Thursday, August 14, 2008

Capturing Apophis

Past blog posts of mine have described many aspects of the expansion of human civilization into space.

Today I'd like to focus on the orbital mechanics of capturing an asteroid, specifically 99942 Apophis (aka 2004 MN4).

Apophis is the near-earth asteroid that made the headlines in 2004 because of it's feared potential impact on Earth on Friday, April 13, 2029. Additional observations revealed that Apophis will miss by a hair (passing closer to earth than our geosynchronous satellites), but its orbit will be changed by that close approach such that there is a small chance of an Earth impact on April 15, 2036.

Apophis is a small asteroid, only about 300 meters in diameter (approximately 1,000 feet). This is too small to create an ELE (Extinction Level Event, to borrow a phrase from the movie Deep Impact), but it could devastate an area the size of Connecticut, or strike the ocean creating tsunamis that would kill millions of people and destroy trillions of dollars worth of property. Note that if we do nothing, Apophis will almost certainly strike the Earth some day, although perhaps not for thousands of years. We must take steps to prevent that catastrophe.

Luckily, one method of preventing a future Earth impact is to place the asteroid into Earth orbit, from which a future Earth impact is impossible. The near-Earth pass will result in a gravitational slingshot, changing its orbit.

As it passes near us in 2029, Apophis will be moving approximately 5 km/s slower than the Earth in its orbit around the sun, dropping in toward the orbit of Venus (and ignoring, for the moment, the additional speed it will gain dropping into our gravity well). If we do nothing, the near-miss will speed up Apophis by a few km/s, turning it from an Aten Asteroid (a near-Earth asteroid whose orbit is primarily inside of the Earth's) into an Apollo Asteroid (one whose orbit is close to the Earth's orbit, at least on average).

My own rough calculations indicate that if we speed up Apophis by a relatively small amount, such that it passes even closer to the Earth, then it will gain even more speed from its slingshot around our planet. A deflection into an orbit nearly co-circular with the Earth's will also speed it up to approximately Earth's orbital speed (a 5 km/s velocity increase is needed--well within the range of possibilities). Apophis only needs to reach closest approach about 500 seconds earlier than on the current orbit, still passing 10,000 kilometers above the Earth's surface.

It will have too much speed (due to the earth's gravity well) and will speed away (and outward), but will return to the vicinity of the Earth with a low enough speed that another slingshot around the moon will drop Apophis into Earth orbit. As a result of these two slingshot maneuvers, Apophis will have an orbit whose apogee is near the moon, and whose perigee (closest approach) can be tuned by small adjustments in its orbit before it performs the Lunar slingshot.

Over time, some additional velocity should be removed (by ion thrusters or other propulsion methods) so that its orbit is entirely within the moon's orbit, or some other permanently stable orbit. We don't want it crashing into the moon, either. Apophis is a far too valuable resource to waste.

I'm confident that the orbital changes needed to capture Apophis are within current technology capabilities, although more detailed analysis is certainly needed. And this is an opportunity that should not be missed: a billion dollar mission to capture Apophis will result in a trillion dollar resource in high-Earth orbit, and avoid a trillion dollar catastrophe at the same time.

Apophis masses perhaps 50,000,000 tons. While the largest percentage is oxygen, approximately 20% is metals (primarily iron). It contains large amounts of magnesium and aluminum, and significant quantities of hydrogen (think millions of tons of water). It contains more than enough silicon to build all of the power satellites we'll ever need.

Who could pass that up? If not NASA and the U.S. government, then perhaps the Chinese, or Dubai. Or even private enterprise; this project is well within the funding capabilities of large corporations or even a few individuals. Perhaps Bill Gates would like to have a private moon around the Earth. Or the Disney corporation (I'm thinking Disneymoon), or Hyatt Hotels (I'd love to stay at the Apophis Hyatt some day).

Any takers?


beowulf2700 said...

Sound like a good idea.... have you done the math?

Stephen D. Covey said...

