Monthly Archives: March 2014

All You Need Is Water

water_messier_81

Water, water, water. It’s essential for human settlement of space. Its uses are legion. Astronauts need water to drink. Permanent settlements beyond Earth will require water for crops, medicine, and washing. Water serves as an excellent liquid radiation shield. Or freeze it and use it as a structural material. Water, or ice, can bind other materials, for example producing mud bricks for construction in space. Water-soluble materials might be 3D-printed. Water efficiently, safely, and conveniently stores hydrogen and oxygen for use as rocket fuel. If we remove the oxygen from water—to breathe it—the leftover hydrogen can combine with carbon to produce methane, another rocket fuel and, in liquid form, an even better radiation shield. Water is the basis for batteries known as fuel cells. Water can be a coolant, a lubricant, and a hydraulic fluid.  And it’s non-toxic. Use the water for all of the above, trading off among them as necessary.

In my opinion, if we are to become a spacefaring species, we must direct our exploration architectures, our space technologies, and our scientific investigation of the planets toward a sustainable and coherent vision for space exploration centered on using the resources that are already in space. Chief among these is water.

In the spirit of Spacecraft a Week, let’s think about a single spacecraft that could exploit this abundant resource: a robotic spacecraft that explores asteroids, refueling as it goes.

It’s easy. All you need is water. And water is on the moon, on asteroids, and on Mars. Saturn’s rings are mostly water. Europa has oceans of it.

What makes this design possible is a water-based propulsion technology that Rodrigo Zeledon is developing at Cornell University. His is not the only one. Tethers Unlimited Inc. has done a great job with a related technology. In fact, the basics were well understood decades ago. What has changed is the rise of small satellites and the advances in fuel-cell technology, both of which we can now infuse into new space systems that haven’t been seen before. We expect Rodrigo’s solution to be uniquely mass and volume efficient thanks to a new flight-dynamics concept and simplifications. It would be capable of accelerating a 3U CubeSat by 1000-2000 m/s, unheard of in the early days of space exploration.

A brief aside about Rodrigo’s breakthrough research. The spacecraft has a water tank, where an electrolyzer from a fuel cell uses solar power to separate oxygen from hydrogen. The resulting gas has been given many names over the years. Let’s call it Zeledine. The electrolysis continues until the pressure in the tank reaches about 10 atmospheres (maybe higher in some applications). After that point, whenever the mission calls for thrust, the spacecraft can open a valve that sends some Zeledine into a combustion chamber. The valve closes, a spark plug ignites the gas, and the two reunite as water, shooting out the rocket nozzle with very high efficiency.

Unlike typical electric propulsion systems, there is no need for a battery to store energy. The water itself stores that energy. Unlike cryogenic oxygen/hydrogen propulsion, this technology doesn’t need heavy insulation, cryo pumps, or other hardware associated with keeping the separate oxygen and hydrogen as super-cold liquids. This propellant—water, remember—can be stored indefinitely and even transferred to some other spacecraft with the help of mundane terrestrial technology. And unlike the fuel in other propulsion techniques, the Zeledine is stored as a single fluid, kept separate from the water in the tank by the spin of the spacecraft, just like samples in a centrifuge. That spin has other benefits. It helps cancel out misalignments of the rocket nozzle, gyroscopically stiffens the spacecraft so that a little torque imbalance from the rocket doesn’t tip it over, and guarantees safe and reliable flight dynamics.

Here are some pictures that may help explain how this works on a 3U CubeSat, where one gram of water at a time combusts to produce half-second pulses of thrust.

 

3u_spinner  3ucubesat_cutaway

3U CubeSat with Electrolysis Propulsion.  Left: spinning spacecraft; right: cutaway view

But I have in mind something larger than a CubeSat. This asteroid explorer would be about the size of the brilliantly successful Hayabusa-1 spacecraft, which famously retrieved samples from the Itokawa asteroid a few years ago. Its mass was 530 kg. That spacecraft was able to visit an asteroid, with the help of an Earth-flyby gravity assist, and bring back a sample. It did so with 65 kg of xenon for its ion-propulsion system and another 50 kg of chemical bipropellant for attitude control. It used only 22 kg of that xenon.

For this asteroid explorer, I’ll trade in the 20 kg (or more) that Hayabusa dedicated to its sample return capsule for a drill, a heater, and a hose to melt ice and pump it into the propellant tank. Yes, ice can be found on some asteroids, including Themis (Itokawa, not so much, by the way). We’ll use that subsystem to refuel the spacecraft after it lands.

