Technologies for Asteroid Capture into Earth Orbit

The following is my presentation “Technologies for Asteroid Capture into Earth Orbit” given at the International Space Development Conference in Huntsville, Alabama, on May 19, 2011.

The focus of this presentation is on a specific technical approach which enables us to capture an asteroid using essentially current technologies; the missions, tools, and complications of that approach; and then some asteroid selection criteria and a few specific asteroid capture opportunities.

Using the asteroid 99942 Apophis, I outline a possible capture mission, its requirements, and a timeline.

So why capture an asteroid? The main reason is to gain convenient access to its resources. Even a relatively resource-poor low-iron, low-metal LL chondrite contains 20% iron, significant quantities of water and other volatiles in the form of minerals such as clays, and oxygen to burn.

The asteroid Apophis (likely one of those LL chondrites) contains enough materials to construct about 150 five-gigawatt solar power satellites at 25,000 tons of steel and silicon each, plus Kalpana One style habitats for 100,000 people, all shielded by the slag remaining after iron is smelted out of asteroid ore. The oxygen freed from iron compounds during smelting amounts to well over a million tons more than is needed for the habitats, valuable fuel mass for ion thrusters to move the habitats and solar power satellites into their chosen orbits and to spin them up.

Of course, a space habitat providing food, water, oxygen, fuel, construction supplies, gravity, radiation shielding, and skilled human workers situated above much of the Earth’s gravity well is an ideal platform from which to continue the exploration and exploitation of space.

And we should not forget that placing an asteroid into a stable Earth orbit prevents it from colliding with the Earth.

So, how do we capture an asteroid? Even a tiny one masses millions of tons, and we don’t yet have the technologies to manhandle them and put them wherever we want. Luckily, we don’t have to. When a spaceship or asteroid passes close to a planet or large moon, its orbit is changed, sometimes dramatically.

In principle, the Earth can impart a delta-V of up to 60km/s to an asteroid in orbit around the Sun, although in practice the limits are a small fraction of this. More importantly, small changes in the position or timing of an existing close approach are enormously magnified.

We aren’t limited to the Earth, in that close encounters to other planets might be used to alter an asteroid such that it passes close to the Earth at a later time where its orbit can be further tuned by the Earth’ gravitational field.

If we can adjust the asteroid’s orbit such that it makes a subsequent close approach to the Moon with a relatively low velocity, the resulting slingshot can drop that asteroid into an Earth orbit. The Moon can (in principle) remove up to 2 km/s of velocity relative to the Earth, although less is easier.

A point I’d like to emphasize: In my opinion, gravitational slingshots are as much art as engineering, especially when considering the variations involved in multiple slingshots around one or more bodies. The people who dreamed up the Cassini and Messenger missions are both geniuses and artists, and I have every confidence that they can find suitable mission plans to capture any potentially hazardous asteroid into Earth orbit, although the missions may be very long and complex thanks to a shortage of appropriate close encounters and/or the need for significant changes to the asteroid’s orbital parameters.

When selecting an asteroid for a potential capture, the most important consideration is simply the proximity of an asteroid’s orbit to a useful keyhole through which the orbital engineers can design a capture mission in a reasonable timeframe.

The second consideration is the size of the asteroid. Bigger is not better when a 1 kilometer asteroid masses fifty times as much as Apophis, and thus requires a fifty-fold increase in the product of mission time and fuel mass. On the other end, a small 120m LL asteroid massing 2 million tons (and relatively poor in useful metals and volatiles) still has sufficient materials to build a single small Kalpana One style habitat for 8,000 colonists plus a dozen 5 gigawatt SPSs. Thus I view 120 meters as the smallest asteroid worthy of (first) capture, since it is barely large enough to build a permanent habitat rotating at 3rpm for Earth-normal gravity and with adequate radiation and meteoroid shielding.

Another consideration is the V-infinity of the asteroid, because slower asteroids are easier to move a distance large enough to make a significant difference in the slingshot.

The potential magnitude of a gravity assist is also constrained by how close to the center of the Earth the asteroid passes – and I think it’s important to keep it out of the lithosphere. Also, for a rubble pile we don’t want to pass closer than the Roche limit or the asteroid may be torn apart by tidal effects, much as Jupiter’s tide tore the comet Shoemaker-Levy into 20 fragments. The actual Roche limit depends upon density, but is likely to be of the order of 20,000 kilometers for a rubble pile asteroid passing near the Earth, and perhaps 5,000 kilometers for the Moon.

One might think that the composition of an asteroid would be the number 1 criteria, but in reality most asteroids should be quite valuable (see Mining the Sky by John S. Lewis). A common carbonaceous chondrite might contain 25% nickel-iron mostly in the form of metal grains, 10% water, and several percent carbon plus everything else needed for life in space. But even a lowly LL chondrite will work.

The last consideration here is the opportunity for intercept missions. We need to modify an asteroid’s orbit when it is easy, some months or years before the targeted close approach. This is difficult for a high-inclination or long-period asteroid because it might only approach closely enough to the Earth for low-delta-V intercept missions once every ten or a hundred years. But an asteroid with a two-year period might present suitable launch windows every two years. Also, for asteroids with periods close to a year and with low inclinations, there may be two launch windows per year as the asteroid passes inside and then outside the Earth’s orbit.

This table presents some possible asteroid capture candidates as of 25-APR-2011, all brighter than 24^th magnitude and expected to pass within 120 Earth radii in the next 50 years. Some of these may be eliminated by further refinement of their orbital parameters, while others can likely be added as new asteroids are discovered, or as orbits are corrected for known ones.

The entries on this table were gleaned from the Near Earth Object Close Approach database. The various tables, databases, and lists at the NASA web site are inconsistent, sometimes even on the same page. For example, the orbit visualization tool often has significantly different closest approaches than the “close approach” data on the same page.

A side note: Many asteroids have only been observed over a few days, resulting in large uncertainties in their orbital parameters. The shapes, diameters, and masses of most asteroids are estimated, not known. Diameters are estimated from an asteroid’s brightness and distance. But we can’t measure the actual albedo, and observations at multiple wavelengths are used to judge the asteroid class, and from that a typical reflectivity, and from that a formula results in an estimate of the diameter, and assuming an average density, we calculate the mass. This process has extremely large error bars. In April of 2010, radar imaging resolved the asteroid YU55. Previous estimates were that its diameter was 140 meters and its mass 4Mt. The actual measurement revealed a diameter of 400 meters and an estimated mass of 87Mt, a 22 fold mass increase.

Let’s consider these asteroids.

Apophis is fairly well characterized, although it may not be an LL chondrite, and may therefore have a different albedo, diameter, and mass. As a candidate for Earth-orbit capture, it has the advantages of passing quite close, and relatively slowly, plus launch windows occur in Aprils and Octobers near close approaches, suitable for a 1, 1.5, 2, or 2.5 year mission. It masses 27 million tons, roughly twelve times larger than the minimum useful capture size.

2001 WN5 is a bit on the large side, but it may pass about halfway between the Earth and Moon in 2028 which offers an opportunity to adjust its subsequent Earth approaches in 2037 and 2046. But being more than 20 times as large as Apophis means a lot of fuel is required, so 2001 WN5 will have to wait for a later, poorer opportunity, probably with a robotic mission.

2005 YU55 is three times as massive as Apophis, and approaches Earth, Venus, and Mars, giving multiple possibilities for gravity assists. Next year it will pass about 20% closer than the Moon’s orbit, but it won’t be that close again for quite a while. It makes frequent approaches, about every 11 years, with relatively close approaches in April of 2021, 2032, 2043 (etc), and in November of 2022, 2033, 2044 (etc). We can likely tune one close approach to allow a closer approach 11 years later that can lead to a capture 11 years after that.

1999 AN10 is a large (50x Apophis), fast, and dangerous asteroid which will pass about as close as the Moon in 2027. It is large enough to build 7,500 5-Gigawatt Solar Power Satellites, or to house 2 million people in a 2 mile diameter habitat. Actually, we can solve Earth’s energy problem for the next thousand years AND build a habitat for one million people, with materials to spare. While it is difficult to capture, it should be worth the effort.

2009 WM1 is only half the size of Apophis, and should be easy to capture some fifty years from now at its next close approach.

Lastly, 1999 RQ36 is 7 times the size of Apophis and passes 1.2 Lunar distances from the Earth in 2060. It, too, won’t be easy to capture, but is also worth the effort.

I’d like to point out that every one of these asteroids were placed into their current orbits by a slingshot around the Earth, a fact clear at a glance at the orbital simulation on the NASA web site. One of the principles of orbital mechanics is that an orbiting body (in a 2-body system) will always return to the altitude and velocity vector of its last orbit change. Ignoring hyperbolic orbits, one near Earth pass means more, until the body collides with the Earth or is deflected away by another planet.

Note, too, that capturing Apophis in 2029 would provide ample fuel to capture those big asteroids a few decades later.

But it seems that nothing is ever simple. Part of the problem is that we don’t really know much about asteroids. Many of them appear to be rubble piles, and in some cases these spin so rapidly that their shape is constrained by their spin, yielding flying-saucer shapes. Others are contact binaries which might be exceptionally awkward to manipulate. We have more options with solid bodies, but we can’t plan on that.

