Solving the biggest problem of relativistic interstellar spacecrafts

In FTL-free universes, interstellar travel is often done by vessels capable of continuous acceleration (the drives themselves are often magitech), which can use the effects of relativistic time dilation to "shorten" travel times. However, while we often talk about the vacuum of space, space isn't a true vacuum. The interstellar medium isn't a perfect vacuum, per $$cm^3$$ between $$10^6$$ and $$0.0001$$ particles can be found. Crashing into anything, even ionised hydrogen gas, at velocities above $$0.9c$$ is a very bad idea. The kinetic energy of relativistic objects is given by this formula.

$$E_k=\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}-mc^2$$

This tells me that a spacecraft with a cross-section of $$50 m * 50 m$$ moving through dense interstellar medium ($$10^6$$ particles per $$cm^2$$) and average interstellar medium ($$0.5$$ particles per $$cm^2$$) at $$0.9c$$ will have to deal with $$2.6*10^{14} J/s$$ and $$6.5*10^7 J/s$$ respectively. For comparison, this is about the energy of a $$100 kt$$ nuclear bomb or a $$9 kg$$ TNT demolition charge each second respectively. To say that this is bad is an understatement.

Some sci-fi authors have suggested using ice as a shielding to deal with this, but running the numbers shows that this is a ridiculous proposition. Assuming that:

• the sublimation of ice in a vacuum can be viewed as an isobaric process;

• all of the collision energy is absorbed by the ice at 100% efficiency and used to heat it;

• the ice will, according to phase diagrams, sublimate at $$213 K$$ or $$-60 C$$;

• the ice is at $$5 K$$, to begin with; and

• its heat capacity in this temperature range is roughly $$4000 J/kg*K$$

We'd need about $$25*10^9 kg$$ of ice for a 10-year voyage at $$0.9c$$ and for the same voyage at $$0.99c$$ we'd even need $$110*10^9 kg$$ of ice. For anyone who wonders, this would be a 10 and 44 km stack of ice respectively. This wouldn't be a spacecraft anymore. It would be an interstellar comet. The "strap your spacecraft to an icy Kuiper belt object and fly to the next solar system" idea sounds interesting but it isn't what I'm looking for.

The Solution Are Energy Shields

While energy shields are pretty much considered to be the antithesis to hard-SciFi, they aren't that fictional. Most of the gas out there is already ionised, and the non-ionised part can be ionised using UV lasers. Rocks and dust grains are vaporised by a point-defense grid before the vapor is ionized as well. The spacecraft itself is covered in superconducting magnets, whose fields deflect the ionised gas away before it hits the spacecraft.

Design-wise I think this would result in kilometre-long spindles, which are thickest at the midpoint. During the acceleration phase, the spindle will plunge through the interstellar medium like an energy dagger. The deceleration phase is slightly more complicated, as the engine would be at the front. I don't think this will be a problem however since an engine capable of continuous multi-gee acceleration will have no problem punching through the interstellar medium. The rest of the vessel is now protected by the magnetic shield and point defense on the lower decks.

Are my assumptions about the damage the interstellar medium will deal with relativistic spacecraft correct? Did I mess up my calculations? Is my idea for dealing with this any good?

• You wouldn't even need to cover the ENTIRE ship with magnets, just the tip. That'd generate enough of a field to deflect everything around your spindle. – Morris The Cat Nov 4 '19 at 19:44
• The problem you'd encounter is that you'd need to deflect these ions fast - after all, you are moving at .9c. So you'd either need a magnetic field of ludicrous power or ludicrous range - and I'm not sure how feasible those are. Someone (i.e. not me because my magnet knowledge is a bit rusty) should run the calculations and see how much energy that requires. – Halfthawed Nov 4 '19 at 19:49
• I had to delete my answer, for I screwed it up becauseI had not really taken in acount the actual number of such particles you'd meet while moving at 0.9 c. With 0.5 particles per cubic cm, you'd face over 30 000 000 000 particles per 1 cm squared a second (after the adjustment for time dilation). At such numbers, even the extremely small odds of a particle hitting another particle inside you would unlikely compensate for the amount of particles passing through you. Thus I deleted my answer so as not to mislead. I apologize for rushing to answer before checking my numbers. – Failus Maximus Nov 4 '19 at 21:12
• I've wanted to ask this question before but was afraid I'd phrase it in an off-topic way. Thanks for asking this, I look forward to the answers. – BMF Nov 4 '19 at 22:34
• The physicist Isaac Arthur has a great youtube video that covers this exact topic (and much more): Interstellar Travel Challenges. It doesn't go heavy into the math, so I'm not sure it fits with the hard-science tag as an answer, but it's a good place to start. – Harabeck Nov 5 '19 at 2:19

I think your math may have seemed overly daunting because you need to consider that you are spreading the force out across your 25 million cm^2 surface area.

The most dangerous speed will be about 0.6c. At this speed, your hull is impacting about 18 billion atoms = 3.29e-17 kg of of hydrogen/s /cm^2

At 0.6c you are looking at 1.62E+16 J/kg of hydrogen meaning your actual resistance tops out at about 0.1 J/cm^2 in a normal vacuum or 100 J/cm^2 in dense space which is well within the tolerance for many materials. For comparison, a passenger airplane moving at 250m/s in Earth's atmosphere experiences about 0.9 J/cm^2. So, as long as you avoid any thick nebulas, your hull should be just fine as long as you have a basic method for dispersing the heat.

If you ship is adequately long for its front profile, you should be able to be able to use a cooling system to circulate the heat throughout your ship and either find ways to recycle or radiate it off.

• " 25 million cm^3 surface area" do you mean cm^2? I did adjust for that in the calculations. – TheDyingOfLight Nov 4 '19 at 20:37

I think, you are not getting it right. It's better to look at situation as spaceship is staying in place and hydrogen is coming for it at relativistic speed.

From this point of view your ship practicaly under bombardment by proton beams, like from particle accelerator. 0,9c is not that big number - it's only GeVs. We do not need extreamly large accelerator to achive this energy, and we already deflecting such proton beams with magnetic fields in relativly small installations : about tenth of meters and tens to hundres of tons. You don't even need to spend energy for it, if you ar using superconductros (energy goes from spaceship moment reduction - i.e. from your engine)

So yes, magnitic shielding is a good way to reduce corrosion and induced radioactivity of spaceship.

And you shouldn't be vary much about structural integrity: while energy of this proton beams is high, there total impulse is very small. They will not push spaceship with much force. So its more like very bright light (i.e. from nucler explosion), then stream of gas.