And I’ll also swap out the three tanks—xenon, monomethyl hydrazine, and nitrogen tetroxide—for one water tank. The Zeledine can serve both to change the orbit (where Hayabusa used xenon) and to impart reaction-control torques (where Hayabusa used MMH and NTO).  Let’s guess that Rodrigo’s solution would need only half of the 70 kg mass of Hayabusa’s electric propulsion subsystem and about the same mass again for its 12 attitude-control jets. Furthermore, we won’t need the roughly 6.8 kg power-processing unit. I also suspect we’ll need fewer batteries than Hayabusa, but let’s leave them alone just for some mass margin. We’ll also keep the solar arrays, which can provide 1400 W to Hayabusa’s propulsion system, along with the rest of the spacecraft. And we’ll design our system to match Hayabusa’s roughly 1250 m/s velocity-change throughout the mission.

Remember, it did so with only 22 kg of xenon propellant. We’ll need a lot more because xenon ion propulsion is much more efficient than water propulsion: it offers a specific impulse of 3000 sec, while ours is about 300 sec. But we save a lot in other hardware. Conservatively, about 218 kg is now available as water storage. That figure neglects efficiencies gained in the tank, which needs not be pressurized as much as Hayabusa’s, and in general plumbing and mechanical bits. Thanks to those mass savings, it turns out we need only another 53 kg of water to achieve the same propulsion performance. The tank volume would have to roughly double, in part because xenon and bipropellant are denser than water, but that’s merely an increase in linear dimensions of 28%. At such low pressure, the tank doesn’t have to be spherical to be mass-efficient, unlike high-pressure propellant tanks one finds on typical spacecraft. So, these water tanks can be any old shape, whatever fits in the unused nooks within the Hayabusa structure.

If Hayabusa could make it all the way to Itokawa and back, I believe this design could make it to the asteroid belt as well but survey asteroids continually, reporting back to Earth when it finds something valuable. I don’t know, platinum group metals, perhaps? DNA? Water, for sure. Some day, NASA may be in the business of buying water from commercial entities, as some entrepreneurs hope. Such purchases are not in NASA’s current plan, but I argue that we need to think quite a bit bigger than the individual spacecraft that we discuss when we talk about space exploration. We need more than a flexible path.  We need a sustainable path, a paradigm that ends our reliance on mass sent from Earth. 

There’s nowhere you can be that isn’t where you’re meant to be. It’s easy. All you need is water.

LEOHive

leohive1

Modestly sized structures in space can be diaphanous. That’s because they’re not subject to particularly powerful gravitational effects or other forces. This fact enables contemporary geostationary satellites to deploy solar arrays longer than the wingspan of a 737 that weigh only a few hundred kg. So why spend weight on making them strong? One reason is that the process of in-orbit assembly might require it. Partly built structures may collapse unless they’re strengthened during the construction process.

These forces can be large in the case of large structures. For example, they can be strong enough to prevent the construction of space elevators with any conceivable materials. So, what if we work with the orbit mechanics instead of against them? It turns out that we could construct very large space structures that can be assembled with the help of spaceflight physics. Let’s look at one example, which I’ll call a LEOHive, to suggest its use as a large-scale habitat in low Earth orbit.

The key innovation here comes from research that Ben Reinhardt and I are conducting at Cornell. We found this interesting principle that tells you where it’s safe to stand on the outside of the space station, among other things. I mean “safe” in that you, as an astronaut, can stand with your feet planted on certain surfaces while the physics of orbits presses you into that surface, albeit very gently. That’s awfully good to know if you find yourself in a Sandra Bullock sort of situation or if you’re just interested in wing-walking.

By the way, those of you who are already fans of the Clohessy-Wiltshire equations will wonder if there’s anything new to this. I’m telling you that both Ben and I have looked, and we can’t find any references that talk about reaction forces on the surface of orbiting bodies, despite that it’s a very simple consequence of these venerable equations.

northsouthorbits

To be clear, two objects in orbit don’t attract one another because of a gravitational pull between them. Let me explain with a thought experiment that involves two astronauts. Say they’re both orbiting in the same circular orbit, more or less around the Earth’s equator. An equatorial orbit lets me say “north” and “east,” and you’ll know what I mean, but the same principle applies regardless of where above the earth these things orbit. Let’s tilt one of the orbital planes away from the other, but keep it identical in every respect. Once they’re in these two intersecting orbits, the two astronauts encounter each other twice per orbit. If one begins north of the other, he or she will eventually pass the other astronaut toward the south, and back up again half an orbit later, forever. The figure above shows these two paths.