So how do we apply thrust? Two ways come to mind: dock and push, or use a gravity tractor to pull. Gravity tractors can only apply tiny amounts of thrust, but that might work, especially on longer missions. It would also help to dangle heavier components such as nuclear reactors and fuel as close as possible to the asteroid, with the thrusters some distance away so they can aim off to the side without much loss of thrust efficiency. But a 1,700 ton mass dangling 170 meters from the center of Apophis would be needed to apply the necessary delta-V over a 10 month period. Gravity tractors generally require very long missions.

We can dock with an asteroid and push against it in a traditional way, but there are complications due to microgravity and asteroid rotation. It is possible that a number of cables could be looped around the asteroid to hold the tugship securely in place. Even then, a spinning asteroid means that thrust can only be applied during a fraction of each rotation, wasting thrust and fuel to the extent that the applied thrust isn’t directed in the correct vector.

Let’s consider a specific example. The asteroid Apophis will approach Earth to within 30,000 kilometers on April 13, 2029, significantly inside the orbits of our geostationary satellites. If we do nothing, the Earth’s gravity will slingshot Apophis into a new orbit as it deflects it by about 28 degrees and boosts its velocity by 3.04 km/s. The result of this is that Apophis changes from a 0.89 year period Aten class asteroid orbiting mostly inside the Earth’s orbit to an Apollo class asteroid with a 1.167 year period and an orbit mostly outside of the Earth’s. I should point out that we don’t yet know with any degree of certainty exactly what the resulting orbit will be, because tiny changes in the position of closest approach have a huge impact on the resulting orbit. The period I’m quoting here corresponds to the keyhole that targets an Earth impact in 2036.

My main point is that delaying Apophis’ arrival at the Earth’s orbit by changing its velocity by only 10 cm/s results in a 1.5 km/s reduction in delta-V - a velocity gain of a factor of 15,000. I chose that particular slingshot because it results in a semi-major axis of exactly 1 au, with a period of 1 year. I used a program named GravitySimulator by Tony Dunn to model several Apophis orbit variations, and simultaneously to gain a true appreciation of the art and genius needed to find useful orbits.

The Tisserand criterion indicates that it’s possible to change Apophis’ eccentricity to zero at the same time, although that would result in an inclination of about 10.5 degrees, and requires a much larger delta-V. In any case, what we really want is not a near-Earth orbit, but rather a subsequent low-speed slingshot around the Moon to remove excess velocity and drop the asteroid into Earth orbit. That may require some finesse and multiple slingshots, but I’m confident it can be done. Look at the success of Cassini, Messenger, and other missions that have relied on gravity assist slingshots to achieve what once was considered impossible for our current technology.

We still need to give Apophis that 10 cm/s nudge. I don’t suggest abrupt changes from nuclear bombs or high-velocity impacts, partly because we need finesse to fine-tune the orbit, and that’s best done by the equivalent of titration. We need a tugship, a long-mission, highly fuel-efficient spacecraft to gradually move the asteroid into a new orbit.

Magnetoplasmadynamic or VASIMR thrusters are likely the best choice to apply delta-V, as their high exhaust velocities reduce the total fuel mass needed, they can generate significant levels of thrust, and they should be able to achieve sufficiently high reliability.

Of course, we need to push or pull the asteroid, which isn’t simple, partly because they are rotating, undoubtedly along an inconvenient axis. And they have enormous angular momentum which we can’t simply cancel. This means we’ll either have to dock – not land – at an appropriate location and thrust a fraction of the time, or use a gravity or magnetic tractor approach which might limit us to lower thrusts and longer missions.

Note that ion thrusters take copious amounts of energy. 25 megawatts can be generated by a 300 by 300 meter solar array, or by a single compact nuclear module available commercially. We do have a lot of experience with high-power nuclear modules in submarines and aircraft carriers, so that’s an option I personally lean toward, but politics may dictate a less proven approach. Also, working fluids and cooling grids need to be addressed for nuclear or for solar dynamic electric generation.

Given an appropriate power supply, we still need enough time and fuel to move an asteroid. So how much do we need?

From our mission-time derived flight plan, we compute the needed delta-V, and conservation of momentum allows us to compute the needed momentum change and the product of fuel mass times exhaust velocity. The asteroid’s mass is a given, but we can choose to some extent our mission time, and thus the needed delta-V. Double the mission time, halve the delta-V.

Note that doubling the exhaust velocity quadruples the needed energy (100 times the energy is needed for 10x velocity for a given amount of fuel). But doubling Vex also halves the fuel mass required, so the net effect is doubling the required power for a given thrust duration. At a specific impulse of 5000, consuming 55 tons of fuel over a 10 month period requires 5 megawatts of continuous power.

With a lot of energy, we don’t need much fuel at all. These numbers are all well within our technological capabilities. Of course, additional fuel will be needed to deliver the tugship and its load of fuel to the asteroid, but again, the numbers are within our capabilities. We can do this.

However, remember that Apophis is rotating and we may only be able to apply thrust half of the time. This doubles the thrust and power required.

I’m proposing a mission with two main phases and a three-year (or so) timeframe.

The first phase is to launch the necessary components and assemble them in orbit, some time in 2027.

The actual deep-space phase begins with a lunar slingshot for intercept injection in October of 2027, and docking with Apophis some 5 months later. This requires 3 km/s of delta-V, and about 15 tons of fuel.

We would grapple Apophis, and apply 400 Newtons of thrust (enough to deliver 1.0 cm/s/month of acceleration) for half of every 30-hour day. Ten months of thrust consumes 55 tons of fuel. Then there is a three-month coast until the slingshot.

The major slingshot must occur on April 13, 2029. The goal is to change Apophis’ orbit to achieve a lunar slingshot 1 year later to capture the asteroid into Earth orbit. Note that the initial thrust moves Apophis further from the Earth, and the subsequent lunar slingshot is necessarily even further out.

I want to talk briefly about that tugship.

It must support an extended deep-space mission, providing everything the crew needs to thrive. My supplies estimate assumes ammonia provides hydrogen for carbon dioxide recycling, and food to be dehydrated.

My mission plan requires 55 tons of fuel to change the asteroid’s orbit, plus 15 tons for the intercept and docking, plus contingencies. I’d suggest at least 100 tons total, perhaps more. Note that if properly oriented, the fuel can provide significant radiation shielding during the trip to Apophis, and then the asteroid itself provides even more, especially if the crew quarters can be partially buried.

We need to apply 200 newtons of thrust continuously for 10 months, or double that for half of the time. We’d need to double the power as well, 10 megawatts total. A 200 meter square array of 25% efficient solar cells generates 12 megawatts, the extra needed since ion thrusters aren’t 100% efficient.

Lastly, we need some way to grab hold of the rotating asteroid. I suggest using 6 harpoons with 1-km lines launched around Apophis, the ends retrieved and securely tied to the tugship. This would function as an effective net and friction applies sufficient traction to apply thrust even at high angles of attack. We could break several of the lines and still hold on. Note that this is a good example of where people can easily accomplish a task which might be nearly impossible for an automated system.

This project plan assumes a separate launch of a construction shack housing six or more workers for several months.

Their job is to assemble all of the components, as I’d expect at least 5 launches of 50+ tons each are required.

-Two launches for the solar panels and supporting structures – total 100 tons

-Two launches for the fuel and thruster assemblies – another 100 tons

-One launch for the tugship (crew quarters) itself

-The construction shack is a sixth launch, and the assembly crews, mission crew, and supplies are likely two more man-rated launches. Note I’m assuming the assembly crew is launched early, and the mission crew at the last minute, because the deep-space mission already requires a very long time. The number of people in each is an estimate, of course. While 6 workers may suffice to assemble the tugship during a two month project, double the people would simplify training, ease workloads, and provide significant redundancy.

-Likewise with the deep-space mission crew. Two people may be able to handle the workload, but that is cutting it close. I’d suggest four at a minimum, and six is better.

Continued research tops the list of the several logical next steps we should take. NASA is ideally suited for several of these, and the continuing search for potentially hazardous asteroids identifies the same candidate asteroids as a search for potentially capturable ones.

We do need to address several legal issues, which pose a serious problem for Western civilization private enterprise. Key among this is the right to own and exploit objects in space. If a person or company does not have the right to exploit space-based resources, they can have no incentive to acquire them, and the future of humanity in space is effectively dead.

We must also address the liability of moving asteroids. Certainly this should be done with the utmost care and intense oversight tempered with some sense of practicality. For example, the adjustment to Apophis orbit that I propose appears to pass through the 2036 impact keyhole. Does that mean we must move the orbit out and around that keyhole, or simply that we use reliable, even redundant systems, and closely monitor to track the potential need for additional intervention? I’m afraid that science and logic may have little to do with the outcome of that discussion.

We need to design and build a tugship using thruster and power technologies available in an appropriate timeframe. Of course, that research is an excellent task for NASA’s Marshall Space Flight Center. I think the biggest challenge here might be in supporting deep-space, long-term missions with the human crews I believe are necessary to get the job done.

The bottom line is that we CAN capture asteroids into Earth orbit, thanks to the amplification of delta-V due to gravitational slingshots.

There are several candidate asteroids today, and there will be more tomorrow. Also, I did not look for opportunities where the asteroid close approach was to Venus, or Mars, or Mercury, and there is every chance that good candidates exist although longer missions (and an extra slingshot or two) would be required.

