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Why we need this idea:

Everything we do in space today is trapped within the context of what I call the Apollo Equation:

1 kg of equipment or consumables in space

=

1 kg of equipment or consumables that must be LAUNCHED FROM EARTH INTO SPACE.

This is a crippling problem because launching even one kg into orbit can cost thousands of dollars. If human beings are ever to become a space-faring civilization, the we must address the problem of the Apollo Equation in some way. There are basically three approaches to solving the problem of the Apollo Equation:

Develop cheaper rockets to lift things into space.

Develop ways to lift things into space that do not involve the use of rockets at all.

Use material that is already in space to build equipment and manufacture consumables so you don't have to launch it from Earth.

In my opinion, the third option of industrialization of space, or what NASA calls "In Situ Resource Utilization", is the best approach.

Pretty much all the material in space is either on the Moon, or in asteroids. Planets have atmospheres and gravity wells that make getting extracted resources anywhere else expensive. The moon is a tempting target, but it still has a significant gravity field and is well outside of Low Earth Orbit. Asteroids have trivial gravity, but are even farther away. But, what if we could change that? The best case scenario would be for a sizable asteroid to be captured by Earth's gravity in Low Earth Orbit where it could be mined with relative convenience and safety.

We could wait a very long time for this to happen by chance, but I am going to make the case below that it is well within our capability to cause a SMALL asteroid to be captured. To do this several things must happen:

1. An appropriate SMALL near-Earth-asteroid must be identified.
2. A maneuvering probe must rendezvous and dock with it.
3. Once docked, the probe must maneuver the asteroid such that, rather than flying past Earth it will be captured into Earth orbit.
4. Mine and sell the asteroidal material in orbit.

Each of these steps present difficulties. However I believe they are feasible and I discuss them each in their own sections below:

Section I. Targeting the right rock.

There are several concerns that must be addressed if such an endeavor is to leave the planning stages. The largest of these is safety to terrestrial populations. The last thing one would want would be to risk causing a damaging Earth-impact with the target asteroid. This means that the target asteroid must be small enough that it poses no danger if it impacts with the Earth. Conversely, it must be large enough that the harvested asteroidal material can be profitably sold.

5-meter-wide asteroids are both small enough to be safe, and large enough to be potentially profitable.

We know asteroids of this size-range are harmless because they hit the Earth's atmosphere all the time. Observations by satellites of meteors entering the Earth's atmosphere have demonstrated that small asteroids obey the same power-law that governs the sizes of large asteroids. That power law is: N( > D) = 37D ^- 2.7 where N(>D) is the expected number of objects larger than a diameter of D meters to hit Earth in a year. 5-meter-wide asteroids therefore hit the atmosphere of the Earth 0.45 times per year... 5 times a decade. If meteors were causing significant damage to the Earth's surface 5 times a decade, we would know about it. Therefore 5-meter-wide asteroids do not cause significant damage. These calculations are confirmed by observation; the 2-5 meter asteroid 2008 TC3 was observed to strike the Earth with no significant damage.

An M-type mostly metal asteroid's density is about 2g/cc. A 5-meter-wide sphere has a volume of 36815538 cubic centimeters. Therefore, a 5-meter-wide asteroid would have a mass on the order of 73,000 kg. Using the cheapest heavy lifter likely to be available in the foreseeable future, the Falcon-9 Heavy, that much mass would take 4.9 launches to get into GTO at 78 million dollars per launch. Therefore, as much as 382 million dollars of material can be mined from one object of a size that we know to be harmless to Earth. Note, the value of such material is not derived from its composition so much as its location. For more on potential composition-independent markets for asteroidal material in Earth orbit see section IV.

It should also be pointed out that many more asteroids in the 5 meter wide range pass NEAR the Earth than actually hit it. A crude estimate of the number passing within a given distance of the Earth can be extrapolated from the results of the above power law. The cross section of the Earth is nearly a circle with a radius of about 6371 km. As derived above, this cross section intersects with a 5 meter asteroid's path 5 times a decade. Thus, a planet with the mass of Earth, in the Earth's orbital path, that was ten times larger in cross section would intercept 100 times as many asteroids of this size because it's cross section would be 100 times larger (The area of a circle is proportional to the square of the radius). Thus, 500 five meter wide asteroids come within 57339 km of the Earth's surface each decade, or about 50 a year. To put that in perspective that's still only 1/6th of the way to the moon. If we consider any five meter wide asteroid that would naturally pass within the Moon's orbit (384400 km) as a reasonable target for capture, then based upon the above reasoning, there should be 1629 asteroids to choose from each year! This means that efforts to capture such an asteroid have the luxury of being able to choose a target that is moving at a convenient velocity and trajectory. (See section three for more details).

Section II. Docking a probe to the asteroid.

A 5-meter-wide rock has negligible gravity, so simply "landing" a probe on it would not be sufficient for the purpose of maneuvering it. I envision the docking-mechanism to resemble a large Kevlar bag. One primary advantage of such a docking structure is that it totally encapsulates the asteroid, ensuring that should the asteroid become fragmented as a result of maneuvering stresses all of it will remain inside the docking bag. In addition to ensuring the maximum mass is recovered from the asteroid, this will protect against the risk of seeding asteroidal debris into Earth orbit.

In addition to the actual docking mechanism, the probe must also carry maneuvering thrusters capable of altering the asteroid's spin, and angle of attack relative to the Earth's atmosphere.

Section III. Capture of the asteroid.