Here’s where the Reinhardt principle comes in. If the southerly astronaut extends an arm up to the northerly astronaut, the northerly one can stand on it. The arm reacts the forces that would tend to pull that astronaut southward, without the need for the bottom one to grip the top one at all. In this case, both astronauts now travel on a single circular trajectory that averages the two earlier orbits. If they ever lose contact, they’ll return to their north-south dance.

astronauts

The Reinhardt principle applies to many more situations than only this north-south oriented pair of objects in orbit. In fact, Ben has come up with equations and a convenient picture that shows where, on the surface of an orbiting sphere, an object always feels some inward acceleration. He’s also working on a 3D plot that shows all the places on the International Space Station where something can park in this way.

In particular, the Reinhardt principle simplifies building a large, delicate structure in Earth orbit. It tells you where to place elements of this structure relative to a perfect circular reference orbit so that the components stay put while the glue dries, cement hardens, epoxy cures, genetically modified lichens grow, water freezes, astronauts attach 3D printed rivets, what have you.  Here are the rules:

  • Any component that we place above or below a surface—again, in this north-south sense—wants to press itself into that surface.
  • Any component we place inside or outside a surface—in the direction toward the Earth or deep space —wants to accelerate away from that surface. However, a component placed on the Earthward side of a surface that is outside the orbit (toward deep space) wants to stay on that side, as does its counterpart placed on the spaceward side of a surface that is Earthward of the reference orbit.
  • Any component that we place ahead of or behind a surface—in the east-west sense—feels no need to accelerate toward or away from the surface at all. However, all these rules apply simultaneously. So this rule in combination with the others still allows us to adhere components to one another.

So, consider a sort of rover that assembles truss elements or other large components. It does so autonomously, moving from component to component, adhering them together and moving on while some time-consuming chemical process hardens the structure. Again, that could be any one of a number of ways to adhere structures together. The LEOHive built this way takes shape first in a north-south direction and then extends outward in the other two dimensions leaning on interlocking connections made possible by the placement of earlier components.

Quite a few subtleties remain. As the structure takes shape, its mass distribution should conform to the principles of gravity-gradient stabilization. Long story. Ask me another time. Also, as the rover adds components, the mass center shifts, possibly changing how the rules apply across the structure. Planning the assembly to accommodate these subtleties doesn’t seem like a show-stopper to me, although coming up with a general algorithm will require the attention of at least one interested graduate student.

We do the same sort of thing on Earth, although we don’t typically think very hard about it. We assemble buildings from the ground up, parallel to gravity, because it just makes sense that way. The Reinhardt principle provides the insight we need to establish an analogous process for in-orbit construction.

Dust off the Moon

regolith_rocket

A ready and ample supply of propellant in space sure would be useful, on the Moon or Mars, particularly. What if we could use regolith—the sand or dust present on planetary surfaces—as a propellant, directly? Would a spacecraft accelerated by dust even lift off the surface? If so, could this technique serve as a means of transport from point to point on the Moon?

Maybe you’ve already encountered the idea of a regolith rocket, which is not quite what I’m talking about. But let me describe it anyway. A classic regolith rocket involves preheating the regolith to give it some additional energy and then mixing it with a high-pressure gas. As the expanding gas flows out of the spacecraft, it sucks in and transports, or “entrains,” the regolith particles, thus producing thrust. It’s very similar to a sandblasting machine.

That’s all well and good, but you need to bring that gas with you, perhaps from Earth or from some mining operation off Earth. Once it’s used up, you’ll need to replenish the gas.

I think we can do better. Specifically, we can accelerate the regolith without any entrainment, without adding a gas. A vehicle with such a propulsion system could take off and land repeatedly without needing to recharge a tank of working fluid. It would scoop up dust to refuel. That’s all.

