Relativistic time dilation

Hello all. I have been kicking around a story idea which involves time dilation. Essentially the premise is that you have some guys on a space ship that can travel extremely fast. Their business essentially involves stopping by a primitive civilization and seeding it with a religion based on a returning Messiah, then zooming off to the next one, and the next one. They take a big looping course back to the first planet.The plan is that because of time dilation, thousands of years will have passed on the planet, whereas in the ship's frame of reference a much shorter time will have elapsed. They reveal themselves to the (hopefully religious, Messiah-awaiting) descendants in a blaze of manufactured heavenly glory and gratefully accept millennia of priceless relics, gems, etc.

So I guess I have two questions: the first, to SF experts, is: has this been done? I'm aware of that one Star Trek: TNG episode on a similar theme, and there's a bit of Dune in it too; but SF being what it is, something even closer has probably been done before.

Secondly, to the physicists out there: what might be plausible values? i.e. for the length of the trip for the con-artists, the speed they'd have to travel to give them a useful ratio of rate of time passing on ship:rate of time passing planetside?

Any help filling in the blanks and indeed correcting my no doubt laughable relativistic fallacies would be much appreciated.

OneWriter said:

Do you want one year on the spaceship to correspond to, say, one thousand years on the planet? You would need a speed very close to c. The formula to use is:

(time unit on planet) = (time unit on spaceship) / square root( 1 - v^2/c^2)

if you want 1,000 years on earth to correspond to 1 year on spaceship, you get that the spaceship should travel at 0.99 times the speed of light.

Disclaimer: this is from a strictly mathematical point of view.

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That is amazingly helpful: thank you very much indeed!

RJK said:

Then you'd have to ask yourself, how may planets supporting intelligent life would exist within a few light years of each other. The closest star to Earth is 4.3 light years away. It would take your culprits a lifetime to carry out their scheme.

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This is a good point. I think the interstellar travel would be accomplished with some sort of Whatever Technology that allows instant travel - the ever-popular wormhole perhaps. The near-c acceleration would be purely for the time travel aspect rather than to get anywhere - the equivalent of driving round the block a few times.

Or indeed one could include some sort of suspended animation scheme where the lifetime isn't really a problem - you just wake up now and again to pull a con, then back in the pod...

Drachen Jager said:

Then of course there's the further problem. If you have a ship that can travel between solar systems so quickly, why on earth would you care about the primitive junk a bunch of savages could provide for you? I mean it's a little like using the DeLorian to travel back in time so you can trade glow-sticks for glass beads or something.

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This is also an excellent point. I think I was basically thinking it would be the way to get hold of most of a civ's most priceless historically significant antiquities - low volume, high value. They'd have some sort of impressive prestige value even in a post-scarcity, post-money society; it'd be nice to have a few Van Goghs. Or indeed you could just hang out on planets as history's most pampered tourists.

Lhun said:

If you just need the time dilation as a story device, it's probably easier to just give them some kind of magic stasis field. Near-c velocities cause all kinds of difficulties, so if there's FTL (i.e. magic) anyway, not much reason not to use a tiny bit more to make it easier on the characters.
Or you could just park them close to a black hole or neutron start for a while so they make use of gravitational time dilation.

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I think I would be wilfully ignoring all gnarly relativistic effects except for the one(s) that suits me...