solar sails

Okay, there’s more ∆v out there for free: photons from the sun!

To understand these slow but sure space ships we need to understand two things: how orbits work in a bit more detail, and where momentum comes from. So first, orbits.

Okay, let’s say you’re in a nice circular orbit with altitude r (for radius).

Now let’s say you want to leave here and go somewhere else. You need to expand this orbit. What you do is accelerate along your path of travel (a tangent to the orbit). We’ll show this acceleration with, of course a vector. We’re not showing the vector for your existing velocity (which is in the same direction) and the gravity vector. But they are there. What we’ll show instead is how your increased vector changes your orbit.

As you burn, your orbit begins to elongate (and widen, but mostly elongate) on the opposite side of the orbit from your burn.

Let’s say you continue this burn and eventually you wind up with something like this:

If that long side reaches out close enough to, say, the moon, then eventually the moon will dominate in the gravity equation and you will be able to transfer from Earth orbit to lunar orbit. If you burn long enough the ellipse will expand until suddenly (when you reach escape velocity) it’s a circle centered on the sun instead of the Earth! Then you have escaped the gravity well of the Earth and are on an interplanetary journey.

The same principle exactly applies to your solar orbit. If you continue to burn then your nice circular orbit will elongate until you cross the orbit of, say, Mars. Then you can slow down a bit while close to Mars and orbit there.

To shrink your elongated orbit, you decelerate while on the short side of the orbit. To circularize you accelerate while on the long side (which runs this process in reverse).

Point is, all you need to do to get to Mars is, barring some fine tuning, accelerate and decelerate along the tangent to your orbit at the right time.

So how does a solar sail do that?

Well it turns out light has momentum. Photons from the sun reflecting off your space craft provide a very tiny amount of thrust. It’s not much, but it’s enough that it will deflect your ship by hundreds or thousands of kilometers from your careful orbital course. Our space probes must deal with this to arrive safely. It’s a real thing.

But if you build a giant, very light, reflective sail then you can reflect enough photons that their momentum is significant. And continuous. And free. You don’t need any reaction mass because this isn’t a rocket. It’s slow to build, but build it does.

So if you orient your sail at 45° to the sun, the photons will bounce off as shown in the dotted line. In doing so, thanks to Newton, you will get a vector full of momentum following the solid line. You are now accelerating and your orbit will elongate as desired! To slow down, just flip around 180° and bounce the light the other way. With these two moves and some minor adjustments you can fly anywhere there are enough photons from the sun. Practically that’s probably out to Jupiter or so.

But wait a second: photons have no mass. Momentum is mass × velocity. So where does the momentum come from? Well it turns out that mass is very intimately related to energy. It’s a pretty famous equation: E=mc². And the energy of a photon is its frequency time Planck’s constant. So though it seems like magic, photons have momentum. It’s not a lot since a little algebra gives us m=E/c² and c is huge. But again, it’s constantly on and it’s free.

This seems useful to me for a number of things:

Space probes. Since no one’s on board it doesn’t matter that it can take a while to increase that orbit usefully.

Cargo trains. If you wanted to move a continuous stream of cargo, it doesn’t really matter how long any given deliver takes since one is leaving/arriving every six days (or whatever your launch period is). And your six million tons of ice doesn’t care how long the trip takes.

Emergencies. It’s pretty scary that you might lose all your reaction mass and drift forever. Packing along a solar sail is like carrying a parachute. And it will be really bright!

In the context of Diaspora in particular, this is a pretty much perfect way to station-keep a space station at the slipknot.