# 61 Virginis Mission Design: Long Term High Gee Acceleration and the Human Body

I'm designing a mission to a planet orbiting 61 Virginis (27.9 ly distant), and want to stay within physics that we're aware of (e.g. no warp drive). I've asked questions here and here, and the answers to those tell me that it's a tall order. For one, getting up to a reasonable fraction of the speed of light in a reasonable period of time seems to require accelerations that would be unreasonable to the human body.

So, my question: if I'm going to have my passengers in cold storage of some sort, but not so cold that they've gone solid (no "carbonite", but deep sleep and slowed biology), what sort of acceleration can I use?

I'd like the trip to be in as short an amount of time as possible for story continuity, so multi-thousand year transit won't work. Ideally they'd get there in less than sixty or so years, but a couple hundred years would be OK. Is it feasible?

• Is it feasible? - no Apr 4 '16 at 21:38

One thing we have to take into account is that you can only accelerate for the first half of the trip. You then have to decelerate for the second half; otherwise, you won't be able to stop unless you crash into your target! So the proper time observed by someone onboard a ship for the first half of the journey, $\tau_1$, is during a period of acceleration for the first 13.95 light-years. The total proper time, therefore, is $\tau=2\tau_1$.

This report states that humans can survive an acceleration of two to three times the acceleration due to Earth's gravity for about 24 hours without adverse effects. Let's see what would happen if we were to send our intrepid explorers off at this acceleration. This comprehensive answer by John Rennie gives a formula we can use for $\tau_1$ and $x_1$: $$x_1=\frac{c^2}{a}\left(\cosh\left(\frac{a\tau_1}{c}\right)–1\right)\tag{1a}$$ We can then rearrange this to solve for $\tau_1$: $$\tau_1=\frac{c}{a}\text{arcosh}\left(\frac{x_1a}{c^2}+1\right)\tag{1b}$$ Plugging these values into my calculator, for $\tau=2g$, I get $\tau=2\tau_1=2.96$ years.

If we cut the acceleration in half, to the much safer $g$ we feel on Earth, this brings the proper time to about 6.65 years - again, well within your time frame.

John Rennie added a couple graphs into his answer, so I feel compelled to do the same. Here is the graph of $\tau(x)$, assuming an $x_1$ of about 13.95 light-years and a total travel distance of 27.9 light-years: Unless you are planning to shoot the passengers out of a railgun, then there really isn't an issue at all.

Without getting into a lot of heavy duty math, accelerating at a constant 1*g* for a year will bring you to a very high fraction of c (in fact you will have traveled half a light year and be moving at just under the speed of light). Then you can coast towards your target and at the appropriate time start to decelerate.

Marshal Savage, in his book "The Millenial Project" suggested that in the far future instead of starships, there would be mass drivers that span the length of the solar system and accelerate pods to high fractions of c, and corresponding mass drivers at the target star systems to capture and decelerate the pods. In his conception, the launch tube is 3000 AU in length, and the pod inside travels at 10 g for a month to reach 99.99 c. Obviously that is far beyond what a normal human could withstand (trained fighter pilots in g suits handle accelerations of up to 9 g for short periods of time), but if the person is suspended in some sort of fluid filled capsule and all their internal spaces are filled with an oxygenated fluid then they will be far less affected.

So these probably represent the two extreme ends of the spectrum for travel at near luminal velocities. Naturally, moving at this speed requires massive amounts of energy to accelerate or decelerate (Robert L Forward's laser driven light sail needs 70,000TW of laser energy to accelerate to a modest .5*c*), and you would also need some pretty impressive shielding to protect the cargo and crew from impacts with even molecules of interstellar gas.

• I'm really intrigued by this concept. Perhaps my original solar sail idea should be abandoned in favor of a solar system-scale rail gun. Apr 5 '16 at 17:15
• A solar system wide mass driver is probably more of an artifact that a very advanced and mature space faring civilization could build. 3000 AU is 3000 times the distance from the Earth to the Sun, so a major engineering project indeed. Apr 5 '16 at 18:23
• Indeed. However, how about a 30 AU driver? How much acceleration can we achieve with something that long? Apr 5 '16 at 18:44
• To achieve the same sort of final velocity with 1/10 the length, you would need to increase the acceleration to 100 g or more. The amount of acceleration is controlled by the amount of energy you can deliver, and this can be arbitrarily large in a spacefaring civilization (if you can get 70,000TW of energy for a laser you can get that for a mass driver as well) Apr 5 '16 at 23:38
• I got all excited and asked this question: worldbuilding.stackexchange.com/questions/39507/… BTW, are you aware that the distance from Earth to Neptune is around 30 AU? A 3000 AU mass driver would extend well into the Oort Cloud. Apr 5 '16 at 23:48