How would such a regolith-only propulsion system work? I propose a design that uses a mechanical pump—a fan or turbine—that expels the regolith from the back of the rocket as the propellant. Let’s consider the specific case of a lunar transport. Clearly there’s no lunar air with which to blow the regolith through the rocket. I’m thinking of a turbine that mechanically accelerates the regolith that falls into it from a hopper, or a tank, thanks to gravity. Unlike a classic regolith rocket, the regolith here provides all the mass flow, and a source of power on the spacecraft provides all the energy to spin the turbine.

Here’s a potential problem. In the process of moving the regolith through the turbine, the blades might ablate somewhat. So, one goal would be to choose a material for those blades that is tough enough to withstand all this internal sandblasting for the duration of liftoff and landing. However, it turns out that if the dust can be sifted down to particles of 20 microns or smaller, we don’t need to take any extraordinary measures. Even terrestrial turbine blades aren’t damaged by such tiny grains. They carry too little energy to impart stress in the blades beyond the yield strength of the material.

Another issue: how do we get the regolith into the turbine? You have to fill up the tank somehow—a shovel and a sieve?—but then mere gravity feeds the regolith into the fan, just like it pulls sand through an hourglass. As the spacecraft lifts off and accelerates further under the power of the engine, the mass flow rate could be allowed to increase naturally or could be throttled back with an adjustable aperture, depending on which is more efficient.

Now let’s look at a design that may support lunar businesses, i.e. commerce among Moon bases. I’ll describe the design of a printer-size transport vehicle: 10-20 kg total mass. Sure, there is probably some economy of scale that would make a larger vehicle more efficient. But let’s take this small example to be an existence proof for a larger one. Also, this little one is inexpensive enough that a person might actually build and test a prototype in the near term. (Or maybe someday Amazon will want to deliver little packages via drones on the Moon, too. They’ll see the wisdom in this idea and will come knocking at the door of my lab at Cornell looking to sponsor the research. One can dream.)

Let’s first consider a lunar transport design that offers very low specific impulse (abbreviated Isp, a measure of the efficiency of propulsion). This transport hops, if you can call kilometer-scale trajectories “hops.” The engine expels propellant at 0.14 kg/s and lifts off at an angle of 45 deg. to the vertical, which optimizes the trajectory for distance. It accelerates until it reaches maximum speed at an altitude of about 540 m. Doing so expends about 74% of the propellant, at which point the engine shuts off. The transport continues to coast ballistically, through a peak altitude of 940 m, and then drops down to 390 m altitude, at which point regolith is fed into the turbine once more. Applying that final thrust slows the descent, and the vehicle comes to a stop at the surface of the Moon. It lands 3.7 km from its starting point, if it’s carrying no load. The flight takes only a minute or two. Carrying a payload means sacrificing some of the regolith propellant, so that the total mass can still lift off. And less propellant leads to shorter trajectories, of course.

The vehicle is designed to carry 13 kg of propellant, which is enough to accomplish these hops. The rocket equation tells us that this 0.14 kg/s mass-flow rate, with an exit velocity of 240 m/s, leads to an Isp of 24 seconds. That Isp would be shamefully low for a chemical propulsion system, where Isp is typically in the hundreds of seconds. But remember—the propellant is everywhere you look. A scoop and a sieve constitute the gas pump here. This convenience comes at the cost of efficiency, but I think it’s a good trade for this particular concept.

Limitations on the speed of the turbine ultimately drive the design. The speed at which a turbine rotates is limited by the tensile strength of the material that it’s made of, as well as the bearings that support the rotating portion. The AMT Mercury small turbine for unmanned aircraft, for example, is designed to rotate at 151,000 RPM. Let’s base our Moon transport design on this turbine, but I’ll assume that we can boost its rotation by about 20%, for 181,200 RPM. It will need considerable redesign so that the flow is straighter, since the goal here is not to compress gas but simply to accelerate the particles. But I hope that this example suffices as an estimate of the weight. They say it’s about 2.2 kg for this great little turbine.

We’ll model the turbine blades so that the twist along the blade length reaches 45 deg. halfway along each blade. Using two turbine stages might be important so that the expelled propellant doesn’t carry significant angular momentum, which would be in the same direction as the rotation of the turbine that imparts its axial velocity. That momentum would cause the vehicle to spin up in the opposite direction, and that spin would be difficult to dissipate before the vehicle lands. This simple model has the propellant exiting the turbine stage(s) at an axial velocity equal to that of the blade midpoint in the plane of its rotation: i.e. the dust bounces off the 45 deg. angled blade and acquires an axial speed equal to the blade’s lateral speed when they were in contact.

