ScienceDirect – Planetary and Space Science : Direct contact among galactic civilizations by relativistic interstellar spaceflight.
Carl Sagan caused some academic excitement in 1963 [i.e. the academics blasted him] by modestly proposing that interstellar travel was a reasonable way for civilizations throughout the Galaxy to pay each other a visit every few thousand years, and that at some point in history (the last 10,000 years) we had actually been visited – or at least it was worth checking myths and legends for a sign of such a visit. Robert Bussard’s Ramjet paper inspired Sagan’s optimism – here was a seemingly reasonable design which could give a technological civilization the Keys to the Cosmos.
A lot of arguing over interstellar travel, alien life and the Fermi Paradox has happened since then. Can we conclude anything from all the arguments? One positive thing is that interstellar travel can be achieved at relativistic speeds even if interstellar ramjets can’t be made to work. All sorts of beamed-energy designs mean that it’s an unreasonable objection to visits by aliens to claim interstellar travel is impossible. It’s not.
But could it be made even easier than we imagine? One technology that would enable easy interstellar travel – in so far as packing a closed-loop environment or a lot of frozen meals is “easy” – would be total annihilation drives. Frank Tipler’s current formulation of the Omega Point Theory requires the invention of macroscopic sphaleron generating… somethings to annihilate matter and in one version he proposes the conversion of baryons into lots of neutrinos. This would allow the drive to be operated without melting down the local topography with terawatts of gamma-rays – in otherwords it could launch from the surface of a planet, even your own backyard.
Once you’re in space what else is liable to impede one’s progress? Interstellar matter. So turn a problem into a virtue and Bussard scoop the lot into one’s mass annihilator. Thus a ravening proton-storm becomes one’s neutrino-beam to the stars. The Galaxy is yours.
Except… well there is the travel-time issue. The basic equations are well known for constant acceleration flight:
let me introduce B & g (actually a beta and a gamma.) B is the ratio, v/c, where v is your velocity and c is lightspeed, then g = (1 – B²)-1/2.
The travel time, onboard ship, is then…
t = (2c/a)*arcosh(g)
…a is acceleration and arcosh(g) is the inverse hyperbolic cosine (“cosh”) of g, which is ln[g + (g²-1)1/2]. Thus, at large g values, it simplifies to good approximation to:
t = (2c/a)*ln(2g)
…but one variable is missing: distance, S. It’s a part of g i.e. g = (1 + aS/2c²) …notice I’m computing a trip starting and finishing at zero relative velocity to the starting point.
So what does that mean for the people at home? Well Planet-time – as measured by observers at rest with respect to one’s starting point – is computed pretty straightforwardly as T = 2v.g/a. Of course you can expand v and g out in terms of S and a to get…
T = [4S/a + S²]1/2 …or…
T = 2[(S/a)(1 + aS/4c²)]1/2
…or even purely in terms of g & a…
T = (2c/a)(g²-1)1/2
…which shows us that the ratio of the two, t/T, is…
ln[g + (g²-1)1/2]/[g²-1]1/2
which simplifies in the high g limit to…
ln(2g)/g
…so to get one’s experienced trip-time down for a given distance, then you have to hit very high g factors. Now at an acceleration of 1-gee (Earth gravity) the distance travelled to increase g by 1 is c²/a ~0.97 light-years.
To get to high g factors in a short time requires high acceleration. Some fictional examples…
- Robert Forward illustrated this quite memorably in his book “Timemaster”, wherein the hero has to accelerate at 30 gees for 5 weeks to get to a g factor of 10. Naturally he’s floating in a gee-tank.
- Stanislaw Lem propels his heros in “Fiasco” to the planet Quinta, some five light-years from the mothership, in 3 months of subjective flight-time at 20 gees.
Other examples, as meticulous, are harder to find. Alastair Reynolds is an SF-writing astrophysicist (like Greg Benford before him) and probably is as careful with the time-factors – I’m yet to finish one of his books, so I’ll let you know.