The most important consideration to me is that capturing an asteroid such as Apophis places millions of tons of raw materials into Earth orbit where we need them to build solar power satellites, permanent orbiting habitats, and to advance humanity’s exploration and further exploitation of the vast resources of space.

Lastly, we should never forget that capturing a potentially hazardous asteroid converts a dangerous threat into a resource of immense value.

President Obama needs a grand goal for NASA and the nation in the next decades, one comparable to Kennedy’s “We choose to go to the moon in this decade.” I believe that capturing Apophis into Earth orbit is such a grand goal, with benefits to global energy and warming (via those solar power satellites), and to space exploration, and to permanent, self-sustaining habitats in space. And it removes a threat to the Earth.

If you agree that we need a space-faring humanity and that exploiting asteroids is key, if you agree that sending cheap solar energy to Earth simultaneously helps humanity and reduces global warming, if you agree that we should act to prevent asteroid impacts on the Earth, then please share the word. Follow this link (Project Apophis) and tell President Obama that he holds the key to the future of humanity in space, that capturing Apophis is feasible, affordable, solves many problems in a single step, and is a Grand Goal worthy of his – and this nation’s – focus. Thank you.

A Project Plan for Space Based Solar Power

OVERVIEW OF A SPACE BASED SOLAR POWER PROJECT

In my post, Space Based Solar Power, I present an overview of SBSP and its value to humanity. I also propose the use of asteroids for raw materials to reduce the cost to profitable levels. Still, the construction of the first Solar Power Satellite (SPS) is special, as we must incur all of the up-front (bootstrap) costs in addition to building the SPS itself.  I will demonstrate that it still can be a profitable venture. However, this project plan targets the initial construction of a dozen SPS’s, because the slag by-product of that much steel is the correct mass of shielding needed for a Kalpana-One style habitat for the workers (see my post, designing a space habitat).

The approach I recommend is to capture an asteroid (see  Asteroid Capture into Earth Orbit) and use its resources to produce the steel and other materials needed to construct and operate a constellation of SPS’s.

This approach has a relatively high up-front investment and results in a relatively low per-SPS cost. The project has many phases:

1. Research & Development
2. Capture a suitable asteroid into Earth orbit
3. Launch Mining & Manufacturing Tools
4. Launch Construction Shacks & Workers
5. Construct & Deploy the SPS(s)
6. Construct the Kalpana-One style Habitat(s)
7. Repeat 5-6 as long as asteroid resources remain

For the purposes of this post, I make several assumptions:

• we have chosen the asteroid 99942 Apophis, which also locks us into a 2029 timeline (project start in 2027, launch capture mission in early 2028).
• use of SpaceX’s Falcon 9 Heavy launch vehicle (announced with pricing, but not yet built, yet alone flown).
• pricing in 2011 dollars which must be adjusted for inflation.
• Worker launch costs initially average $24M/person, but in a 2031 timeframe human-rated transports will be built for the Falcon 9 Heavy (or eventually Falcon X Heavy) that can transport 30 to 100 people per launch into LEO at a price of $1,000,000 per ton (also per person).
• I ignore in-space worker salaries (small compared to launch costs)
• For income, I only consider Solar Power Satellites, ignoring tourism, the sales/rentals of housing and retail space, sales of propellants to outside parties, product placement, tie-ins, naming rights, or any other potential revenue sources.

RESEARCH & DEVELOPMENT

It may be an unreal oversimplification, but I will ignore the R&D costs for this project although they are large and unknown. I believe that NASA, the various governments, and the network of universities should bear this cost as part of their normal operations (supported by tuitions, taxes, and donations), although the more directed research will be borne by the corporations that will profit from the sales of related equipment and supplies. Known areas of research & development include:

• Heavy lift launch vehicles
• Space taxies / trucks (using ion thrusters to cheaply change orbits and to capture the asteroid)
• Long-term life support (recycling & farming in space)
• Zero Gravity Mining, Smelting, Refining, and Manufacturing (note need to recycle reagents and to capture and utilize bi-products such as CO2).
• Manufacturing Solar Photovoltaic Panels from asteroid materials
• High-efficiency Muilti-Gigawatt Microwave Transmitters / Receivers
• Large-scale in-space construction techniques (of SPS and habitats) with limited resources

CAPTURE A SUITABLE ASTEROID

How to capture an asteroid is largely covered by my previous post, Asteroid Capture into Earth Orbit, and a future post will detail the components of the capture project, including a proposed project breakdown of the needed components, launches, delta-v budgets, and a project timeline.

The Asteroid Capture Project begins in 2027 with construction (in orbit) of a space tug. The tugship launch from LEO to intercept Apophis occurs in April of 2028, and the final Lunar slingshot of Apophis effecting capture into Earth orbit occurs 18 months later, in October of 2029. These dates are driven by orbital dynamics.

A simplified overview of the Apophis Capture Project (using current or near-term launch vehicles) is:

1. Launch tugship, fuel, solar panels to LEO: total 150 tons, needs 5 Falcon 9 Heavy launches ($500M); cost of tugship, etc. another $1.5B. This cost is lower than many space-based projects because of the extensive use of modular components assembled by humans in space(reducing the need for first-time perfection).
2. Launch in-orbit assembly crew: 1 @ $100M, probably another $1B for training, tools, supplies, support staff.
3. Launch mission crew & supplies: 1 @ $100M
4. Intercept mission uses ion thrusters and a lunar slingshot to enter Apophis intercept trajectory in April 2028.
5. 2 months to intercept; 3 months of thrust to change Apophis orbit; 1 month of contingency; 6 months of coasting. After the slingshot around the Earth in April of 2029 there is another 6 months of coasting (with likely trajectory tweaking) before the final drop into Earth orbit via a Lunar slingshot in October, 2029. Capture Mission duration is a little over 18 months; with recycling of water & oxygen, 600 days of food & water & hydrogen (to recycle CO2) for a crew of 4 masses four tons; a similar mass is needed for the associated equipment (triply redundant).

Total capture cost: $3.2B (ignoring R&D and ground support costs).

LAUNCH MINING & MANUFACTURING TOOLS

This is a big unknown, in that we don’t yet know how to best do mining, smelting, refining, and manufacturing in space (microgravity, necessity to recycle & save everything) from asteroid resources. We can make good guesses, however. Also, the facilities should grow over time, but the initial launches should suffice for starting manufacturing, especially since we are largely launching tools to make tools. After the initial launches, most of the needed additional equipment will be manufactured in space. These launches would begin in 2029; I expect the tugship will be used to transport these components from LEO to the asteroid now in Highly Eccentric Earth Orbit.

• Solar Power generator: 1 launch, $200M
• Mining facility (ore movers, grinders, separators): 2 launches, $400M
• Solar smelter, gas collection & refining, metal purification: 5 launches, $1B
• Steel production: 5 launches, $1B
• Rolling mill (girders, rods, sheet metal): 3 launches, $600M
• Finished metal product plant (nuts, bolts, rivets, connectors, pipes, tanks, etc.): 2 launches, $400M
• Silicon refinery, solar panel manufacturing (3 launches, $600M)
• Slag processing, shaping, rock wool production, & slag handling (1 launch, $200M)

Total estimate is $4.4B for equipment and 22 launches, and this phase begins in 2029, ends in early 2030.

LAUNCH INITIAL WORKERS & THEIR CONSTRUCTION SHACKS

The initial workforce for all of the mining & manufacturing  equipment, even assuming significant automation, is considerable. I estimate 36 workers, needing 6 launches using Falcon 9’s and Dragon X capsules (total $600M) just to get started. Each crew member will likely require a ton or more of life support equipment and supplies.

The Construction Shacks are the living quarters, recycling equipment, supplies, and solar panels for the initial mining and manufacturing workforce, intended to be buried beneath asteroid regolith for radiation and meteorite shielding (alternately regolith may be bagged and packed around the shacks). This will need to be repeated as the workforce grows (until a permanent habitat is at least partially completed).

The Falcon 9 payload faring may be equipped to house up to 12, with room for supplies and equipment. Three of these would provide adequate housing and first-year supplies for the initial 36 workers, at a cost of $600M bringing the total cost to $1.2B ($33M/person).

Subsequent workers initially have similar high launch and support costs, ramping down to $15M per-person as capacity grows to produce living quarters, water, and oxygen in space. When the interim habitat is ready and larger capacity people launchers (32 workers/launch) become available, per-worker launch costs should plummet to roughly $3M per person (in 2031), and as low as $1M per worker in subsequent years (with use of dedicated people-carrying spacecraft ferrying 100 workers into space per launch). Note that a 1 ton per worker mass allowance includes some essentials that cannot be easily fabricated in space, such as high-efficiency LEDs for the farms,  some fertilizers, and medical supplies.

The workforce & construction shack launches could begin in late 2029.

This initial 36 worker contingent will be sufficient to prove the feasibility of mining, refining, and manufacturing in space, but will be inadequate to achieve sufficient volumes of production for a timely project completion.

A ramp up to 500 workers during 2030 should result in a steel production rate of roughly 100 tons per day, which in turn allows construction of the habitat pressure shell plus containers for the volatiles (oxygen, CO2, and H2O) in one year. At this point (an interim habitat consisting only of a spinning pressurized shell with partial radiation shielding), many of the workers can work without pressure suits, gravity prevents long-term health problems of zero-G living, and in-space production of food can begin. 