I've done the "back of the napkin" energy/momentum calculations. What I've not done is a full 3-D model. I'd hoped that some reader would have access to an existing orbital mechanics model (the kind used to compute spacecraft slingshot maneuvers) and do it for me.

No such luck.

The slingshot needed to impart enough energy to Apophis is easily achieved during its near-miss.

By choice of a suitable orbit, a second slingshot past our moon can remove (or add) additional velocity (up to 1.5 km/s) to drop Apophis into an extremely eccentric Earth orbit.

The total change in Apophis's arrival time is less than 1000 seconds, which our technology can achieve (given several months or a year or more lead time, depending upon which technique is used).

I did that math as part of a short story I wrote, in which I proposed the use of a cluster of Ion drive thrusters to accelerate Apophis at the hellish rate of 6 one-millionths of a G for several months. That would do it, and ion thrusters of sufficient size have been demonstrated in the lab.

What I have NOT done is model an actual slingshot and the subsequent second slingshot by the moon. In my story, I assumed the Lunar pass would take place several months later.

While I'm confident of my energy numbers, the actual timing is completely a wave of the hand, and the reality may be shorter or much longer, even a year. During the 2029 near miss, the moon is in the new phase, not in a favorable location.

It does take an enormous amount of energy to change the orbit of a 50,000,000 ton asteroid. That's why I left it in a poor orbit (near the moon's orbit at apogee, relatively close to Earth at perigee). It is extremely difficult to make significant momentum changes to Apophis without some larger body to slingshot past.

Also, if you use the moon to do a slingshot (to drop Apophis into Earth orbit), orbital mechanics requires that the resulting apogee be near the moon's orbit; no way around that.

The bottom line: my energy numbers are, I believe, valid. We CAN make the needed tuning to Apophis's orbit. However, my timing estimates (how long it would take to achieve a final Earth orbit) could be way off, and may require more than one Luna slingshot to optimize the orbit. Note that we would want to ultimately change it's orbit to avoid possible Lunar impacts.

Others have proposed that the ideal orbit is a 2:1 resonant orbit around the moon (a two-week period). I don't like it because it still takes a lot of time and energy to rendezvous with an object in that orbit. I'd rather have one closer to Earth; perhaps a 4:1 resonant orbit, but that may be too close for comfort.

What I'd REALLY like is an orbit much nearer the Earth (a much lower apogee, requiring less energy for rendezvous), but I don't see a way to achieve that without another asteroid to use as a slingshot to further adjust the orbit.

Thad Beier said...


Well, if you use aerobraking as you go by the earth, you can change the speed quite a bit. You'd have to be very very sure of your math though!

Stephen D. Covey said...


Aerobraking won't be helpful, for two reasons. One is that orbital mechanics thing: the last position of acceleration is part of the new orbit, and we don't want Earth's atmosphere to be part of its orbit!
The second reason is that Apophis is almost certainly a rubble pile, and would be torn into a stream of gravel, no longer a gravitationally bound asteroid.

michael Hanlon said...

An Earth orbit or a Moon orbit is too risky. That is why I recommend a "system" orbit and park the devil at one of the Lagrange points (Preferable would be the one between the E/M. You'd have the moon as a backdrop to watch the progress of building a station around it. And, you'd have it near low earth orbit which you'd prefer.).

Stephen D. Covey said...

Michael, you picked an unstable Lagrange point. Only L4/L5 are stable. The one you suggest is also far from the Earth (closer to the moon). I agree with you on the desirability of choosing a safe orbit, and by safe I mean stable to perturbations from the Moon, Sun, Jupiter, and other planets.
Personally, I'd prefer an eccentric orbit that comes much closer to the Earth at apogee, so we can get to it in a relatively short spaceflight. And an orbit whose apogee is a few thousand kilometers outside of our geosync satellites (perhaps at 45,000 kilometers) would be a great place from which to maintain them, or to build and launch solar power satellites.

michael Hanlon said...

