Stochastic Exploration

There’s strength in numbers.  Many hands make light work. The whole is greater than the sum of its parts. It takes a village to explore the solar system. These aphorisms are so familiar—well, three of the four, anyway—that we rarely recognize their potential to change how we think.

So, let’s recognize it. What would it mean to explore space the way that cottonwood seeds and maple samaras drift across the landscape, blown randomly and yet ensuring that some small number of new saplings take root? What if we could use sheer numbers of spacecraft to design a mission that reaches its target—not focusing on high-precision trajectory control but seeking a statistical guarantee that some fraction of the many spacecraft arrives at the intended destination? Let’s take this idea further. What if the destination were a region of space? The entire solar system? What space-system architecture would guarantee good odds that one of our many spacecraft would encounter a celestial body?

What makes this idea even remotely credible is the possibility that someday soon we’ll see some very small spacecraft. Launch costs are what they are, and the U.S. Congress is willing to budget relatively little for new ideas in space. So, for the foreseeable future, the only way to put more spacecraft into orbit is to make them smaller. Sprites are a start. They’re one way to do more with less. The current Sprite technology demonstrator weighs about 5g. I’m confident we can knock that down to 500mg if we could find the resources to support that technology development. (The fact that there is so little funding—public or private—for this kind of research is one reason for the blog. So, I might as well put these ideas out there for free).

Let’s posit that the SpaceX Falcon Heavy will be able to launch 10,000 kg on our desired Earth-escape trajectory. SpaceX expects that it will carry 13,200 kg to Mars. So, a lighter, 10,000 kg payload would go even farther. And let’s say that 30% of this payload has to be dedicated to spacecraft infrastructure, such as something to tie the Sprites together and later deploy them, as well as communicate with the ground at the time of this event, which takes power, and thermal control, etc. The remaining 7000 kg worth of 500mg Sprites would comprise 14 million individual explorers.

Some of us have been thinking about this idea for a while: Cornell graduate students Lorraine Weis and Zac Manchester, for example. Zac wrote a paper about some of the mathematics.  Lorraine is working on ways for a large number of such spacecraft to exploit solar pressure and other subtle physics.

Here’s how it might work.

A mothership launches on a Falcon Heavy. It’s a 10,000 kg spacecraft that includes 100 kg worth of solar panels to power a 10 kg communications subsystem, a 50 kg traditional propulsion subsystem, another few hundred kg of other structural and electrical bits and hardware for guidance and navigation. Those spacecraft-design details are straightforward. Here’s what isn’t. About 2500 kg of material is an ultraviolet-degradable binder (if you’re an applied chemist), or mortar (if you’re a mason), or matrix (if you’re a geologist). This mortar is shot through with Sprites. They are frozen in temporary amber, which keeps them safe during launch and enables them to travel together after the launch vehicle upper stage separates from the mothership. Or maybe they’re like pineapple chunks in Jell-o. You get the picture.

Operators on the ground design a trajectory-correction maneuver of some kind, upload it to the mothership, and initiate it. Now the mothership’s job is done, and the Sprites are en route to somewhere. They should head for the nearest on ramp to the Interplanetary Transport Network. The ITN is a chaotic, multidimensional set of gravitational pathways through the solar system. Gravity from the Sun and planets is partly responsible for its existence. So is the rotational churn of the planets as they orbit the Sun. These pathways are hard to predict exactly, and no spacecraft has ever tried hitching a ride.

Until this Sprite mission. Arguably some of NASA’s interplanetary spacecraft, like Cassini, leverage parts of the ITN to cut down on propellant and enable them to travel to the outer planets affordably. However, it’s risky to depend on the ITN exclusively because of its mathematical subtlety and its chimerical behavior—risky for a single, exquisite, expensive spacecraft anyway.

