I once worked the math out for acceleration of a starship using some sort of ‘conventional’ rocket capable of 1G acceleration.
I made some simplifying assumptions.
The ship had some ‘empty’ mass when it had no fuel.
The fuel itself had mass.
Fuel consumption was a first-order linear equation based on the force to apply to moving the ship forward. (fuel_per_second = c1*thrust + c2, c1 > 0, c2 >= 0)
The quick and dirty of it was that if you work from an empty ship backward in time, there is a point at which the combined mass of the ship plus the fuel cannot be moved forward at 1g. With higher mass, a higher force is needed to achieve 1g. With higher force required comes higher fuel consumption. With higher fuel consumption comes greater need for fuel over time.
If you work the calculus out there is a finite point in time where the fuel needed runs off to infinity, no matter what values of c1 and c2 you use.
You can make it arbitrarily far back in time with more efficient engines (improving c1) or less wastage (improving c2), but there is still a limit.
End result, working forward in time, there is a finite duration of time that you can thrust at 1g no matter what engines you use and no matter how much fuel you take.
Of course, fuel consumption isn’t necessarily linearly related to thrust, but it isn’t going to get better by adding higher order terms.
So, have really efficient engines, or provide less acceleration, or provide thrust using off-board power source (solar sails and laser?).
Well, as someone pointed out in Great Debates, when you are decelerating you do not fly into a cloud of your own exhaust- the exhaust will continue to stream away from you with whatever velocity your motor gave it. Just as it does when you are accelerating.
If a respectable motor and fuel can be developed, enough to provide acceleration of 1/3 gee for a reasonable proportion of the voyage, that would be enough to prevent most space related medical problems, and would acclimatise any traveller to a low-gee planet, moon or habitat.
(it is my opinion that constructed space habitats would be best built to rotate at 1/3 gee as well, and as big as possible)
(but then again, it is difficult enough to get into space.)
another option might be genetic engineering to avoid space related medical problems
It’s been a while since I played with Special Relativity, but IIRC the formula for time dilation is basic algebra. I used to plug in various factors of c to see how much time dilation you’d get at certain velocities. What I remember is that the effects don’t become noticable (as opposed to measurable) until .8c. The effect is flat until you reach high percentages, then begins to curve. I think you’d have to go at least .9 before you see a 1:2 ratio of stationary:spaceship time.
At .2c, I don’t think astronauts would be missing any birthdays. Then again, I’ve forgotten a lot of math.
Thanks for all of the answers. I suppose accelerating at 1g or any fraction of it using today’s technology is a little implausible.
Personally, I think that anything we do long term in outer space will need to be done at 1g or at least at a fraction of it. It is all very well asking how bears prevent wasting during hibernation, but they are still coping with gravity. And from what I know about genetics, things like hibernation or preventing wasting by turning on or off genes is not going to be easy. We are fighting a few billion years of evolution when it comes to those things. It is not going to be matter of plaing with just one or two genes.
In answer to your question, TeleTronOne, in Robert Heinlein’s novel “Rolling Stones” (from some time in the 1950s), the phrase “tumbling pigeon” was used to refer to a spaceship that spins to produce an artificial-gravity environment. I’ve never encountered the phrase anywhere else, not even in Heinlein’s other novels, all of which I have read; nor have I ever encountered an alternate name for the effect, even in novels where spin-gravity is featured – e.g., “Mars” by Ben Bova.
Now, what TeleTronOne wondered about was when you accelerate half the trip, flip the spacecraft over so the exhaust points ahead and then deccelerate the next half. I have a very vague feeling that Heinlein used a special term for it in “Have Spacesuit, Will Travel”, but it was a long long time ago since I last read it.
It seems to me the maneuver is close enough to an aircraft maneuver, that one might very well have called an “Immelman”. Larry Niven certainly used this maneuver, but I don’t know if he bothered to supply a name.
An Immelman would be very hard to do in vacuum and turning around like that isn’t very fancy in the first place. Spacecraft have done it ever since Gagarin when they return to Earth.
If you accelerate at A gravities to midpoint, then turnover and then decelerate at A gravities to your destination, elapsed time is approximately 4 SQRT (D/A) days, with D in astronomical units.
The distance to Pluto varies from about 29 AU (AD 1990) to about 49 AU (AD 2114). So travel time at 1g constant acceleration would be about 22 days if you did it now, or about 28 days if you waited a century to start.
The straight-line approximation is certainly good enough for accelerations over 10% of g, for any purpose short of actual navigation.
The reason for the ‘skew’ was because in Heinlein’s book the acceleration continued throughout the manoever. If you ever played “Asteroids”, you know what that looks like - the ship ‘skews’ while it’s turning.
In the real world, you might shut down the engines for the turn to prevent stressing the craft. In which case you’d just use gyros to rotate it. There’d be no ‘skew’, just a rotation and braking.
I have done such simple calculations too and have found out that such a trip to Alpha Centuri would require a ship that is apx 95% fuel if you happen to be using a matter-antimatter drive and opperating at 100% efficency.
So for every one pound of actual ship mass you would need apx 10 pounds of matter fuel and 10 pounds of antimatter fuel.