Who cares if the L1 is unstable or not? It is exactly where you need the resources to construct the power generating facilities you envision. By the time any effort need be exerted to change where it is or headed, it shouldn't even be there any more. We, or our inventory control people should have juxt in timed it to the assembly floor. Easiest place to get to. Perhaps the most difficult position to target with insertion math, but who's afraid of wearing out their slide rulers these days. (Took my civil engineering final using a slipstick and walked out a full hour before those who were using Calculatabators.
Now comes my well earned swirlly word.

michael Hanlon said...

I will post this one on several sites. As it deals with a sensitive military program, I must be wary of the crumbs I can toss to the public. But since the system is over twenty years old, most of the technology should be out there already and not violate any secrecy level.
Microwaves or lasers? Both generate photons. The laser, being a higher frequency, puts out more energy per oscillation. But our application is not looking for bang for the buck. We want slow and steady. We currently have a "mazering" system. The Navy uses it in their Aegis Program. Directed, coherent beams of microwaves can be focused on a target in far space, though with weak effect when it disperse at that range. A small Phased array antenna and a solar powered microW transmitter could easily be placed to chase Apophis within a year. It's off the shelf technology.

michael Hanlon said...

In all my journeys through this virtual library, everywhere I looked, It was boom or bump. The bump methods would be applicable to a capture effort. Ways to bump/push: ion drives, nuclear engines, small booms to effect velocity deltas. Not noted was a mention of my photon push or another way, land an E/M mass rail driver on it and toss off matter to impart dv/dt. jack.123 thinks a net and tug engines may work, but I feel that would cost more to build, deliver and operate than we would realize in new material. I think that an Earth orbit Xmitter of microwaves, solar powered, coherent and phase directed at the object whenecer it is out from behind the sun over the next two decades will do the trick!!! Think of it as a repulser ray and maybe we get some imaginative thinkers on board.

michael Hanlon said...

Regarding your response right there <--- ( oh, yeah, this'll move when entered). ReBoot whirrr. Ahem.. Regarding your answer to beowulf2700 and needing an anomation in 3-d, jack.123 says the same @ SA planet blog. For the life of me, I see no detrimental effects to the cause if such a media presentation existed. Would not the NASA or ESA organizations have that capability already in house and need only a work order generated to see it gets created?
And my swirlly word is:::: honest, I gotta look it up, preendo!!

Stephen D. Covey said...

Michael Hanlon's post about L5 got me thinking about what I think is a perfect target orbit that might just be achievable. But I don't know that it's possible. It partly depends upon whether a slingshot is possible through the virtual gravity well at L5.
What if we could insert Apophis into a 3:1 Moon synchronous orbit with L5 at perigee (400,000 km) and apogee near 40,000 km?
Intuitively, it feels like that orbit could be stable (as are the L4/L5 orbits), and useful (as near the geosync orbits where we'd also place our solar power satellites).
A 3:1 Moon synchronous orbit would have a period of 9.1 days, and would pass through L3, L4, and L5 in successive loops.
Wouldn't a Lagrange Touring orbit be cool? Not to mention useful!
Looking at an Earth-Moon gravitational potential diagram, I don't see how we could possibly insert Apophis into such an orbit. Remember, it takes a big moon or planet to impart a significant delta-V. But perhaps some clever engineer can see something I don't. I never dreamed we could do something as clever as all those gravitational slingshots used by the Cassini probe, so apparently anything is possible if you are sufficiently creative.

michael Hanlon said...

I know I have poor vision, but am I seeing things right? In the NASA still diagram of what happens in 2029, it sure seems like Apophis first passes through the E/M L3 point behind the Earth, gets bent (sling shotted) and proceeds to pass through the L1 point before it gets to the moon. We needthat German kid to figure out how close the encounters are to each at L3 and L1.

michael Hanlon said...

I think I mean if it's there at L3, we can easily adjust its direction. Easiest place to move orbit headings is at a Lagrange point. Then after L3, if we've put it right at L1 we can almost not do anything but put it into a lazy eight orbit, slowly precessing with the moons center each time it slings around the Earth.

michael Hanlon said...

