Thursday, June 3, 2010

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 13th 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,, 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.