See also parts I, II, III, IV, and VI.
We've covered a bunch of ways of moving ships around in space by shoving stuff out their backs. But there are some ways of moving around in outer space that actually don't involve the rocket equation at all. When you fly in a plane on Earth you can push around all that nice air that surrounds you in your environment in order to fly. Well, you can if you have a plane. It's very convenient in terms of not having to carry around huge amounts of fuel. There isn't any air in space but that doesn't mean that space is entirely featureless either. There are basically three things I know of that you can push off against in order to go places in space: the light of the sun, the solar wind, and planetary magnetic fields.
The principle behind solar sails is pretty simple. You still have sunlight in space and it's very bright too, at least within Earth's orbit. By Einstein's good old e=mc2 we know that since light has energy it has to have mass as well and thus momentum to impart when it's been deflected. Even non-solar sail spacecraft have to take into account the pressure of sunlight if they're going to reach their destinations. The effect is small since most spacecraft don't have large cross sections in comparison to their masses but if you made your spacecraft very thin you could reasonably use this as your main method of travel.
You might think that solar sails would only be useful in moving away from the Sun, since that's the direction the light is going. Thankfully orbital dynamics comes to the rescue. In order for a satellite around Earth to stay in orbit and not fall back down it has to be traveling around 7,800 m/s. By the same principle the Earth is only able to avoid falling into the sun because it's traveling at 30,000 m/s around the sun. By deflecting light in the same direction it's traveling a solar sail can slow down in its orbit around the sun and fall into a lower orbit.
And just like ion drives have already been used by Dawn a solar sail has already been used by a Japanese space probe, IKAROS, sent sunwards to go take a look at Venus and to test out solar sails. Look here for a picture of the probe with its sail deployed. What's really nifty is that it's got solar panels and LCDs build right into the sail. The cells are for power and the LCDs enable IKAROS to control its orientation. The sunlight will exert more force on reflective surfaces than non-reflective ones and by changing the LCDs from white to black the probe can control the forces on different parts of itself. The entire probe is spinning slowly so that the centrifugal force keeps the sail deployed.
How fast does it go? Well according to Wikipedia the radiation pressure from Sunlight around Earth is 9.8 µN/m2. That's for absorption so double it to 19.6 µN/m2 for a perfect reflector. The sail IKAROS has weighed 10 g/m2 so a square of that material would accelerate at about .002m/s2 if it's out in space by itself. That's more than the solar ion drive spaceship we looked at but less than the nuclear ion drive one. Of course there's still the mass of the everything else. IKAROS weighed 315 kg all told and had 200 m2 of sail. That gives .000012 m/s2 of acceleration which is pretty tiny but then again it uses literally zero fuel. Also these guys get better the closer you get to the sun. Around the orbit of Mercury they accelerate 6 times faster than out here around Earth. So if you want to take a solar sail to the outer planets it makes sense to drop in near the sun, pick up speed there, and then coast to your destination where you'll need to find some other form of propulsion for stopping.
On to other things. Besides light the sun spits out a stream of charged particles, the solar wind. Unlike with sunlight we don't tend to notice because the Earth has a gigantic magnetic field that intercepts these particles and traps them in the Van Allen belts. That's a good thing because these particles are a form of ionizing radiation and you'd accumulate an unhealthy dose after being exposed to it for a couple of years. The astronauts at the ISS are safely inside the Earth's magnetic field but the Apollo astronauts were exposed to it for a week and it'll be a big concern for any astronauts going to Mars.
But wait, we just said that are all these fast moving particles that are being stopped by Earth's magnetic field. Doesn't that mean that they're giving their momentum to Earth? Yes it does. The idea behind a magnetic sail is that you use a huge magnetic field to deflect these particles and use the momentum to propel your ship. The solar wind has much less momentum to give than sunlight but since you just need to intercept them with a magnetic field rather than a mirror the idea is that you can make your sail much bigger for the same mass and so end up accelerating faster. Another idea is to use electric fields to repel the solar wind rather than magnetic fields and the electric sail is something being worked on now by the European Space Agency. It's easier to make but harder to control the direction of thrust.
Finally we have the direct use of a planet's magnetic field. If you run a current through a wire that is in a magnetic field you get a force. If you're got a nice electrodynamic tether in orbit you can either trade the kinetic energy of your spacecraft for electrical energy or use electrical energy to increase the kinetic energy of your spacecraft. When you're boosting the trade offs are essentially identical to those of other sorts of electrical drives except you have to do it in a magnetic field and you don't have to use propellant. When you're braking, on the other hand, you get paid to slow down and that's really nice. You do need a handy source of electrons to grab to run through the wire but thankfully they don't call it the ionosphere for nothing. There's at least one company seriously working on these.
So there you have it, three sorts of useful space non-rockets. They're not as far along as electric thrusters but they're certainly possible.
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