As the regolith passes through the blades, it tends to slow down the turbine. The power required to keep this turbine spinning is roughly equal to the change in energy of that accelerated dust. With a mass-flow rate of 0.14 kg/s, accelerated to 240 m/s, the change in kinetic energy (or power) is 3.98 kW. Let’s use a 4 kW electric motor to provide this power. A nice brushless DC one is available off-the-shelf and weighs only 3.3 kg. We’ll also need a transmission of some kind that gears up the 8000 RPM peak rate of the motor to the 181,200 RPM that the turbine demands. Prof. Brandon Hencey at Cornell tells me that some aircraft-engine turbines, e.g. from Pratt and Whitney, include a transmission that reduces speed, sometimes for noise purposes. Our vehicle would use a similarly designed transmission but run backwards so that the gear ratio allows the motor to drive the high-speed turbine.

Batteries. Ah, batteries. It is my belief that the highest-priority technology advance for space technology is increasing energy density (J/kg) and power density (W/kg). So many extraordinary systems would be enabled if arbitrarily large energy storage were possible and if it could be expended as power arbitrarily fast. That technology development is not necessarily NASA’s responsibility, though.  Using commercially developed technologies might be the fastest way to see improvements. Today the best lithium-ion batteries provide about 360,000 J/kg. They’re very slow to discharge, i.e. to expend their energy. That discharge rate is limited to 10-15 A, which means that the energy drools out over the course of half an hour or longer. The 13 kg of propellant in this design has to be expelled over the course of only 93 seconds. So, ultracapacitors are better choices than batteries here. They’re less mass-efficient in storing energy (only 230,400 J/kg) than lithium-ion batteries, but they can discharge quickly enough to impart the power that the motor demands. These ultracaps total about 1.6 kg. Another alternative would be flywheel energy storage. Interesting as it may be, this technology is not much more appealing than high-performance ultracaps when you take into account the hardware necessary to make the system work.

The motor, batteries, turbine, transmission, electrical harness, mechanical components, and propellant of our lunar transport total 18 kg. The thrust available from the engine is 34 N, which means that the 20 kg vehicle taking off in lunar gravity has another 2 kg available for everything else: tank, structure, guidance sensors, solar cells, flight computer. That’s not much, perhaps, but remember that the “tank” is just an unpressurized bucket, and other than the batteries discharging, there is no thermal activity on this vehicle to require special materials, insulation, et al. This tank needs to hold 13 kg of regolith powder, which (at 1800 kg/m3) could fit in a cube 20 cm on a side. And the electronic guts of a CubeSat (no more than 0.5 kg worth of boards and solar cells) should be sufficient for the rest of the electronics.

One more thing. This spinning turbine will take time to reach full speed. There is likely a lot of kinetic energy stored in the turbine itself. I propose that solar power be used to charge up the ultracaps and spin up the turbine while it’s on the ground, without expending energy from the batteries that would be indispensable in flight. Once it’s spinning, a single-stage turbine would helpfully store angular momentum that gyroscopically stiffens the attitude in response to disturbances, such as misalignments of the rocket engine or liftoff and landing perturbations.

This low-Isp design is based on a 2.5 cm radius turbine, in which the regolith impacts the blades at, on average, about halfway along their length. Now, let’s consider a higher-Isp design. A 4 cm-radius turbine gives the regolith higher exit velocity: 380 m/s instead of 240 m/s. However, for the same 4 kW electric motor, the system is a lot lighter: only 11 kg, of which 4.6 kg is propellant. The higher exit velocity means that more power must be applied to a given amount of regolith, and that requirement limits the total performance. The mass flow rate must drop to 0.055 kg/sec, and the total engine on-time to 83 sec. The upshot is that the trajectory of the higher-Isp design is only about half as high (460 m) and half as far (1.9 km) as the low-Isp vehicle. What we see here is a classic trend in propulsion design: that you pay a power penalty for higher efficiency. And that’s why in-space propulsion is often electric, and launch propulsion chemical. No current electric-propulsion technology can even lift its own weight on Earth. This regolith transport concept lives in a sandy border town between the two.

