Follow the Light


On a hot day, we might say that the sun beats down on us. It’s literally the case: those photons carry momentum, despite that they’re massless. As they bounce off a surface, they impart momentum, i.e. they provide a propulsive force without propellant. Because of this force, mere light can accelerate a spacecraft to high speed. There’s your interplanetary spacecraft, right there—a solar sail. Here’s the spacecraft design question: what opportunities present themselves when we consider very small solar sails? Can we do better than the classic approach to the problem?

The idea of a solar sail has been around for quite a while. Arthur C. Clarke wrote “The Wind from the Sun,” a story about a solar-sailing regatta in which large, diaphanous spacecraft race one another with light propulsion. Small, meter-scale solar-sails have been launched, with modest success. The basic physics are not really in question. In fact, NASA is now building a 1200 m2 experimental solar sail to investigate the technology, the largest ever, known as Sunjammer. It’s an inexpensive demo of a very lightweight structure, including inflatable booms and other wonderful innovations from L.Garde, Inc.

Solar sails accelerate in proportion to the surface area that reflects solar photons, and in inverse proportion to the mass of the total space system: i.e., the larger the faster, and the heavier the slower. So, an ideal solar sail is super-thin, yet rigid. Dupont now makes a 0.1 micron-thick material that is suitable for solar sails. But the sheer dimensions of typical sails require an explicit effort to stiffen the structure, e.g. with booms (hence Sunjammer’s inflatable components). Some have proposed spinning a thin sail so that centripetal acceleration keeps the sail stretched outward. Spin also helps keep the attitude fixed in a convenient way. To be precise, let’s say that there’s a linear dimension, L, that characterizes the width or diameter of the sail. That area goes with L2. And let’s say that its mass, or volume, changes with L3. The acceleration changes with area per mass, or L2/L3=1/L. So, as L decreases, acceleration increases, all things being equal.

Of course, they’re not quite equal. There’s a lower limit on the thickness of the sail, and larger spacecraft can have disproportionately thin sails. But remember that the larger the sail, the more mass is devoted to keeping it stiff. That’s where a satellite-on-a-chip comes in. It’s an idea that we’ve been working on at Cornell since early 2005. We call them chipsats. We even made some prototypes, thanks to collaborations with Draper Lab and Sandia Labs. In fact, in a few weeks about 128 circuit-board prototype versions will launch and will be deployed. They’re called Sprites (the name given them by Dr. Justin Atchison) and will be launched on the Kickstarter-funded KickSat led by Zac Manchester. By early April, we may know how well this basic concept works.

One thing a chipsat does exceptionally well is that it remains stiff despite being very thin. A single silicon wafer (maybe 25 microns thick), about 1 cm square, might be enough to transmit very small amounts of data from space. Its tiny antennas are essentially rigid, too, despite being thinner than a human hair. But it’s a got a great “lightness number,” comparable to typical solar-sail designs. Think about it. If you shrink a spacecraft uniformly, so that the acceleration due to pressure effects changes with 1/L, that little chipsat has a big advantage. As L becomes small, that acceleration grows. So, a chipsat may be a perfectly adequate solar sail, without any of the complexity that larger solar sails bring.

We can do better than the Sun, at least this far away. We can concentrate the light that acts on a chipsat, maybe with a parabolic mirror. Or maybe with a laser. Sure, let’s use a laser. How much power we need depends on how much momentum we want to impart. More precisely, the photon pressure P, in Newtons per square meter (N/M2), is simply the power per area (e.g. in Watts per square meter) divided by the speed of light: P=E/c.

For example, if a 1 cm2 chipsat is fully face-on to a beam of light that covers its surface, the area is A=0.0001 m2. If it’s essentially solid silicon, whose density is 2330 kg/m3, its mass is m=0.000005825 kg, i.e. 5.825 mg. Let’s say m=6 mg. The acceleration would be a=F/m, where F=PA. So, P=ma/A and E=cma/A. The power W would be W=EA=cma.

To lift off from the surface of the Earth, this little thing would have to feel a force just a little greater than gravity, whose acceleration at Earth’s surface is about 9.81 m/s2. The laser power would need to be W = 300,000,000 x 0.000006 x 9.81 = 17,142 Watts.