Doubling the population and production annually allows the first SPS to be completed by the end of 2031 (when steel production is 200 tons per day, comparable to a small mill on Earth). 2032 should see 2 more SPS’s completed, and 2033 results in 4 more and completion of the habitat structure (with room for 8,000). By the end of 2033 the habitat capacity is reached, and the associated manufacturing facilities should be capable of building 8 SPS’s per year. Remember, it takes all of the slag associated with building the first 12 SPS’s to fully shield the habitat, which occurs during 2034. By the end of 2034, the first permanent habitat (8,000 person capacity) is complete, along with 15 Solar Power Satellites.

The total worker cost through completion of the first SPS and the habitat shell would be $15B (by the end of 2031, a total of 1,500 workers). Adding 2,000 more workers in 2032 and 4,000 more workers in 2033 would cost only another $6B.

This analysis has ignored the cost of salaries for space workers (and the cost of ground support). One reason to ignore the salaries is that they are insignificant compared to launch and equipment cost in the early years.

Another reason to ignore them is that portions of each “salary” may be offset: workers may be charged for rent (or purchase of a condo), for food, water, recycling, even oxygen. The cost of living is very high in space, and salaries should reflect that, but the net cost of a worker is difficult to estimate. Many of the readers of this blog would likely volunteer to work for little more than the right to permanently live in space and be a part of humanity’s spacefaring future – I know I would. Very few of the workers would view these orbiting factories and habitats as temporary jobs and expect to return to Earth in a few years, especially if they were afforded the opportunity to buy a home and raise a family in the habitat.

CONSTRUCT & DEPLOY THE SPS

The construction of a Solar Power satellite requires multiple components, most of which will need to be built in orbit. For more details, see Solar Power Satellite Design Considerations. The components are:

• Solar Panels (from high-grade silicon, in thin sheets such as commonly manufactured today)
• Steel structures to frame and aim the panels.
• Steel structures and motors to maintain alignment of the panels with the sun, and the antenna with the target Earth station.
• Microwave transmitting antenna
• Microwave transmitter
• Shield mass to protect the electronics from meteorite damage.
• Fuel to insert the SPS into the target geosynchronous orbit

I expect that the motors and electronics (including the microwave transmitter) will be launched from Earth, for which I’ve budgeted $200M per SPS.

A considerable amount of fuel is needed to move each newly constructed SPS from the near-Lunar location of its birth and insert it into an appropriate geostationary orbit. The total delta-V needed is roughly 2 km/s, the total mass is 25,000 tons, and even using 5,000 ISP VASIMR ion thrusters, 1,000 tons of fuel is needed. Luckily, that is a tiny fraction of the 15,000 tons of oxygen produced as a by-product of the smelting of iron ore into steel for each SPS. Also luckily, we’ll have a lot of power available, so the time required for this orbit change is limited largely by the number of ion thrusters (and thus the fuel flow rate) we wish to dedicate to this task. We’ll have plenty of oxygen to spare, so our ion thrusters should be optimized for this most available rocket fuel.

Each SPS will require a matching ground receiving station consisting of a large (10+ kilometer) rectenna plus power conversion and distribution. These costs are only a guess, but I’d estimate that $1B each is more than enough. I have not included this portion of the per-SPS cost in my summary, as this cost would be born by the receiving local electric utility.

CONSTRUCT THE HABITAT

Another post details the Design of a minimum Kalpana-One style Habitat: a 100-meter radius cylinder, 130 meters wide, spinning at 3rpm for 1G along the outer rim, lined with 3 meters of slag which provides excellent shielding against radiation and meteorites.

The outer pressure shell is built using average strength (easily welded) steel plates nearly 1 inch thick, and masses approximately 28,000 tons. Completed first, once spun up it provides a shirt-sleeve environment with gravity, boosting the productivity and health of the workers.

Over time, blocks of slag are brought inside to line the exterior walls, and interior structures are built as housing, workspaces, and farmland. Most of the volume is left open to eventually become a 12 acre cylindrical park. The core will be available as a low-gravity industrial and research space. Agriculture space (primarily for crops) is more than 5.5 million square feet; residential space is over 2.5 million square feet, there is 1.5 million square feet of offices / light industrial and a million square feet of storage and overhead space. The total internal structures including the outer 15 meters along the endcaps and perhaps 6 stories of rooms lining the cylinder rim, plus a 40 meter diameter core structure, masses 126,000 tons (a generous allowance). This is less tonnage than an Oasis Class Cruise Ship (225,000 tons carrying 8,000  passengers and crew) yet much more spacious.

Power (6 kw/inhabitant or 50 megawatts total) is provided by solar panels lining the exterior surface of one endcap, plus a ring extending 100+ meters beyond the cylinder (effectively a 425-meter diameter solar panel array).  Additional power needed for exterior factories (such as the smelter) is included in their structures and allowances. The spin axis of the habitat points to the sun, requiring a massive gyroscope at the center of the habitat to slowly precess the spin axis at one revolution per year.

Speaking of spin, it takes a lot of fuel and energy to spin up the habitat to 3rpm: about 1150 tons of fuel (oxygen) at an ISP of 5,000. Using 25 megawatts (half of the habitat’s available power), the spin up takes nearly 2 years. However, the empty shell (no shield mass) spins up very quickly; the majority of the energy is needed to maintain the spin as roughly a million tons of shield mass is gradually added to the habitat’s periphery. 

Once complete, this habitat houses 8,000 workers / colonists, and provides all life-support needs. All of the steel (154,000 tons) and shield mass (1,600,000 tons of slag) are from the asteroid, along with the oxygen, water, and carbon needed for the life support system. The known components to be launched from Earth include the LED’s and other light sources for the farms and interior (see Lighting our Space Habitats), various electronics, seeds, and perhaps 50 kilograms of nitrogen (per inhabitant) needed as fertilizer.

There are no additional launch or equipment costs not included elsewhere (possibly excluding the ion thrusters needed for spin-up).

REPEAT

This project is an eight-year plan (5 years to the first SPS) culminating in the deployment of a permanent, self-sustaining habitat with a population of 8,000 and fifteen 5-gigawatt Solar Power Satellites in geostationary Earth orbit. By completion, the project will have consumed approximately 10% of Apophis, leaving  90% available to build additional habitats and Solar Power Satellites.

The capacity will be in place to build additional Solar Power Satellites at the rate of 8 per year, but note that demand is much higher: current global electric demand would need 400 five-gigawatt SPS’s to fill, and total projected energy demand might require more than 4,000 by 2050 (most energy is used for heating, generally by burning fossil fuels). Apophis alone has sufficient resources to build up to 150 Solar Power Satellites (while building 10 habitats accommodating 8,000 people each), but in the long run additional asteroids will be needed.

We should build additional habitats, including larger ones, as part of an ongoing project. We’ll likely need a “mining town” for each asteroid we capture, and an SPS construction / maintenance habitat just outside of geostationary orbit, and even a large habitat in low Earth orbit (as low as possible without serious atmospheric drag) as an Earth to LEO launch target and tourist destination. Good arguments can be made for additional habitats in various Lagrange points such as L5, and for transition orbits such as LEO to Geostationary, or to the Lagrange points. There may even be a 3:1 Lunar synchronous stable Earth orbit that visits L3, L4, and L5 in succession, 9.1 days apart – an ideal platform from which to host interplanetary missions, including to Mars.

SUMMARY

It all sounds time consuming and expensive: $22.8 Billion before that first SPS is operational. But remember, in 2032 that first SPS will generate $1.3B in cash flow (at a wholesale price of $0.03/kwh), in 2033 the 3 deployed SPS’s generate another $3.9B, in 2034 the 7 deployed SPS’s generate $9.1B, and subsequently the 15 SPS’s generate nearly $20B/year. The steel production rate is 800 tons per day, allowing 8 or more additional SPS’s to be built each year. The peak cash outlay is $25B with all investment repaid in 2035 – and huge net profits after that.

Even considering only that first SPS, the total cost is comparable to the $5 billion per gigawatt that my local power company may spend on a nuclear power plant, without any need for radioactive waste disposal or refueling, and without quite as much local objection to the installation.

Yes, I’ve been accused of being an optimist. Yes, it is likely to take longer than this project plan, due to unforeseen setbacks. Yes, I’ve ignored the cost of money in this analysis. I’ve even ignored the cost of bringing all these workers back to Earth (assuming they’d want to return). But even if it takes another year or two before breakeven, even if the costs might run 20% (or 100%) higher, even if you factor in the up-front R&D costs, even if you add a generous salary for every in-space worker plus free room & board, it is still a wildly profitable venture.

And did I mention that Apophis has enough raw materials to repeat this project another nine times, at a fraction of the cost each (and completely funded by free cash flow)?

Is there an entrepreneur listening that likes the sound of $200 Billion per year of free cash flow for a measly $30 billion investment? And with the bonus of earning a permanent place in the history books as the party responsible for bootstrapping humanity’s move into the Solar System?!

Solar Power Satellite Design Considerations

The major considerations driving solar power satellite design decisions are:

• location (geostationary, LEO, other)
• energy delivery method to Earth
• solar panel photovoltaic versus turbine generator (efficiency/cost tradeoff)
• size of an SPS (dimensions, mass, power)

LOCATION

Most studies recommend a geostationary orbit for Solar Power Satellites. This choice simplifies designs, and is the only choice that can deliver continuous power from a single SPS – the others require a constellation of satellites with any given ground station receiving power from a sequence of satellites. The disadvantages are that a relatively large transmitting antenna is required, and it takes more energy to reach those geostationary orbits.