So, dust off your plans for lunar colonization. Now we have a way to deliver water, rare elements, spools of 3D printer material, and really just about anything to neighboring lunar outposts, in small batches at least. The demonstration-scale vehicle described here may be a precursor to a much more capable, larger transport vehicle. And thanks to bypassing chemical propulsion systems and avoiding the use of refined materials and expendable matter from Earth, we may have found a pretty cheap way to fulfill lunar e-commerce orders.

Tag the Sky

clowes

How about a constellation of small satellites that serve as pixels in an orbiting display?  We could use that for skywriting in orbit.

It turns out that you can see an LED shining from space, at least with binoculars. FITSAT-1, designed by students at Japan’s Fukuoka Institute of Technology, proved it. That spacecraft was an elegantly designed project that shows how clever use of commercially developed technology can inform completely new ideas in spacecraft architecture. In fact, the FITSAT mission opens up the possibility of low-cost optical communications for the masses. At one end—the technological leading edge—NASA’s recent success with the Lunar Laser-Communications Demo sets a high bar for deep-space communications with light. At the other, FITSAT shows what you can do with some elbow grease and some smart students. And I have a feeling they’ll do even better in the years to come.

In fact, FITSAT wasn’t the first to write on the cosmos. Two months before FITSAT launched in 2012, NASA’s Mars Science Lab rovers imprinted the red planet with Morse code that spells out J-P-L. And a decade before MSL, many of us sent our names to NASA for inclusion on the Cassini mission, which carried them to Saturn on a DVD. Maybe it was Carl Sagan and Ann Druyan who started it, sending that gold record into space on Voyager, with the thought that some distant civilization might find it and learn something about our race, by that time likely long gone. But however we might trace this history of writing in space, FITSAT brought home to us the idea that personalizing space and communicating through light is within reach of all of us.

Sure, it’s true that these bright LEDs are a form of light pollution, and astronomers probably aren’t keen on that. However, I would point out that the diodes can be chosen to emit light in very narrow bands, and even in regularly spaced pulses like FITSAT did. That sort of specificity would provide astronomers with a digital means to filter out the LED signals, if there’s a risk that they’ll compromise science. But to the naked eye, these flashing lights can be much more than noise. They can be art.

With dimensions of 10x10x10 cm, and a mass of only 1 kg, many CubeSats can be launched at once. FITSAT itself was part of a group of three 1U CubeSats launched from the International Space Station in one go. This feature confers a very powerful advantage: a constellation of CubeSats can be launched and can begin performing formation maneuvers almost instantly, without needing to catch up with one another the way they would if members of the constellation were launched separately. Some initial activities—maybe a day’s worth or two, at most—and the spacecraft would be ready for operations.

Let’s create a constellation that is basically a matrix of dots, and we’ll take as our guide the venerable Epson MX-80 dot-matrix printer. Its print head consisted of a 9×9 pixel array. So, we’ll need 81 CubeSats for 1980s-caliber printing. How far apart? The Moon subtends an angle of 0.54 deg. in the night sky. And I think you’ll agree that the moon is plenty noticeable. Let’s go for half that width, about 1/4 deg. So, in LEO—specifically, at the ISS altitude of 325 km—the spacecraft would be about 158 m apart.

At this altitude, the constellation flies overhead quickly. The CubeSats orbit the Earth in about 90 minutes, and they’re visible from a given city for not much more than 10 minutes. So, it is tempting to consider what such spacecraft would look like if they were in geostationary orbit (also known as GEO). At that altitude, 35,768 km above the surface, spacecraft in orbit travel as slowly as the Earth rotates. So, this constellation would remain fixed overhead. That’s convenient, but for the LEDs to seem as bright as they do in LEO, they would have to put out over 12,000 times the power. I suppose one would simply use 12,000 as many LEDs, and the spacecraft bus to power them would resemble a high-end geostationary communications satellite. Remember, though, that we are contemplating 81 of these things. At well over a hundred million dollars each, not including launch cost, a constellation of GEO spacecraft would be dauntingly expensive. It would cost about as much as the James Webb Space Telescope, with hardly that level of scientific impact. So, I think LEO is the way to go.

The tricky thing about formation flight is that you can’t have an arbitrary arrangement of satellites travelling with exactly the same velocity. Three subtleties come into play. (1) The spacecraft need to orbit the Earth in the same time; if they don’t have the same orbital period, the constellation drifts apart. But since orbital period isn’t affected by (2) inclination (tilt) or (3) eccentricity (non-circularity) of the orbit, we can use those parameters to define the shape of the constellation.