In order to maneuver an asteroid into Earth orbit, it must be moving at a velocity that will let it orbit the Earth. The fastest orbital velocities are at low altitudes, and the lowest stabily orbiting satellites orbit at around 200 km above the Earth's surface. At an altitude of 200 kilometers, the required orbital velocity is just over 27,400 km/h (7.61 km/s). Asteroids that naturally come close to the Earth arecalles Near Earth Objects(NEOs). Such asteroids are moving at velocities between 4 km/s and 40 km/s relative to the Earth. Therefore, many of these objects are already moving at velocities that would allow for them to be captured into Earth orbit. The only thing that needs to be changed is the angle of attack that the asteroid has as it approaches the Earth. For example, lets say that we choose an asteroid that is moving at, 7.61 km/s. It would need to have it's trajectory, which being a NEO is already coming close to the Earth, modified so that it passes the Earth at an altitude of 200 km. This would cause the Earth's gravity to balance against its pre-existing momentum such that it would be deflected into Low Earth Orbit (LEO). If it was moving slower than 7.61 km/s, then it would need to be deflected into an orbit that was at a higher altitude, and if it was moving faster than 7.61 km/s into an orbit that was lower than 200km. Note the fuel-intensive (and therefore expensive) job of reducing the velocity of the asteroid to Earth orbital insertion velocity is NOT necessary for a substantial fraction of NEOs. Only the relatively easy task of tweaking the angle of its approach is required. (I expect that rectifying the spin of the asteroid would also be needed to do that).

Section IV. Marketing asteroidal material in orbit.

As I mentioned in the introduction, right now, the Apollo Equation causes us to launch huge amounts of mass into space which is ruinously expensive. Let's briefly look at the consequences of this simple fact. Because of the Apollo Equation, we can not afford to launch into space the needed structural steel elements to allow for the construction of habitats that spin to produce artificial gravity. As a result our astronauts suffer from bone and muscle degeneration. Because of the Apollo Equation, we can not afford to provide space habitats, such as the International Space Station(ISS), shielding against cosmic and solar radiation. The ISS is partially protected by the Earth's magnetic field, but if we ever intend to push out beyond Low Earth Orbit, a more general solution must be found. Our space-probes and habitats are in a shooting gallery of space-debris and micro-meteors. The obvious solution to this problem is to armor them with enough material that they can not be damaged by such impacts. However, because of the Apollo Equation, our space craft are made of paper-thin, super-light, aptly-named "space-age materials". Asteroidal material in orbit could be used as a solution against such problems by breaking the Apollo Equation. In order to sell asteroidal material to space agencies, it must be refined into a useful product. Fortunately, many such products require little to no such refinement to be salable. Possible products include:

• High-tech sand-bags. If the asteroid can be ground into gravel, then that gravel can be placed into bags (launched to orbit empty and thus cheap). Filled, such sand-bags would constitute armor and shielding that could be mounted onto the exterior of space stations, or space craft. Sand bags have been used for years to stop bullets, and could be used in a similar way to protect space craft from micro-impacts. Likewise, by placing more mass between the occupants of the space craft and the space environment, such sand-bags would provide increased radiation shielding. The gravel might be mixed with a foam binder to provide increased stability to the final product. The only in-space refinement that this product would require would be to grind up the asteroid and bag the resulting gravel. This product is close to 100% independent of the composition of the asteroid. The asteroidal material need only be non-volatile, and non-radioactive.
• Sample Return. The entire idea of capturing an asteroid into Earth orbit is in effect a sample return mission. Science Institutes across the globe might be induced to purchase asteroidal cores that had not been contaminated by terrestrial matter. Alternatively, fragments of a captured asteroid could be sold to the public with suitable marketing. The only in-space refinement this product would require is the ability to extract small portions of the asteroid and return it safely to Earth. Again, this product is largely independent of the asteroid's composition. If sold to the public, one would want to ensure it was non-toxic, and/or encase it in plastic, but that's about it.
• Vibration Dampening. Space telescopes such as the Hubble must employ gyroscopes to hold themselves perfectly stable as they make observations. This is needed, in part, because as they orbit they are subjected to slight variations in the gravity of the Earth, the Moon, and other astronomical bodies such as the Sun. This problem is exacerbated by the fact that the telescopes are not very massive, so it does not take much of a shove to move them. If they were docked to an asteroid, the asteroid's mass would act as a dampener making them less subject to vibration. They would still need gyroscopes, but would need them less, letting the gyroscopes operate at lower velocities in a manner much less likely to break. The only refinement that this product requires is the attachment of a gimbaled Space-Telescope docking point to the already encapsulated asteroid. Once again, this product is almost perfectly independent of the actual composition of the asteroid.
• Soil and Microbial Nutrients. As our presence in space expands, we are going to want to be able to grow food in space to reduce or even eliminate the need for supplies sent from Earth. This use of asteroidal material is semi-independent of its composition. One would want to ensure that the asteroid-manufactured soil was devoid of heavy metals and other toxins.
• Refined Metal. Unlike the above products, this product requires substantial refinement infrastructure in orbit. It would be hard to get investment to cover the deployment of such infrastructure until the capture of one or several asteroids had been demonstrated. However, the sale of structural steel in orbit would be the target product for long-term development.

None of this requires technical capabilities that we don't already have. Numerous space agencies have demonstrated that we can send probes to rendezvous with and even land on asteroids already. We have demonstrated that we can insert objects into orbit of planets. We have demonstrated that we can detect approaching NEOs and predict their orbital paths.

I would like to thank Austin Pivarnik for catching several math errors that I made in the first version of this essay. Thanks to his diligence, I now know that the velocity numbers of NEOs make this scheme of asteroid mining MUCH more feasible than I had initially believed.

NOTE: This is a revision of the original article, available here

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