Another disadvantage is that it is inefficient to deliver power to high latitudes; multiple satellites with Molniya orbits are one possible alternative.

An SPS constellation in medium Earth orbit has been proposed, because of the lower cost to launch from Earth and the smaller size of the transmitting antenna. The disadvantages are that both the transmitting and receiving antennas may need to be dynamically aimed, plus the “dark” time due to passing through the Earth’s shadow is much greater, requiring still more satellites to deliver continuous power.

The remainder of this post will focus on geostationary locations, which have been studied more thoroughly.

MICROWAVE ENERGY DELIVERY TO EARTH

The minimum size of an SPS is driven by the size of the energy transmitter and the Earthside receiving station. While several alternatives have been considered, the best option appears to be beaming microwaves to Earth receiving stations from geosynchronous orbit. To achieve sufficiently narrow beams that arrive at sufficiently low energy densities (so as not to cook anything in their path), we’ll need a transmitting antenna one kilometer wide.

The receiving station is larger at 10 kilometers east-to-west and as long north-to-south as necessary to appear circular from the SPS (a 10 kilometer circle at the equator, a 10 by 15 kilometer oval at 30 degrees latitude, 10 by 20 kilometers at 45 degrees latitude, perhaps 10 by 30 kilometers at 60 degrees). Note that 60 degrees latitude is approximately the limit of feasibility due to both the size of the receiving array and the amount of atmosphere that must be traversed. Luckily, this supports serving the vast majority of the global population, excluding only the Artic regions, Alaska (U.S.A.), northern Canada, and the European Nordic countries and northern Russia. Note that St. Petersburg (Russia), Helsinki (Finland), Stockholm (Sweden), and Oslo (Norway) are near the limits of servable destinations.

An Earth-side energy density of 23 mW/cm² (chosen as safe for all life forms) equates to 5 gigawatts as a minimum power limit near the equator and proportionally more at higher latitudes. Building smaller SPS systems can be done, but the antenna arrays would not be smaller (or cheaper), and thus would be less cost-effective. Note that some sources suggest a minimum size of 4 gigawatts. In any event, at 2.45 Ghz (the highest frequency with negligible absorption by rain, snow, clouds, and people), a one-kilometer transmitter could not possibly focus higher intensities upon the Earth, making this a safe and non-military technology.

The likely technology for the receiving station is a rectenna array, a network of many simple wires with diodes. It can be deployed above cropland (and herds of cattle, even forests) with only minor loss of productivity of the farm. Receiver losses will be of the order of 10%, much less than typical long distance power transmission.

A side point: direct-to-home power transmission is perfectly feasible. A home rooftop rectenna could easily capture 5 or 10 kilowatts of power, several times the average household demand. The problem is all the power wasted between rooftops, including undesirable electric currents induced in most metals and wiring. But perhaps this is not a problem in a military environment, where an energy beam could be directed to the conflict zone, not as a weapon, but for providing electrical power wherever needed. This also has direct military applications: SPS powered drones could fly indefinitely.

HOW BIG IS A SOLAR POWER SATELLITE?

So how big is the SPS itself? That depends critically on the efficiency of solar energy capture and thus the technology used. There are two likely technologies: solar cells (photovoltaic) and solar dynamic (mirrors and gas or steam turbine powered generators). Both methods take advantage of the near-constant sunlight (only shadowed by the Earth for a few total hours near midnight twice a year, and never for more than 75 minutes at a time) – a net 99% availability. Also, the intensity of solar energy in space is greater than on the Earth’s surface due to the lack of air to absorb energy. About 950w/m² strikes the Earth’s surface at noon on the equator on a clear day, while in orbit the solar energy density is 1367w/m² all of the time.

Solar Photovoltaic versus Solar Dynamic

Solar cells vary hugely in cost and efficiency. Common cells convert about 10% of the incoming energy to electricity. But modern cells convert 20% (thin film) to 40% (optimized) of the incoming energy. Caltech claimed to achieve 85% in a highly experimental demonstration in March of 2010. We don’t know what technology will be the most cost-efficient. Note that 25% efficiency implies a 4km by 4km photovoltaic array would generate 5 gigawatts in orbit, although it would take a 4.25km square array to deliver 5 gigawatts to the Earth assuming an 80% efficiency in the transmitter / receiver.

Solar dynamic may be more efficient, as large, low-cost mirror arrays focus the sun’s heat on a boiler driving a turbine electric generator. The mirrors are relatively inexpensive, and the cost will be dominated by the need to remove the waste heat using large cooling arrays. But the efficiencies are quite high, typically 40% to 50% (potentially even higher, depending upon the fluid used). Ordinary steam turbines can achieve 40% efficiency. Hybrid designs with a gas turbine followed by a steam turbine can achieve 60% or higher efficiency. The problem with solar dynamic is that moving parts imply mechanical failures. These units would likely require a nearby crew for maintenance – something easily provided from a space-based habitat. Note that at 60% efficiency, a circular mirror of 2.8 km diameter (or a 2.5 km square array) is sufficient for a 5 gigawatt SPS. 

Solar dynamic has other advantages: lightweight flexible mirrors (such as ordinary aluminum foil) are not significantly affected by radiation, ultraviolet light, or micrometeor punctures. Disadvantages include that the turbines and generators are heavy, high-tech components that may have to be launched from the Earth. Also, the working fluid in the gas/steam turbines may not be cheaply available. The only gas available in large quantities is oxygen, which is very corrosive to many metal surfaces, at least until we capture the resources of a live or extinct comet which is likely to contain enormous quantities of water and ammonia.

PHYSICAL SIZE OF A SOLAR POWER SATELLITE

Using assumptions listed above, the width of an SPS might range from 2.5km to 4.25km, or as large as 6.75km if we use the cheapest solar cell technologies. But 4.25km looks like a reasonable target. Note that at geosync orbital distances, these would be as visible as the larger planets, and easily resolved with binoculars. Once hundreds were in orbit, they would appear as an arc of lights to anyone who looked up on a clear night.

There is also a nearby 1.0km microwave transmitting antenna, visible using binoculars. One problem is that the solar cells must always point at the sun while the transmitting antenna must always point to the Earth side receiving station. Proposed solutions include:

• use the same structure with phased array techniques to steer the beam (always pointed at the sun), difficult for certain orientations;
• use separate structures with some connecting mechanism that rotates one or both arrays;
• use a smaller integrated array of a 1km transmitter (always pointing to the Earth) backed by a (fixed) 1km photovoltaic array, and a separate large mirror to track the sun and focus its light on the back of the transmitter. While appealing in several respects, this does have its own problems: dissipating roughly 15kw of waste heat per square meter, which implies a blackbody temperature of 240^oC if there is no additional radiating surface (it couldn’t be a manned structure, and would have to cool off prior to maintenance). The mirror and the transceiver would have different orbits – one would require constant adjustments. Lastly, it would be difficult to focus sufficient light on the transceiver near local noon each day. But some clever engineer may find a solution to all these problems.

MASS OF A SOLAR POWER SATELLITE

Using modestly optimistic assumptions for solar photovoltaic panels, supporting structure, power collection, and for the microwave transmitter and its own antenna, I estimate a total mass of 25,000 tons for a five-gigawatt SPS. Early estimates were closer to five times higher, and some optimists currently estimate that thin film panels would weigh one-fifth as much, although a supporting structure and the transmitter must also be considered. Note that if the solar panel array is 4km on a side, then 1.0 kg/m² of panels, structure, and wiring results in a total mass of 16,000 tons, leaving the remainder of my mass allowance for the transmitter, its antenna, and other support structures.

A 1.0kg/m² mass allowance solar cells, wiring, and structure seems like a significant challenge, requiring a substrate similar to a sheet of paper in thickness. Note that a silicon wafer sliced 1.0mm thick weighs 2.3kg/m². However, the typical thickness of photovoltaic silicon wafers today is only a tenth that, and thus weighs 0.23kg/m2, leaving adequate allowance for structural components and wiring.

When using the resources of an asteroid to build the Solar Power Satellite, the mass of the photovoltaic panels is only a minor concern, as there is more than enough silicon and iron in even a small asteroid to build them as crudely as desired. Indeed, using a convenient asteroid allows the construction of large and inefficient but presumably simple and reliable solar power satellites. The final technology choice may be one of minimum labor costs or total time-to-market. Those tradeoffs are not simple, because using a less efficient technology (that is simpler to produce) implies a significantly larger structure with more materials and thus more time and effort to build.

But by using an asteroid for raw materials, we at least have choices to make beyond “is it even feasible?” Launch costs of people and tools to bootstrap the process will be high enough as it is, but having the cheap and convenient asteroidal resources in orbit where we need them gives us the flexibility to try not just one approach, but several approaches and learn which is the best way to deliver clean and cheap energy to the inhabitants of Earth.

Space-Based Solar Power

Many people have written pages, papers, even entire books on the subject of Space Based Solar Power. Certainly many of the authors are better qualified than I am. What my posts add to the mix is the cost reduction and simplicity gained by using an asteroid captured into Earth orbit for the bulk of the materials.

