Splish, Splash, Draw Me an Extrasolar Bath

With all of the hoopla this week surrounding the announcement of the discovery of Gliese 581e (the smallest exoplanet yet discovered at 1.9 Earth-masses) and the refinement of the orbit of Gliese 581d (placing it firmly in the habitable zone of the Gliese 581 stellar system – meaning it may have liquid water at the surface), I thought I’d offer an engineering perspective. A number of sites have discussed the theoretically possible means of getting there. But what about realistic means of getting there?

Are We There Yet?

Gliese 581 is a stellar system 20.4 light-years distant. Barring some sort of faster-than-light technology (such as hyperspace or wormholes), any travel must take longer than 20.4 years, as measured from earth. However, the same physics that prevent FTL permit the journey to take less time as measured by the ship making the journey. So we need to factor that in to our considerations. Another thing to consider is that as velocity increases, there is a Doppler effect, which can allow high energy radiation to shift into wavelengths that may interact with the ship. Last thing you want to do is turn the ship into a giant microwave and cook the crew. And of course, kinetic energy is proportional to the square of velocity. Even a speck of dust at near-light speeds can be fatal to a ship without proper shielding.

For the purposes of the argument, I am going to have to make some assumptions. I hope that these are realistic – and if you disagree, at least you have a starting point for your own analysis, eh? First, I am going to assume that the upper limit for shield technology is around a velocity of 0.85c (where c is the speed of light). This is a low enough speed to avoid the Jiffy-pop Doppler effect with reasonable radiation shielding, and I feel that kinetic shields could reasonably be expected to deal with small particles at that speed. Of course, in engineering, there’s a difference between upper limit and upper safe limit. Engineers like to include at least an 20% margin of error. Keeping in mind that kinetic energy is proportional to the square of the velocity, a safe speed would be about 0.77c. This is fast enough to take advantage of relativistic effects without turning the crew into interstellar popcorn or pate.

The question remains – how do we get going that fast? Bound by inertia, we’re restricted to a comfortable acceleration. Might as well choose something that everyone is familiar and comfortable with, one g, the acceleration we experience on the surface of the Earth. Accelerate long enough, and we will attain our max speed, at which point we coast (probably spinning the ship to create a centripetal acceleration of 1 g). And since we don’t want to just zoom past, we’ll eventually need to decelerate. So how long does it take?

According to this site (h/t Science After Sunclipse), if we accelerate at 1 g for one year ship time, we will attain a velocity of 0.77c! (Not entirely by coincidence – my reasonable estimate for maximum speed was originally a range of 0.8-0.9c – I figured I’d go with the number that worked out well). Decelerating is the same, so that leaves us with the coasting portion of the journey. According to the site, we’ll have travelled 1.12 ly during the first and last stages, leaving 19.28 ly spent travelling at .77c. Simple arithmetic gives us 25.04 years. But that is in Earth time. Using the table from the site, only 15.85 years will have elapsed. So a trip to Gliese 581 will take about 27 1/2 years from the perspective of someone on Earth, but only 18 years for the traveler, allowing for some terminal maneuvers.

Fill ‘Er Up

Seeing as there are no Centauri Hydrogen stations along the route, we’re going to have to take all our fuel with us. How much will that take? The relativistic rocket site referenced earlier has a discussion on that. Basically, use a matter-anti-matter reaction to convert mass into energy and use that energy as a ship drive in the form of a gamma-ray laser. This is the most efficient means in an inertial universe to create an acceleration. Unfortunately, the site assumes 100% efficiency. But entropy is a harsh mistress, and it is impossible that we could get such an efficiency. Some of that energy will not be suitable for a graser, and though that excess energy can probably be diverted to maintain the ship’s systems, it is ultimately going to be lost to omnidirectional radiation (that, or the crew becomes pork roast). So how to account for that inefficiency?

The first equation, conservation of energy, we will assume to be correct. I see no reason not to assume that the matter-anti-matter reaction won’t completely convert mass to energy, and we can fudge it in later if it doesn’t. So the modification needs to be made in the second equation, conservation of momentum. There, the author assumed that all the energy was directed in the opposite direction of the acceleration. But as I indicated, the inefficiency will ultimately result in a certain amount of omnidirectional radiation. The sum of the momentum of this energy will be zero, leaving us with the ship momentum and the portion of energy that isn’t wasted. We can rework Equation 2 as follows:

0 = γmv – ηEL/c

where η is the efficiency of the drive. We can now get the following fuel: payload mass ratio:

M/m = cosh(1.03T)[ 1 + tanh(1.03T)/η ] – 1

where T is the number of years spent accelerating or decelerating at 1 g. To make th math easier, we can estimate tanh(1.03T) ~ 1

M/m = cosh(1.03T)[ 1 + 1/η ] – 1

For a one-way trip, T will be 2, but to get there and back again (without refueling at the local Glihyco), we have to set T at 4. The following table shows the effect different efficiencies will have on the fuel:payload mass ratio:

η          T=2          T=4
.1         31.6        337.5
.2         22.3        183.6
.3         15.9        132.4
.4         12.6        106.7
.5         10.7         91.3
.6          9.4         81.1
.7          8.5         73.7
.8          7.8         68.3
.9          7.3         64.0

At even fairly low efficiencies, this isn’t a bad fuel:payload ratio, at least for a one-way trip. For a two-way trip, you’re might be better off just including a fuel plant in the payload, assuming that such a fuel plant would be capable of generating enough fuel while the crew is exploring Gliese 581 to make the return trip. Note, however, that the drives and the fuel containment is counted against the payload, and as more fuel is required, these will increase in mass as well (though not as quickly).

That’s a Big Ship

Assuming a fairly reasonable 8:1 fuel:payload ratio, a one megatonne spaceship would have a core about the size of a Nimitz-class aircraft carrier. These carriers have a total crew complement over 5,000 strong. A complement of about 500 crew would probably be sufficient for our spaceship, large enough to allow sufficient social interaction while permitting sufficient space to avoid cabin fever. However, I would think a two or three megatonne ship with only slightly larger crewing requirements would be better for exploration purposes, allowing for more auxiliary craft. It would have to be capable of supporting that crew for about 40 years (allowing for 4 years for exploration and refueling), returning nearly 60 years after it left (to the Earth’s perspective). I think this would be technologically feasible. But not until our knowledge and engineering capability is significantly expanded.

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