The spacecraft in row 5, column 5 of this 9×9 matrix is in the middle. Let’s say that this single spacecraft travels in a circular reference orbit. The others are orbiting at the same period, either ahead or behind the reference orbit, above or below it (in a north-south sense) or inside/outside of it (in an altitude sense). With the right combination of slightly perturbed, non-circular and/or inclined orbits, we can create a constellation that resembles our desired shape. Many spacecraft will be switching places once per orbit, some of the constellation seeming to rotate around a line from the center of the Earth to the reference orbit.

This dance is a straightforward consequence of the Clohessy-Wiltshire equations, which describe the motion of an orbiting body relative to a circular reference like the one we have here. The CW equations describe relative orbital motion, which we perceive as an interaction among spacecraft that happen to have the same orbital period, although in fact there is no gravitational attraction among these satellites that causes their motion.

CubeSat_tag

The figure above suggests a matrix of such CubeSats (larger than they would appear, given their relative spacing). Their attitude need not be particularly well-controlled as long as the LEDs emit a wide beam, and neither is their relative position. As shown, the 9×9 matrix is arbitrarily rotated and is displaying a symbol. Each needs to know its position in orbit so that the constellation, collectively, can produce the image that ground operators have sent it. That is, each one would illuminate its LEDs, or not, depending on its position and the time at which the constellation is supposed to create a certain image.

Flight software would make all this possible. A key ingredient is position knowledge, which would be available from GPS measurements. For example, at Cornell we built CUSat, a pair of satellites capable of detecting their absolute position in orbit to within a few meters. Their relative position would have been known to within a centimeter or so, had the flight computer not overheated and ended the mission prematurely. All that position detection took was a couple of homemade GPS boards, courtesy of the late Paul Kintner‘s lab, and some software conceived by Shan Mohiuddin, one of Professor Mark Psiaki’s students.

We’ll also need some propulsion. Options include electrodynamic tethers, cold-gas propulsion (prohibited by the CubeSat spec, for the most part), and electric propulsion. There are many forms of electric propulsion, but among those I am partial to solutions that involve ionic liquids for their power efficiency and scalability. Or, for a much lower-cost solution, Rodrigo Zeledon has figured out an innovative way to use water for propulsion: the ultimate cheap, green propellant, and compatible with the CubeSat spec.

Having a constellation that can illuminate part of the sky on command offers many interesting possibilities. Here are a few:

  • More is better. A much larger constellation—higher resolution—takes us from dot-matrix characters toward a jumbotron or video billboard in the sky.
  • The opportunities for art are legion. I’ll suggest only one. What if the constellation could behave in a way that seems to interact with the stars as it passes them? The constellation’s light might shudder, change color to blue, or twinkle as it passes an exoplanet. It might warm to the rising sun by changing color, or it might show a sequence of images that resemble Apollo’s chariot. In the case of higher resolution, maybe our formation responds to passage through an astronomical constellation by acting out some scene from Greek mythology.
  • A news crawl in the sky? There might be a business case for this concept.
  • Astronomy lessons: as the constellation passes a particular celestial object, seen from a specific region on the ground, it identifies the object and offers information about it. In fact, if we use the FITSAT trick of high-frequency modulation of the LEDs, we might be able to transmit simultaneously in different languages, asking only that the user look through binoculars with blinking apertures (like 3D shutter glasses for some home TVs), unique to his or her language.
  • A game in which people on the ground can aim a laser pointer at the constellation—not recommended when aircraft are present—with the goal of interacting with the light: turning on or off LEDs, or changing their color. The constellation would be a blank canvas, and we Earthlings could paint on the night sky.
  • Interaction like this raises the possibility of a game—maybe celestial 囲碁 (Go), requiring only two colors of LED, to be played in tag-team fashion by those who see the game board pass overhead.

I take the FITSAT existence proof to be enough to convince folks that a 1U CubeSat could be capable of certain aspects of this mission. Propulsion and additional power may require another 2U worth of spacecraft bus volume and mass. At $100K to launch these 3U CubeSats, it’s over $8M simply for the launch cost. Traditionally, one might double that cost as a very rough estimate that accounts for the space hardware. Include the resources for ground stations, and let’s guess a $20M investment is needed for a commercial enterprise that could tag the night sky with Earthlings’ celestial musings.