Also, some of my sources are more recent than many older papers – which makes a huge difference. For example, my earlier posts used a figure of 125,000 tons for a 4 gigawatt SPS, based upon references quoting 20,000 tons per gigawatt, plus structure and the transmitter. But more recent sources propose a very lightweight design requiring only 1,000 tons per gigawatt – a 20-fold reduction. For these posts, I’ll be using an intermediate figure of 5,000 tons per gigawatt, or a total of 25,000 tons for a 5 gigawatt SPS (measuring 4 km on a side).

Even with current high launch costs, at least one company believes they can build a cost-effective SBSP system using all Earth-sourced materials. I don’t see how, since fifty to a hundred or more 100-ton payload launches would be required. But the people with their money on the line have put more thought into justifying the ROI, and I wish them well.

More commonly, pundits believe that Lunar materials (typically using a launch-rail system to lower the cost of launching materials from the Moon) might reduce the total cost to an acceptable level for as few as 50 to 100 SPSs (to amortize the costs of landing a great deal of equipment and people on the Moon).

Asteroidal resources are much more readily available, and several sources have proposed robotic mining missions to various asteroids (chosen for a low net delta-V, especially for returning material to Earth orbit). Some proposals return raw material to Earth orbit for processing; others return materials processed to some degree (such as iron). Robotic missions are often assumed to eliminate life-support and radiation shielding costs.

Note that a 100-meter radius Kalpana One style habitat (housing and feeding up to 8,000 residents) can be built from a single 120-meter asteroid, along with 12 five-gigawatt Solar Power Satellites, using the slag from iron smelting as radiation shielding.

My proposal (see Capturing an Asteroid) is to use gravitational slingshot maneuvers (around the Earth, the Moon, or even Mars or Venus when appropriate) to capture one or more asteroids into Highly Eccentric Earth Orbit (HEEO), then to launch the tools needed to mine the asteroid, smelt it into valuable materials, and build the SPS network in orbit. Of course, this is simply a logical extension of the proposals to return asteroid raw materials to Earth orbit. I propose to send the whole asteroid (which we can do given the extraordinary special circumstance of an existing close approach of an asteroid).

This approach requires large numbers of people in space, because people are good at problem solving. Using robotic approaches requires that the engineers anticipate all possible contingencies, and, speaking as an experienced computer programmer, I absolutely guarantee that we will never succeed at anticipating every possibility.

But people are resourceful, and their ingenuity will solve all of the little problems, and likely the big ones that crop up, as well. The number of people needed is huge, because each SPS is itself huge (kilometers wide), and there is a lot of work required. We’ll need to smelt ore into steel at impressive rates (but typical of a foundry on Earth). We’ll need to form that steel into plates, girders, pipes, tanks, cables, etc.. We’ll also need tables, and chairs, and sinks, and toilets. It’s expensive to bring those things up from Earth.

We’ll need to use part of that steel (and much of the slag) to build habitats for space workers (see Designing a Space Habitat). We’ll need to produce magnesium for mirrors (assuming turbine-driven electric generators) or silicon for solar voltaic cells (or both – we won’t know what is best until we try). We’ll need to weld or bolt all the pieces together into immense structures, and then maintain them (because parts fail, regardless of how well-built they are). We are likely speaking of thousands of people to build that first SPS, and thousands more to build and maintain a network of them.

Carbonaceous chondrite asteroids and extinct comets certainly contain everything needed. These comprise at least 75% of all asteroids, although they are relatively rare among Earth-crossing ones. However, any undifferentiated asteroid (such as ordinary chondrites) should suffice. All of these contain vast quantities of iron, oxygen, and magnesium. Most asteroids will contain small but significant quantities of carbon and hydrogen, easily extracted by simple heating. The asteroids to avoid are those from parent bodies that melted and differentiated, since that would isolate most metals into an iron core, and deplete the volatiles, leaving ore as poor and dry as moon rocks.

HOWEVER, there are significant ground-based costs to consider as well. In addition to building an SPS with a microwave transmitter to deliver power to an Earth station, we must build that ground station, which (in principle) is easy and low-tech, but is still large (and thus expensive, partly because of land-use costs), plus we must build the power distribution network to get the electricity to the consumer. I do not have a good handle on this cost, which I am certain will vary tremendously from site to site, as it should be much cheaper where land is cheap (and power is not needed), and will be much more expensive close to major cities where the power is needed but land is expensive plus there is always resistance to putting the receiving rectenna in our back yards.

Note that the receiver may typically require an oval roughly three miles wide and six long, but it is sparse and may be placed over a farm with little impact on crops or livestock below. It may also be place in a forest just above the treetops, where it would not even be all that visible. As a very rough estimate, I will assume that the ground-side costs will equal the in-orbit costs per SPS, although I will also plan that all of the up-front capital costs are for the SPS itself (a simplistic approach that ignores the cost of lawyers and politicians).

My next post will discuss specific design considerations for a Solar Power Satellite.

Economics of Solar Power Satellites

Reading my local paper yesterday, I learned that the cost of building new, modern, nuclear power plants was much higher than I had thought. The Jacksonville Electric Authority (JEA) is considering a 20% share of a new 2 Gigawatt plant – at a cost of $2 Billion. The total cost of the plant is $10 Billion – or $5 Billion per gigawatt.

This seems horribly expensive, but the resulting steady, cheap, zero-carbon electricity apparently makes the capital investment worth while.

The cost is indeed high, which is good news for Space Based Solar Power: it may be possible to profitably launch the components directly from Earth to build a Solar Power Satellite (just barely).

But as I have argued in previous posts, there is a much less expensive way to build Solar Power Satellites: build them in orbit using asteroids which provide all the raw materials we need (just add tools and workers).

As a side benefit of great importance to most of the readers of this blog, my plan requires the building of permanent orbiting space habitats, self-sufficient, rotating for gravity, and using the slag from iron smelting as radiation shielding – a topic I’ve discussed before.

My next several posts will discuss various aspects of Space Based Solar Power built using asteroid materials, from some high-level design considerations to construction techniques and ultimately to revenue generation and return on investment.

I am more convinced than ever that we can expand humanity into space using ground-based profit motive, with benefits of lower energy costs, near-zero carbon emissions, and, did I mention, HUGE PROFITS?

Asteroid Capture into Earth Orbit

(This long post is the presentation I delivered at the International Space Development Conference in Chicago on May 30, 2010. Links to additional information have been added, and overhead slides have been deleted.)

Why capture an asteroid? The main reason is to gain convenient access to its resources. Even a relatively resource-poor low-iron, low-metal LL chondrite contains 20% iron, significant quantities of water and other volatiles in the form of minerals such as clays, and oxygen to burn. And the best place to have those resources is in Earth orbit where they will have the greatest value. I will show how an investment of perhaps $20B will result in a trillion dollars worth of resources – a fifty-fold gain, with tremendous benefits for all of humanity humanity.

For example, the asteroid Apophis (likely one of those LL chondrites) contains enough materials to construct about 125 five-gigawatt solar power satellites at 25,000 tons of steel each, plus Kalpana One style habitats for 100,000 people. The slag remaining after iron is smelted out of asteroid ore works nicely as the radiation shield, of which we’ll need 200 tons per person. The oxygen freed from iron compounds during reduction (1 ton of oxygen per 3 tons of iron) amounts to well over a million tons more than is needed for our habitats, and I expect we’ll use that oxygen as fuel mass for ion thrusters to move the habitats and solar power satellites into their chosen orbits.

Kalpana One style habitats are basically stubby cylinders spinning for gravity, with outer hulls containing 10 tons of radiation shield per square meter to provide protection against radiation and meteoroids similar to what we have on the surface of the Earth (which, not coincidentally has 10 tons of atmosphere above every square meter).

Of course, a space habitat providing food, water, oxygen, fuel, construction supplies, gravity, radiation shielding, and skilled human workers and situated above much of the Earth’s gravity well is an ideal platform from which to continue the exploration and exploitation of space.

And we should not forget that placing an asteroid into a stable Earth orbit prevents it from colliding with the Earth. In the long run, I believe that humanity will view Earth-crossing, potentially hazardous asteroids as low-hanging fruit, and each future discovery of an asteroid on a possible collision path will be followed by a gold-rush style race culminating in another new moon for our planet. Of course, each of these new moons will be somewhat temporary, as we convert its resources into more and larger habitats, solar power satellites, and other, perhaps undreamed of tools for the advancement and protection of humanity.

So, how do we capture an asteroid? Even a tiny one masses millions of tons, and we don’t yet have the technologies to manhandle them and put them wherever we want. Luckily, we don’t have to. When a spaceship or asteroid passes close to a planet or large moon, its orbit is changed, sometimes dramatically.

In principle, a slingshot around the Earth can impart a delta-V of up to 60 km/s to an asteroid in orbit around the Sun, although in practice the limits are a small fraction of this. More importantly, very small changes in the position or timing of an existing close approach are enormously magnified.

We aren’t limited to the Earth, in that close encounters to other planets might be used to alter an asteroid such that it passes close to the Earth at a later time where its orbit can be further tuned by the Earth’ gravitational field.

If we can adjust the asteroid’s orbit such that it makes a subsequent close approach to the Moon with a relatively low velocity, the resulting slingshot can drop that asteroid into a highly eccentric Earth orbit. The Moon can (in principle) remove up to 2 km/s of velocity relative to the Earth (although less is easier). Note that dropping the velocity of an asteroid to about .25 km/s (tangential) near the Moon’s orbit would result in an orbital period of about 9 days with perigee inside the geostationary orbits.

