How fast to go 1000 years into the future

[rlinsurf]

How fast (close to c in mph or m/s) would I need to go to go 1000 years into the future relative to an observer on Earth?

In general, is there a calculation which can tell me how fast I need to be going to go x distance in time relative to an observer on earth?

 

[Dale]

How fast (close to c in mph or m/s) would I need to go to go 1000 years into the future relative to an observer on Earth?

In general, is there a calculation which can tell me how fast I need to be going to go x distance in time relative to an observer on earth?

even at rest you will go 1000 years coordinate time in 1000 years of proper time.

The ratio of coordinate time to proper time is:
1/sqrt(1-v^2/c^2)

 

[neopolitan]

How fast (close to c in mph or m/s) would I need to go to go 1000 years into the future relative to an observer on Earth?

In general, is there a calculation which can tell me how fast I need to be going to go x distance in time relative to an observer on earth?

I think the equation you want it this:

t'=\frac{t-\frac{vx}{c^{2}}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}

where t = 1000 and you don't die during the journey. So, let's say you devote 50 years to the journey, how fast do you need to go to end up 1000 years after you left?

Let's say you do the journey in two legs of 25 years each (away from the Earth for 25 years ship time, and back for another 25 years), which means you can eliminate the second term (vx/c²).

Then you get Dalespam's equation.

t'=\frac{t}{\sqrt{1-\frac{v^{2}}{c^{2}}}}

Rearranging:

v=c . \sqrt{1-\frac{t^{2}}{t'^{2}}}

So plugging in your figures (or my figures, since I chose 50 years):

v=c . \sqrt{1-\frac{2500}{1000000}}

v = 0.998749c = 2.996 x 10⁸ m/s

If you want to go a bit slower, and can afford to wait 100 years you can travel a bit slower at 0.9c (2.7 x 10⁸ m/s).

If we assume you take a relatively small spaceship, the space shuttle weighing 2000000 kg, and blithely ignore the fuel issue, the work done to accelerate you (using the first figure) is about 1.8 x 10²³ kJ. This is not terribly far from the total annual energy consumption for the world at 2004 figures - times 500.

So ... I doubt you could persuade anyone to fund your mission

cheers,

neopolitan

(PS the accuracy of my figures might be a bit dicky, but the magnitudes should be right)

 

[rlinsurf]

neopolitan-- That's great, thank you.

So then for a two hour trip that would be

v=c. \sqrt{1-\frac{4}{76737600000000}}v=c. \sqrt{0.9999999999999479}v = 2.998 x 10⁸ m/s

Is that right?

Thanks :)

 

[rlinsurf]

nm. I think I got it.

Thanks again. :)

 

[neopolitan]

neopolitan-- That's great, thank you.

So then for a two hour trip that would be

v=c. \sqrt{1-\frac{4}{76737600000000}}


v=c. \sqrt{0.9999999999999479}


v = 2.998 x 10⁸ m/s

Is that right?

Thanks :)

I was using c = 3*10⁸ m/s but c = 299792458 m/s. I've since then put the equation into a spreadsheet so I can play with numbers more easily.


Using c=299792458 m/s:

Speed to travel 1000 years in 2 hours = 299792457.999992 m/s = 0.999999999999974c

Speed to travel 1000 years in 50 years = 299417482.921418 m/s = 0.998749218c

Speed to travel 1000 years in 100 year = 298289729.449314 m/s = 0.994987437c

So, yes, for two hours 2.998x10⁸ m/s is right, but that's near enough to light speed to prevent your trip anyway. There is talk that neutrinos don't actually travel at the speed of light but slightly less than it, the speed is in the order of 0.999999c so to travel 1000 Earth years in 2 hours of ship time, you'd (probably) have to travel faster than neutrinos.

cheers,

neopolitan

 

[qraal]

To go a 1,000 years in the future you need to travel for 1,000 years - there's a direct relationship between time and distance. As you can't magically leap to speeds very close to lightspeed then you need to take time getting up to speed, then time getting back down. Just how quick you do that determines how long the journey will take for you subjectively.

Fly out 500 light-years and fly-back. At 1 gee the trip takes about 1003.8 years for everyone at home and 1.94*ln(2(1 + 500*1.0323/2))*2 = 24.25 years on-board. Perhaps a bit over-long for what you intended.