For our 14 million Sprites, it’s another story. As the Sun’s ultraviolet radiation washes over the block of Sprites, the UV binder evanesces. The Sprites begin to flake off, and the individual Sprites fan out. The process resembles how the Sun’s heat and pressure burns off ice from comets, producing that characteristic tail. And like a comet’s tail, these Sprites roughly follow their siblings for a while. As time passes, their paths diverge. Differences among the individual Sprites’ flight dynamics separate them. The first Sprites to flake off end up at the statistical extremes. So do the last ones.

The “average” trajectory here is a slippery concept: the mean or median of this statistical distribution involves a cloud of Sprites, and we need to describe its motion with at least six coordinates (Kepler’s orbital elements, for example) or through even subtler mathematics like statistical moments. The goal is to put the average close enough to the trajectory we want that the number of Sprites on slightly different trajectories compensates for unexpected disturbances. Those disturbances would prevent a typical, single spacecraft from reaching its goal. In stochastic exploration, they’re part of a blurred reality in which we design the odds. And thanks to the number of chances, the number of spacecraft, the mission architecture confidently meets those odds.

Assuming we’ve licked the problem of how to plan the trajectory of a cloud of particles, we now have a cloud headed somewhere interesting. How about Jupiter? It’s well known that the combined gravity of Jupiter and the Sun trap asteroids—the so-called Trojans. Their orbits reside in a permanently stable tidepool in the planetary ocean. We call it a “Lagrange point.” Maybe some Sprites end up there. Others may slip past and begin to orbit Jupiter, where they slow down thanks to electrodynamic drag and collisions with gases found among Jupiter’s many orbiting moons. Over time they encounter those moons and the spaces between. Some likely end up entering Jupiter’s atmosphere.

Another aphorism: if a tree falls in a forest and no one is there to hear it, does it make a sound? We could ask, “if a Sprite encounters a planetary body but transmits nothing back to Earth, have humans explored?” A few of us think the answer is “yes.” But, you know, some scientists are all “me, me, me.” For these solipsistic types, let’s consider a couple of ways for these interplanetary Sprites to tell us what they’ve found.

Taking a page from the Kicksat mission, we could use a matched filter to detect special gold code pseudorandom sequences, each a unique signature emitted by one of the 14 million Sprites. The Sprite ground station’s special brand of signal processing helps it pick out a Sprite’s faint transmissions from all the other noise. The longer the code, the better—that is, the greater—the signal-processing gain. And there’s another reason for a long code: each Sprite should have a unique signature, and creating 14 million unique codes demands that they be long. In fact, if it’s to be like the Kicksat Sprites, we’ll need 28 million codes—a 1 and a 0 for each spacecraft. Each would be about 10 gigabits long.

Solar power might be sufficient for spacecraft on ITN pathways among the inner planets. Near Jupiter a more likely choice would be a nuclear power source, a betavoltaic battery. Widetronix, a start-up in Ithaca, NY, is developing this technology, and they’re already able to power integrated circuits with a microchip-scale nuclear source. Some of their batteries have half-lives of a century. So, a nuclear Sprite is well within the realm of possibility. What’s more, it could last far longer than most of the engineers who designed and launched it.

But let’s say that nuclear power is off the table. How about scavenging the energy of impact? When a Sprite strikes an asteroid, for example, a piezoelectric layer in its structure deflects and produces high power for a brief instant. In that instant, current flows through an analog circuit designed to emit a short, high-power pulse at a specific frequency. The Sprite’s swan song is a transmission that confirms an impact (in this case something very short, nothing like the 10 gigabit sequence of that nuclear design). That information could be useful in figuring out the statistics of the Trojan asteroid population—how many, how big, and where they are. How about we design this analog circuit to include a device whose inductance varies with matter that happens to adhere to the Sprite during its voyage? Maybe electrostatic charge makes it stick. That variation would alter the frequency of this swan song. When we detect it, such a transmission might reveal something scientifically novel about interplanetary gases or particulates.

How we ask the question can determine the answer. Rather than asking “how can we build a spacecraft to take high-resolution images of Trojan asteroids,” we might ask “what science can you do with tiny sensors that offer a statistical guarantee of asteroid collisions?” The latter is a question that demands more from our imaginations. It’s the kind of question we need to ask more often.