.1)We lost the Planet Bombardment blog site at SA before I had a chance to record it. I had tracked their deletion activity and I thought that tonight would be its las tnight. Okay, I admit that some things I don't get figured correctly, but many I do.
.2)With SA gone, I lost that link you, Stephen, posted from NASA about the animation. Could you possibly re link it here?
.3)I asked at the Kuiper Zone blog if we might join in as Apophis is possibly derived from objects which developed there. We'll see if they welcome Project Asimov or not.

michael Hanlon said...

I apologize to all. The SA site is still there . There is a page two to their blogging system and the site has simply been shifted to a middle burner. I blame my error on excessive drinking , living too loose a lifestyle, a lack of religious commitment and early onset dementia. Mea culpa, Mea Maxima Culpa. I promise to do it again. No, No. Not do it again wellmaybe just a little? obionf

michael Hanlon said...

Another aspect of the lazy eight orbit for Apophis which should convince all that it is the BEST solution. It dawned on me that in that shaped journey it would be like a Lionel Train set. Once inserted into the orbit it would cicle the Moon and rise to the L1 point, shedding V's the whole way. Once it got there, at some small v of our own, we could jump on and take the piggyback ride of our lives. We'd drop down toward the Earth and jump off at the right place to get it the sling it needs to rise up again to L1 where others wanting a ride out to the moon could easily (or efficiently) hop aboard to a tethered or net attached structure of a living quarteers and chug out to the Moon, drop off at the right time and let the train continue on its schedule. Oh that pesky item, a schedule. Well, I'm at first thinking it will somehow be a reflection of the Moon's orbit time around the Earth, 28 days. The longer leg is around the earth so,16 days to the earth side of L1 and 12 days to the moon side.

michael Hanlon said...

The following link joins to the group of people who are behind the gravity tractor idea of accomplishing dx's, dy's and dv's in regards to moving asteroids. I found a site at ESA that wanted to do a similar thing to my microwave pushing idea. They wanted the foresight probe to carry 500 lbs of black or white paint and coat the thing in one color so that the sun's rays would push or pull it (depending on the hue chosen) But for that to be effective, they'd have to stop the rotation of the rock else when it turned side away, that side would radiate energy off and nullify what was going on on the other side, So, that means landind an engine package and robots to place them at possibly 2AUs away. Think again, drawing boards come cheap. With the microW scenario, if you know the rate of tumble you could pulse or duty cycle control when energy is imparted so that it only effects one side. And do you know any auto body guys who'd travel that far away from their paint shop to do a job? Jesse James maybe?
Back to the tractor pull idea. My microW is an idea for a long term solution. If changes are wanted in the short term, then what ever vessel you send to install thrusters could also after serve as a tiny grav well for the object to fall into. . So, short term and the sooner the better,as far as I maintain go hitch a tractor to a rock in space. Drag it to the L3 point and push it around the Earth toward the L1 point. Go over the poles to do this as a earth-poles/Moon-poles figure eight is the bestest of the best orbit or placement choice..
I blather much, too much. The tractor site then:

And what better thing to do than get a "Foundation" involved in Project Asimov?
OOOH, this one's easy, thank you, Stephen, baker!!

LottoLarry said...

Love the concept, but can I tweak it a bit? What about using a couple of VASIMIRs to settle it into geosynchronous orbit, to mine its content, but also to use as a base for the elevator that will become a reality at about the same time?

Knurd said...

Oh this is a terrific opportunity to apply experimental carbon fiber nano tube technology, build a space elevator, and mine the sucker.

A general philosophy that has guided many lives: if something bugs you, devour it.

Deef Fourjay. said...

Found this intriguing log; but I'm thinking that capture is politically unfeasible, due to public fear of a catastrophic mishap. Maybe we could go up and slice small pieces off (say 50 meter diameters at a time) - big enough to mine but small enough to shepherd into orbit. Anything we can't salvage should be routed far away from our orbit.