A point I’d like to emphasize: In my opinion, gravitational slingshots are as much art as engineering, especially when considering the variations involved in multiple slingshots around one or more bodies. The people who dreamed up the Cassini and Messenger missions are both geniuses and artists, and I have every confidence that they can find suitable mission plans to capture any potentially hazardous asteroid into Earth orbit, although the missions may be very long and complex thanks to a shortage of appropriate close encounters and/or the need for significant changes to the asteroid’s orbital parameters.

Let’s consider a specific example. The asteroid Apophis will approach Earth to within 30,000 kilometers on April 13, 2029, significantly inside the orbits of our geostationary satellites. If we do nothing, the Earth’s gravity will slingshot Apophis into a new orbit as it deflects it by about 28 degrees and boosts its velocity by 2.66 km/s. The result of this is that Apophis changes from a 0.89 year period Aten class asteroid orbiting mostly inside the Earth’s orbit to an Apollo class asteroid with a 1.167 year period and an orbit mostly outside of the Earth’s. I should point out that we don’t yet know with any degree of certainty exactly what the resulting orbit will be, because tiny changes in the position of closest approach have a huge impact on the resulting orbit. The period I’m quoting here corresponds to the keyhole that targets an Earth impact in 2036.

My main point is that delaying Apophis’ arrival at the Earth’s orbit by changing its velocity by only 7.5 cm/s for six months results in a 1.4 km/s reduction in delta-V - a velocity gain of a factor of 20,000. I chose that particular slingshot because it results in a semi-major axis of 1 au, with a period of 1 year (and somewhat ahead of the Earth in its orbit). I used a program named GravitySimulator by Tony Dunn to model several Apophis orbit variations, and simultaneously to gain a true appreciation of the art and genius needed to find useful orbits.

The Tisserand criterion indicates that it’s possible to change Apophis’ eccentricity to zero at the same time, although that would result in an inclination of about 10.5 degrees. In any case, what we really want is not a near-Earth orbit, but rather a subsequent slingshot around the Moon to remove excess velocity and drop the asteroid into a true Earth orbit. That may require some finesse and multiple slingshots, but I’m confident it can be done. Look at the success of Cassini and Messenger and all the other missions that have relied on gravity assist slingshots to achieve what once was considered impossible for our current technology.

We still need to give Apophis that 7.5 cm/s nudge. I don’t suggest abrupt changes from nuclear bombs or high-velocity impacts, partly because we need finesse to fine-tune the orbit, and that’s best done by the equivalent of titration. We need a tugship, a long-mission, highly fuel-efficient spacecraft to gradually move the asteroid into a new orbit.

Robotic missions may make a lot of sense in the future, because asteroid orbit changes are necessarily long-term missions. But until we figure out how to do it from actual experience, I think the ingenuity of real humans is needed to figure out what really works, out there in space, on the job. But manned missions have problems, too, largely revolving around the life support needs of fragile humans who need oxygen, water, and food to survive.

Ion thrusters such as VASIMR engines are likely the best choice to apply delta-V, as their high exhaust velocities reduce the total fuel mass needed, and they should be able to achieve sufficiently high reliability.

Of course, we need to push or pull the asteroid, which isn’t simple, partly because they are rotating, undoubtedly along an inconvenient axis. And they have enormous angular momentum which we can’t simply cancel. This means we’ll either have to dock – not land – at an appropriate location and thrust a fraction of the time, or use a gravity tractor approach which might limit us to lower thrusts and longer missions.

In addition, ion thrusters take copious amounts of energy. 25 megawatts can be generated by a 300 by 300 meter solar array, or by a single compact nuclear module available commercially. We do have a lot of experience with high-power nuclear modules in submarines and aircraft carriers, so that’s an option I personally lean toward, but politics may dictate a less proven approach.

Given an appropriate power supply, we still need enough time and fuel to move an asteroid.

So how much fuel do we need? As a first approximation, we can pick a specific keyhole, which targets a change in position at a future time. From the mission lead time, we easily compute the needed asteroid delta-V, and conservation of momentum allows us to compute the needed momentum change - the product of fuel mass times exhaust velocity. The asteroid’s mass and the needed delta-S (for this example) are givens, but we can choose to some extent our mission time.

Note that doubling the exhaust velocity quadruples the needed energy; 100 times the energy is needed for 10x velocity.

Let’s look at our Apophis example. That 200 second delay over a six month mission requires a fuel mass that varies by a factor of ten depending upon the exhaust velocity. With a lot of energy, we don’t need much fuel at all, barely 4 tons. With a specific impulse of 5,000, we only need 41 tons. These numbers are all well within our technological capabilities. Of course, additional fuel will be needed to deliver the tugship and its load of fuel to the asteroid, but again, the numbers are within our capabilities. We can do this!

But it seems that nothing is ever simple. Part of the problem is that we don’t really know much about asteroids. Many of them appear to be rubble piles, and in some cases these spin so rapidly that their shape is constrained by their spin, yielding flying-saucer shapes. Others are contact binaries which might be exceptionally awkward to manipulate. We have more options with solid bodies, but we can’t plan on that.

So how do we apply thrust? Two ways come to mind, dock and push, or use a gravity tractor to pull. Gravity tractors can only apply tiny amounts of thrust, but that might work best, especially on longer missions. It would also help to dangle heavier components such as nuclear reactors and fuel as close as possible to the asteroid, with the thrusters some distance away so they can aim off to the side without much loss of thrust efficiency.

We can dock with an asteroid and push against it in a traditional way, but there are complications due to microgravity and asteroid rotation. It is possible that a number of cables could be looped around the asteroid to hold the tugship securely in place. Even then, a spinning asteroid means that thrust can only be applied during a fraction of each rotation, wasting thrust and fuel to the extent that the applied thrust isn’t directed in the correct vector.

There are other complications. As I mentioned before, gravity assists are hugely complex computations and the solutions are driven as much by creativity and imagination as by brute force calculations. There are many potential asteroid candidates, potentially multiple bodies to slingshot past, and multiple slingshots may be needed, as with the Cassini and Messenger missions.

At this point we don’t know enough about any of the potentially capturable asteroids, especially regarding their orbital parameters. Position uncertainties for most potential impacts for objects in the Potentially Hazardous Object database are in the tens of thousands of Earth radii once we go out twenty or more years. The uncertainties are not just due to the usual suspects of position and velocity, because things like albedo and asteroid spin have significant impacts over long periods. We would certainly need to know the true present course of an asteroid before undertaking any deflection efforts, accurately enough to eliminate any reasonable near-term possibility of an Earth impact. However, I believe that any deflection mission with a significant net reduction in impact probability over the next hundred (or thousand) years may be acceptable.

We’ll also need to address problems of mining, refining, and manufacturing in zero-gravity which may require entirely novel approaches. This is another area where human ingenuity will be vital, as I don’t think we’ll know what the problems and solutions are until we try something that doesn’t work the first time.

The last complication I’ll mention is that this is largely a bootstrap effort, with most of the costs up-front and the benefits and profits significantly in the future. But I’m optimistic, and I believe that an investment of as little as $20 billion, as described in The Economics of Life In Space, will result in annual revenue of about 1.3 billion dollars (wholesale electricity at $0.03/kwh) for each of the 125 SPSs we could build from Apophis. After building the first few solar power satellites, the revenue stream becomes self-sustaining with no additional investment required, although the population and infrastructure in space would continue to grow.

Lets discuss some of the selection criteria for choosing asteroids for potential capture into Earth orbit.

The most important consideration is simply the proximity of an asteroid’s orbit to a useful keyhole through which the orbital engineers can design a capture mission in a reasonable timeframe.

The second consideration is the size of the asteroid. Bigger is not better when a 1 kilometer asteroid masses fifty times as much as Apophis, and thus requires a fifty-fold increase in the product of mission time and fuel mass. On the other end, a small 120 meter LL asteroid massing 2 million tons (and relatively poor in useful metals and volatiles) still has sufficient materials to build a single small Kalpana style habitat for 8,000 colonists plus twelve 5-gigawatt SPSs, and requires one tenth the fuel (all else being equal). Thus I view 120 meters as the smallest asteroid worthy of capture, since it is barely large enough to build a permanent habitat rotating at 3rpm for Earth-normal gravity and with adequate radiation and meteoroid shielding. We will need at least that many miners, steel-workers, welders, SPS construction workers, and support personnel such as farmers to build the infrastructure and solar power satellites.

Another consideration is the V-infinity of the asteroid, because slower asteroids are easier to move a distance large enough to make a significant difference in the slingshot, and less asteroid delta-V will be needed.

The potential magnitude of a gravity assist is also constrained by how close to the center of the Earth the asteroid passes – and I think it’s important to keep it out of the lithosphere. Worse, for a rubble pile we don’t want to pass closer than the Roche limit or the asteroid may be torn apart by tidal effects, much as Jupiter’s tide tore the comet Shoemaker-Levy into 20 fragments. The actual Roche limit depends upon density, but is likely to be of the order of 20,000 kilometers for a rubble pile asteroid near the Earth, and perhaps 5,000 kilometers for the Moon.

One might think that the composition of an asteroid would be the number 1 criteria, but in reality most asteroids should be quite valuable. Of course, a common carbonaceous chondrite might contain 25% nickel-iron mostly in the form of metal grains, 10% or more water, and several percent carbon plus everything else needed for life in space. But even a lowly LL chondrite will work.