Perhaps you can accelerate at 1,000 gees - and remain alive via some kind of electromagnetic support system. The trip-time drops for you and those at home. On ship the travel-time is now (1.94/1000)*ln[2(1+500*1000*1.0323/2)]*2 = ~0.05 years or 18.64 days. Of course the question of just how you remain alive is up to your imagination. Suspended in some kind of oxygenated fluid might work - salamanders live happily in centrifuges pushed up to about that many gee. Maintaining such extreme acceleration for so long is beyond my imagining in engine terms. Perhaps you know how to make a warp-drive sphere.

 

[michelcolman]

Of course the question of just how you remain alive is up to your imagination. Suspended in some kind of oxygenated fluid might work - salamanders live happily in centrifuges pushed up to about that many gee. Maintaining such extreme acceleration for so long is beyond my imagining in engine terms. Perhaps you know how to make a warp-drive sphere.

Maybe a simpler way would be a kind of cosmic cable car system with black holes flying through space between different destinations. Just wait for one of the holes to pass by, fly your spaceship behind it and let the hole's gravity pull you along. Of course your exact trajectory would have to be calculated by computers, it won't just be a matter of getting behind the hole and then hopping off again later, it will have to be some kind of slingshot trajectory. Anyway, since gravity will affect you and the ship the same way (provided you don't get close enough to feel tidal effects), your body won't feel any acceleration at all.

Of course it might be a tad difficult to set up such a black hole transportation system. Getting those things to the right speed on the right trajectory so they follow a specific course around other, more massive black holes that serve as a kind of "poles" is not going to be trivial.

Actually, it might be safer to use neutron stars for the cable cars, and black holes only for the "poles". The neutron stars won't give quite as much pull, but they should be much easier to handle... ;-)

 

[Hurkyl]

Maybe a simpler way would be a kind of cosmic cable car system with black holes flying through space between different destinations.

Would that work? One of the key features of Newtonian gravity is that it's approximately right -- it's not obvious to me that you could use a black hole as an inertial dampener.

OTOH, you could just use gravitational time dilation to solve the "go 1000 years into the future" problem, although I suppose that would be somewhat dangerous. (and not just because you risk crossing the event horizon accidentally)

 

[michelcolman]

Would that work? One of the key features of Newtonian gravity is that it's approximately right -- it's not obvious to me that you could use a black hole as an inertial dampener.

For example, approach the hole in such a direction that you take a hyperbolic trajectory around the hole. So you fly towards it, get accelerated, turn around it, and fly away again in a different direction, like a comet from outer space that goes around our sun and flies away again. All of this is relative to the hole, which is moving at high speed, so if your exit trajectory is forward, you'll actually end up faster than the hole.

This kind of slingshot trajectories is used all the time to fly spacecraft through the solar system.

OTOH, you could just use gravitational time dilation to solve the "go 1000 years into the future" problem, although I suppose that would be somewhat dangerous. (and not just because you risk crossing the event horizon accidentally)

That would probably work too. The advantage is that you don't need to accelerate the holes, you can just use any old black hole and somehow put yourself on a trajectory that takes you around the hole just outside the event horizon and then out again.

 

[qraal]

Hi Guys

Two words: Tidal Forces.

Stellar mass black-holes have seriously nasty tidal forces. Even neutron stars do.

But a gravity compensator isn't so crazy. Charles Sheffield uses that trick in his McAndrews stories - a disk of high-density matter with a very high surface gravity is placed so the crew section is accelerated towards it while the disk itself is being accelerated away from the crew section. The crew module can ride up and down a central shaft to vary the felt gravity according to comfort. In the stories the disk accelerates at 100 gees and being so high-density it's a very good shield against radiation.

Of course to propel it to relativistic speeds requires a truly staggering power-source which means Sheffield employs a lot of handwavium in the form of zero-point energy. Oh well can't always be perfect... but the 1000 year voyage needed a lot of that handwavium anyway.

 

[Dale]

Two words: Tidal Forces.

Stellar mass black-holes have seriously nasty tidal forces.

Yeah, stellar mass black holes do, but you can make the tidal forces at the event horizon arbitrarily small by making the black-hole arbitrarily large.