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Assuming we never break Newton's third law, in the near future thousands of chemical/nuclear/electric powered spaceships will be flying through our solar system expelling reaction mass.

Since a grain of dust can crack a window on a space shuttle going at a relatively very slow orbital speed would not all these trillions of atoms of propellant put a limit on the upper speed of spacecraft before dangerous abrasion starts to become a problem? or is the kinetic energy of all these atoms too small to account for anything?

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    $\begingroup$ There's enough extra-solar 'space dust' floating around already at velocity that really all you can do is just put a nice thick ballistic shield plate at the front of your spacecraft and accept that you're flying into a giant cosmic sand blaster every time you leave the atmosphere. Besides, the man-made space dust isn't in a focused beam, it spreads out over time lessening its effects and will eventually leave the solar system altogether anyway. So, at the end of the day, the problem fixes itself but wear a good flak jacket in the meantime. $\endgroup$ – Samwise Feb 7 '17 at 0:40
  • $\begingroup$ Thanks guys, so the consensus is nothing to worry about on this one. $\endgroup$ – Boz Feb 8 '17 at 21:42
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I've seen details worked out in the context of concern over salt-water uranium rockets. You might search for that to locate these details.

The kinetic energy is so high that it is not a problem. The exhaust material is well above the escape velocity of the solar system.

If it’s individual atoms, as you imply, then it will be swamped by the solar wind, which the craft is built to withstand.

Now certainly you don’t want to be directly downwind of a rocket. Traffic control and regulations will take care of that.

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The truth is, you could never have quite enough to matter. First of all, most propellant is going to go straight back to nearby planets, or else be blown out of the solar system by solar wind, but also consider just how big the solar system is.

Rounding up, Jupiter weighs $2 \times 10^{27}$ kg. Given that Jupiters orbit is roughly $7.8 \times 10^8$ km that gives us $\frac{2 \times 10^{27}}{\pi \left(7.8 \times 10^8\right)^2} \approx 10^9$ kg/km$^2$ (about 1 ton per m$^2$) if we compressed Jupiter down to a flat plane out to its own orbit.

How thick would the accretion disc be? From http://wwwmpa.mpa-garching.mpg.de/~henk/pub/disksn.pdf (bottom of page 19) I got an estimate of the aspect ratio of about $5 \times 10^{-3}$, giving a thickness of $7.8 \times 10^8 \times 5 \times 10^{-3} \approx 4 \times 10^6$ km.

Our final density then is $\frac{10^9\text{ kg/km}^2}{4 \times 10^6\text{ km}} = 250\text{ kg/km}^3$.

Now that is still quite a bit of mass and could cause problems, but in order to create this mess we had to expel the entire mass of Jupiter into the inner solar system. Keep in mind also that with gas of that density, some will be leaving and much will be grabbed by the planets as they orbit the Sun.

Which leaves the final point. The inner planets would be made completely uninhabitable long before you had to worry about gases in space.

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  • $\begingroup$ You’re not just dumping the material off in an orbital trajectory (forming clouds). As my answer indicates, the material will leave the vacinity of the sun since its kenetic energy vastly exceeds the potential energy. $\endgroup$ – JDługosz Feb 7 '17 at 6:30
  • $\begingroup$ It's a good point, but I'd like to show that even if that weren't the case it wouldn't matter. $\endgroup$ – Alex Stasse Feb 7 '17 at 7:02
  • $\begingroup$ So if you spilled readtion mass, momopropellent, or the like, it would make a cloud that needs to be avoided until it blew away or disappated enough—but that’s another question. And it depends on whether you have sublimated molecules or sand-sized grains. $\endgroup$ – JDługosz Feb 7 '17 at 7:17
  • $\begingroup$ Hi Alex. I edited your answer to use Mathjax for formatting of the formulas. You may want to review to double-check that I didn't mess anything up in the process. $\endgroup$ – user Feb 7 '17 at 9:14
  • $\begingroup$ This answer deserves a bounty. $\endgroup$ – The Square-Cube Law Jun 15 '18 at 13:22
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It depends, but it's probably not a problem.

If the propellant is in the form of a gas or plasma (by far the most common), and it's not travelling at Incredibly High (i.e. relativistic) speed, then it will simply disperse harmlessly. Interplanetary space is so large and there's simply not enough stuff there to fill it.

(you might get gas, or clouds of condensed material, in orbit. The main thing I'd worry about is if there is radioactive exhaust on planet or asteroid surfaces)

If the propellant is in the form of solid pellets (i.e. if your engine is some form of solid-bullet-firing mass driver) then you might have a problem. You will probably need to be careful to direct the stream of pellets on a trajectory that won't cause trouble down the road. If the exhaust velocity is enough to leave the solar system, it's much easier of course.

In general, the combination of high velocity and diverging (and gaseously dispersing) jets means that you're more worried about toasting a nearby ship with your jet (or with the radiation flare many nuclear engines will produce, which may be dangerous to tens or hundreds of kilometers) than having your propellant cause a problem over the long term.

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It's not a problem.

  • Ships won't use that much fuel in the future. It's already incredibly expensive to send ships into space, in part because carrying fuel on board isn't efficient. In order to lift it, you need ... more fuel, which makes the ship heavier. More weight means even more fuel, which means even more weight, etc. Therefore, the most effective way to reduce the cost of space travel is to cut back on fuel! This can be accomplished with sails, an elevator, or something else, but generally ships avoid using too much. This will, in turn, reduce the reaction mass expelled.
  • Space is huge, and atoms are small. Reaction mass will expand to fill the volume given, as fluids do, so most of it will eventually be out of the way - and on its way out of the solar system!
  • Ships already have shielding. We have shields to protect ships from radiation and other particles which should work fine in this context; reaction mass is no different.
  • Momentum is (nearly) conserved in a (near) vacuum. Sure, you may spend fuel and thus release mass while picking a direction to go in, to accelerate, and to slow down, but the vast majority of the trip may be spent drifting.
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    $\begingroup$ In your first point, you are not distinguishing the concepts of fuel, propellent, and reaction mass but are pretty much mashing them together with the implication of current “conventional” rockets. Your link to something else is fiction; I was expecting ion drives, photon rockets, etc. $\endgroup$ – JDługosz Feb 7 '17 at 6:35
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    $\begingroup$ «Propellant will expand to fill the volume given, as fluids do,» I don’t think that’s really applicable, since the transverse energy of the particles is dwarfed by the collaminated motion. They simply leave the solar system in the direction aimed, not expanding to form a cloud that sticks around. $\endgroup$ – JDługosz Feb 7 '17 at 6:39
  • $\begingroup$ The technologies you list as alternatives to bringing propellant have their own drawbacks. For example, solar sails of anything resembling reasonable sizes provide terrible thrust, and besides, only work in the vicinity of a bright star. Ion drives (as mentioned by @JDługosz) are a little less bad, but need the energy as electrical energy rather than chemical energy in the fuel, which presents its own challenges. Space elevators would probably be the most promising if we had any idea how to actually construct them, but only get you part way. $\endgroup$ – user Feb 7 '17 at 9:18
  • $\begingroup$ @JDługosz Edited to distinguish the terms, they are related but I understand how it could be unclear. The "something else" was intended as a joke. $\endgroup$ – Zxyrra Feb 7 '17 at 12:50
  • $\begingroup$ @MichaelKjörling If much (most?) of the reaction mass is used to escape the gravity of wherever you're starting then a space elevator should help quite a bit. $\endgroup$ – Zxyrra Feb 7 '17 at 12:51

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