The last consideration here is the opportunities for intercept missions. We need to modify an asteroids orbit when it is easy, some months or even years before the targeted close approach. This is difficult for a high-inclination long-period asteroid because it might only approach closely enough to the Earth for low-delta-V intercept missions once every ten or a hundred years. But an asteroid with a two-year period might present suitable launch windows every two years. Also, for asteroids with low inclinations, there may be two launch windows in a year as the asteroid passes inside and then outside the Earth’s orbit.

This table presents some possible candidates as of mid May. Some of these will be eliminated by further refinement of their orbital parameters, while others can likely be added as additional asteroids are discovered, or as orbits are corrected for known ones.

The entries on this table were gleaned from the Near Earth Object Close Approach database. Note that the various tables, databases, and lists at the NASA web site are inconsistent, sometimes even on the same page. For example, the orbit visualization tool often has significantly different closest approaches than the “close approach” data on the same page.

A side note: Many asteroids have only been observed over a few days, resulting in large uncertainties in their orbital parameters. The shapes, diameters, and masses of most asteroids are estimated, not known. Diameters are estimated from an asteroid’s brightness, distance, and albedo. But we can’t measure the actual albedo, and observations at multiple wavelengths are used to judge the asteroid class, and from that a typical reflectivity, and from that a formula results in an estimate of the diameter, and assuming an average density, we calculate the mass. This process has very large error bars. In April, radar imaging resolved the asteroid YU55. Previous estimates were that it’s diameter was 140 meters and its mass 4 million tons. The actual measurement revealed a diameter of 400 meters and an estimated mass of 87 million tons, a 20x mass increase.

Lets consider these asteroids.

Apophis is fairly well characterized and has a very close approach on 13-Apr-2029, although it may not be an LL chondrite after all, and may therefore have a different albedo, diameter (currently 270m), and mass (currently 27 Mt - million tons). As a candidate for Earth-orbit capture, it has the advantages of passing quite close (4.6 Earth radii), and relatively slowly (V-infinity of 5.87 km/s), plus a launch window occurs each April 13^th near the close approaches and is thus suitable for a one-year mission. Missions to improve our knowledge can be launched in 2013 and 2021.

2007 RY19 is noted as having possible very close approaches in some databases, but not in others, and the error bars are very large. The best opportunity may be 03-Dec-2024. Its mass (1.8Mt) makes it easy to move, and intercept missions can be launched every 7 years or so.

2001 WN5 is a bit on the large side at 646 Mt, but it will pass about halfway between the Earth and Moon in 26-Jun-2028, which may offer an opportunity to adjust its subsequent orbit that we shouldn’t pass up, even if the actual capture couldn’t happen for a decade or two more. This asteroid is large enough to build thousands of SPSs and habitats for at least 2 million people.

At 87 megatons, 2005 YU55 is three times as massive as Apophis, and approaches Earth, Venus, and Mars, giving multiple possibilities for gravity assists. Next year it will pass about 20% closer than the Moon’s orbit, but it won’t be that close again for quite a while (depending upon its new orbit after the Earth slingshot). In its present orbit, it makes frequent approaches, about every 5 years.

2006 WB is a small asteroid that won’t pass very closely (nearly 2.5 lunar distances) on 26-Nov-2024, but it is small, and we can possibly adjust its orbit for subsequent passes. Note that its mass is poorly constrained, with different databases estimating its mass differently by a factor of four, from 0.5 Mt to 3.0 Mt.

1994 WR12 also approaches Mercury and passes Earth every 2 years in a nearly 3:2 synchronous orbit. Its next close approach is on 26-Nov-2021, and it has a perfect size at 2 megatons (120 meter diameter) making this an early practice possibility for changing an asteroid orbit. It doesn’t pass very closely at all, however, coming no closer in 2021 than 8 times the Moon’s distance.

I’d like to point out that every one of these asteroids were placed into their current orbits by a slingshot around the Earth, a fact clear at a glance at the orbital simulation on the NASA web site. One of the principles of orbital mechanics is that an orbiting body (in a 2-body system) will always return to the location and velocity vector of its last orbit change. Ignoring hyperbolic orbits, one near Earth pass means more, until the body collides with the Earth or is deflected away by another planet.

A legitimate question to ask is, will NASA undertake an effort such as capturing an asteroid into Earth orbit? Personally, I think it’s unlikely, because (at least as I have envisioned it) this is a commercial endeavor. Certainly NASA would not build solar power satellites, although we can task NASA with related aspects of human habitation in space, including habitat design, launch vehicles and tugships, farming, space operations, and other research projects that advance humanity into the Solar System. We might even get NASA to capture an asteroid into Earth orbit as one way to avoid a future Earth impact. I strongly encourage this, as NASA is an excellent organization to make sure the orbital capture is done right (if expensively), and then NASA could sell the exploitation rights to private enterprise and recoup all mission expenses.

China does not face the same political constraints and the Chinese government could easily choose to capture an asteroid and build habitats and solar power satellites.

The United Arab Emirates certainly has the funds to capture an asteroid and build a fleet of solar power satellites. And actually, I can’t envision a more appropriate use for the oil wealth they’ve accumulated. While they haven’t demonstrated the technologies to execute such a mission themselves, they could certainly fund it, buying themselves the resources to build that fleet of solar power satellites, and converting the dwindling stream of oil revenue into a growing stream of solar energy revenue.

Capturing and exploiting an asteroid such as Apophis can be done by private enterprise. I estimated the required investment as about $20 billion, which is certainly within the capabilities of the largest companies. And the prospect of a revenue stream of $150 billion per year should excite their CFOs.

Ignoring the profit motive for a moment, we should also consider that there are other possible reasons to invest in space habitats, specifically: to promote a way of life. There are many churches with the capacity to fund this effort, yielding a platform in the heavens, and a starting point to go forth and multiply. Certainly the resources available in the asteroids and comets dwarf to insignificance the Earth’s resources, so in the long term, the only thing that counts is that move into space.

And whether NASA, China, the UAE, private enterprise, or even some other organization steps forward to undertake this mission, capturing an asteroid is an incredible prize, as is the building of a the first large permanent colony in space -- accomplishments which will permanently record its founders in the history books.

Continued research tops the list of the several logical next steps we should take. NASA is ideally suited for several of these, and the continuing search for potentially hazardous objects identifies the same candidate asteroids as a search for potentially captureable ones. We need much better knowledge of their orbits, size, and composition; we need to explore slingshot opportunities; and we need to seriously advance our ability to move permanently into space via closed-loop recycling of everything.

We also need to address several legal issues, which pose a serious problem for Western civilization private enterprise. Key among this is the right to own and exploit objects in space. If a person or company does not have the right to exploit space-based resources, they can have no incentive to acquire them, and the future of humanity in space is effectively dead.

We must also address the liability of moving asteroids. Certainly this should be done with the utmost care and intense oversight tempered with some sense of practicality. For example, the example adjustment to Apophis orbit that I propose here appears to pass through the 2036 impact keyhole. Does that mean we must move the orbit out and around that keyhole, or simply that we use reliable, even redundant systems, and closely monitor to track the potential need for additional intervention? I’m afraid that science and logic may have little to do with the outcome of that discussion.

Someone needs to design and build a tugship using thruster and power technologies available in an appropriate timeframe. I think the biggest challenge here might be in supporting deep-space, long-term missions with the human crews I think are necessary to get the job done.

Lastly, we should refine the cost estimates for space based solar power from in-orbit asteroid resources and using a variety of technologies, although this is certainly a commercial endeavor.

The bottom line is that we CAN capture asteroids into Earth orbit, thanks to the amplification of delta-V due to gravitational slingshots.

There are several candidate asteroids today, and there will be more tomorrow. Also, I did not look for opportunities where the asteroid close approach was to Venus, or Mars, or Mercury (let along Jupiter), and there is every chance that many more good candidates exist, although longer missions would be required.

The most important consideration to me is that capturing an asteroid such as Apophis places millions of tons of raw materials into Earth orbit where we need them to build solar power satellites, permanent orbiting habitats, and to advance humanity’s exploration and further exploitation of the vast resources of space.

Lastly, we should never forget that capturing a potentially hazardous asteroid converts a dangerous threat into a resource of immense value.

My personal web page, www.StephenDCovey.com, gives too much information on my background and other ventures. But it also contains link called “Project Apophis” which very briefly summarizes this presentation, and concludes with a call to action via a link to the Office of the Whitehouse.

President Obama needs a grand goal for NASA and the nation in the next decades, one comparable to Kennedy’s “We choose to go to the moon in this decade.” I believe that capturing Apophis into Earth orbit is such a grand goal, with benefits to global energy and warming (via those solar power satellites), and to space exploration, and to permanent, self-sustaining habitats in space. And it removes a threat to the Earth.

If you agree that we need a space-faring humanity and that exploiting asteroids is key, if you agree that sending cheap solar energy to Earth simultaneously helps humanity and reduces global warming, and if you agree that we should act to prevent asteroid impacts on the Earth, then please share the word. Follow that link and tell President Obama that he holds the key to the future of humanity in space, that capturing Apophis is feasible, affordable, solves many problems in a single step, and is a Grand Goal worthy of his – and this nation’s – focus. Thank you.