The degree of unreasonableness of this estimate has to do with several issues. First, can you get a laser this powerful? Sure. Off-the-shelf industrial laser diodes are available at 10 kW. (The Army even put one on a truck as a weapon.) Doubling or tripling that number should be within the reach of current technology. How about the fact that the laser will be a little sloppy, or in any case it won’t exactly cover the 1 cm2 chip? OK, let’s gang together a half dozen of these diodes and point them upward in parallel, maybe with the help of an array of precisely steered mirrors. That’s less than six trucks worth of electronics, if we extrapolate from the Army’s design. What about the fact that directing nearly 20 kW worth of laser power would probably vaporize the little chipsat in an instant? Now that’s a good question.

The answer lies with the technology of dielectric mirrors. It turns out that reflecting off metal always incurs losses. The photon that reaches the surface of the metal induces a little electromagnetic response in the metal, which then releases a new photon. That process involves some loss of energy because of the unavoidable electrical resistance of the metal. A dielectric mirror literally reflects the same photons, with no such electromagnetic response (they can’t respond that way; they’re not electrical conductors). Dielectric mirrors reflect better than 99.999% of the incident light, but only in narrow bands. Well, conveniently, laser light has exactly one wavelength. That’s as narrow as it gets. This near-perfect reflection leaves only 0.17412 Watts behind, only about 70% more power than sunlight at Earth’s distance to the Sun. In short, I’d expect the chipsat to get less than twice as hot as if we just left it sitting out in the sun.

It’s also hard for this system to deal with Earth’s atmosphere. Wind gusts would blow the chip around, forcing it off the beam. (Dr. Leik Myrabo’s Lightcraft had a related problem during their White Sands tests, although the physics are entirely different from what I’m proposing here.) Setting aside atmospheric disturbances for a moment, let’s consider the problem of beam divergence, the tendency of the beam to spread out. It’s going to happen. And it happens in proportion to the wavelength. Say we use a 500 nm (green) laser. After a 1 cm narrowest point, which the laser folks call the “waist,” the beam diverges with an angle of 0.000016 radians. After 628 m, the beam has spread out to twice that thickness, so that its intensity is only a quarter of what it was when the beam was 1 cm wide. The beam becomes so weak that the initially high acceleration peters out, and the chipsat reaches only about 117 m/s. Maybe more important, the beam attenuates while the spacecraft is still close to the Earth. That is, the beam weakens faster than gravity does, which means that the chipsat falls back to Earth (in fact, it would hover at some distance above the ground, where gravity balances the photon pressure of the laser).

Two ways to address this problem. Assuming that only modest adjustments in wavelength are possible (so, we’ll assume they don’t help), we adjust the optics, widening the beam as much as possible. If it can be widened to 10 m, the photon acceleration drops slower than gravity. However, this approach is flawed because the intensity is much lower, and 1 g can’t be achieved to begin with.

The second way is to start in space (and now we don’t have to deal with the atmosphere), with a wide beam, say 10 m (a hundred-fold increase). Now the chipsat can accelerate for much longer, reaching 10 times that speed eventually. Another hundred-fold increase in beamwidth (not really possible) provides another factor of 10 increase in speed.

Increasing the beam width won’t get us what we want. It attenuates the power too much. To make the chipsat more effective, we have to change its lightness number, i.e its surface-area-to-mass ratio. Let’s add a skirt, a sort of tiny solar sail, made from that Dupont material, perhaps supported by the chipsat’s own 5 cm antennas, for a 28 cm square patch of thin material. With a density of about 1420 kg/m3, that patch adds only 0.11 mg, an increase so tiny that we can neglect it in the following calculations. And let’s set the beam width at the same number, 28 cm.

Now the chipsat accelerates to LEO escape velocity (11030 m/s) after about 3 hours’ laser firing. And we really don’t need a half dozen lasers after all. The diverging beam actually helps in that regard, bathing the chipsat in ever-widening laser light as it accelerates along the beam, despite whatever imprecision there may be.

So, that’s one way to create an interplanetary satellite-on-a-chip, using what amounts to current laser technology, if we can afford to launch such a laser into orbit and power it. Again, it should be about the size of a large truck, with a solar array not far from what NASA will be building for the asteroid rendezvous mission. But once you do, you can send an unlimited number of chipsats on interplanetary trajectories. And chip the light fantastic.


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s