To keep up with what (by their observations) is a very fast timeline, they are neurally connected and then "overclocked" using drugs, so their brains work faster than normal, counteracting the time difference - as if you just adjusted a clock to tick 10 times per second instead of once a second, to match a clock you can see on the planet.

My aim is to give a valid-sounding explanation of:
1: how their time is slower than that on the planet
2: How they aren't turned to red sauce by the forces involved

The idea is that it takes 500 years to terraform the planet, so if you speed someones mind up to 100x its regular speed (which can be done without harming them because science) and then put them in a satellite going so fast that its time goes 100x slower than on the surface, then you have a mind in orbit for 500 years, which "computes" at normal speed, but when they unplug, it's been 5 years. If that mind controls a robot on the surface, then that's 500 years of terraforming without having to re-train people to do it.

 

[member 656954]

That's an interesting synopsis, @some bloke, you can make that work. My only question is how they get to the planets in the first place? If it's slower than light, you get some interesting societal dynamics. FTL and you can use further handwavium to replace the satellite with exotic matter to create the slow zone (or some such). It's all in the telling, of course, but it sounds like a solid scenario.

 

[some bloke]

I'm content with stasis-sleep for the travel part, as the people on board have no intention of going back, which is why they need to speed up the slow process of terraforming, which has to be slow as they need to start a life cycle and get it established before humans can venture in.

 

[DaveC426913]

Interesting idea but have you considered that, with their minds sped up 100x, subjectively, they still experience 500 years of living on the space station?

 

[some bloke]

Interesting idea but have you considered that, with their minds sped up 100x, subjectively, they still experience 500 years of living on the space station?

Yes, but they will be plugged into their "avatars" for the duration, who will be spending 500 years at "normal" time on the planet. They will experience 500 years as an android on the surface of the planet, but wake up having only aged 5. There will be a fair amount on the psychological effects of such, and the ramifications of things going wrong.

 

[mfb]

@some bloke: If you can "overclock" a brain certainly you can also make the humans live for centuries or forever. Why bother with time dilation and all the ridiculous assumptions you need to make that work? Just make humans live longer.

Actually, the astronauts in the ISS age slightly faster than those of us on Earth, owing to the gravitational time dilation being slightly greater than the velocity-based time dilation. In any case, both effects are insignificant.

No, astronauts on the ISS age slower. The velocity is more important than the effect of gravitational time dilation. The two effects cancel at a point in the medium orbit range, a bit below the GPS satellites (so GPS satellites age faster).

 

[PeroK]

No, astronauts on the ISS age slower. The velocity is more important than the effect of gravitational time dilation. The two effects cancel at a point in the medium orbit range, a bit below the GPS satellites (so GPS satellites age faster).

Is there a calculation for that? I would have thought that in the limit of a very large orbit, the gravitational effect would dominate. And, in the limit of a very low orbit, velocity based time dilation would dominate.

 

[DaveC426913]

Is there a calculation for that? I would have thought that in the limit of a very large orbit, the gravitational effect would dominate. And, in the limit of a very low orbit, velocity based time dilation would dominate.

https://en.wikipedia.org/wiki/Hafele–Keating_experiment

 

[PeroK]

https://en.wikipedia.org/wiki/Hafele–Keating_experiment

Aeroplanes are not in orbit, though. There is no direct relationship between their speed and altitude.

 

[some bloke]

@some bloke: If you can "overclock" a brain certainly you can also make the humans live for centuries or forever. Why bother with time dilation and all the ridiculous assumptions you need to make that work? Just make humans live longer.

It being fiction, I could just have someone fire a "terraforming beam" onto the planet and have it ready by afternoon tea, but that does not a story make.

If people could live forever, it would nullify the need for terraforming at all - just keep looking until you find Earth mkII.

I appreciate what you're saying, but the time difference between the satellite and the ground is somewhat pivotal for the plot. I also think that speeding up neural activity is a lot more achievable than life extension. It's also a more gritty reality. I may even scrap the terraforming aspect and have it as a more "dystopian future" kind of thing - "Come to the ring, where you can live forever as an android on earth!". All the fat-cats living for thousands of years. but that theme has, perhaps, been over-done.

 

[DaveC426913]

Aeroplanes are not in orbit, though. There is no direct relationship between their speed and altitude.

Right. Sorry. I thought you were asking a different question.

 

[mfb]

Is there a calculation for that? I would have thought that in the limit of a very large orbit, the gravitational effect would dominate. And, in the limit of a very low orbit, velocity based time dilation would dominate.

Correct. As Earth's gravitational field is weak you can treat both time dilation effects as independent. Add the velocity/height relation for an orbit and you can get a closed formula. Here is a graph. At 3000 km clocks run at the same speed as on the ground (for circular orbits). Below they run slower, above they run higher.

I also think that speeding up neural activity is a lot more achievable than life extension.

No, not at all.

A life extension only to some centuries instead of immortality would be possible.

 

[PeroK]

Correct. As Earth's gravitational field is weak you can treat both time dilation effects as independent. Add the velocity/height relation for an orbit and you can get a closed formula. Here is a graph. At 3000 km clocks run at the same speed as on the ground (for circular orbits). Below they run slower, above they run higher.

I thought I'd seen the calculation once that the ISS was high enough. Apparently not. I'll remember that. Thanks.

 

[Janus]

Is there a calculation for that? I would have thought that in the limit of a very large orbit, the gravitational effect would dominate. And, in the limit of a very low orbit, velocity based time dilation would dominate.

For a clock in a circular orbit , the time dilation is
$$ t_0 = t_f \sqrt{1- \frac{3GM}{r c^2}}$$
when r is the orbital radius
Ignoring effects due to the rotation of the Earth, time dilation at the Earth's surface is
$$ t_0 = t_f \sqrt{1- \frac{2GM}{r_e c^2}}$$

with r_e being the radius of the Earth

$$ t_f \sqrt{1- \frac{3GM}{r c^2}}= t_f \sqrt{1- \frac{2GM}{r_e c^2}}$$
when
$$ r = \frac{3}{2}r_e $$

or the altitude of the orbit is 1/2 Earth radius above the surface of the Earth.
Below that, clocks run slow compared to surface clocks, above it, they run faster.

 

[member 656954]

but that theme has, perhaps, been over-done

Pretty much any theme has been overdone Only the telling differentiates your iteration from the others. Which is where the challenge of writing arises from, of course, so go with your idea, @some bloke, and make the telling the best it can be. That's always worth reading, no matter how common (or uncommon) the scenario is.