# Near Earth Asteroid Relocation

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#### mikeemmert

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<font color="yellow">you are now a Scientist rather than a Free Space troll. Congradulations! <br /> </font><br /><br /> I wish I could take creditfor these calculations, but I am just a lowly Chef<img src="/images/icons/crazy.gif" />, I get these calculations from another thread I have on this message board; http://www.activeboard.com/forum.spark?forumID=33011<br />there is much more activity on SDC than there is over there, so I get his help, & bring those answeres over here. <div class="Discussion_UserSignature"> <font color="#993300"><span class="body"><font size="2" color="#3366ff"><div align="center">. </div><div align="center">Never roll in the mud with a pig. You'll both get dirty & the pig likes it.</div></font></span></font> </div>

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Here is GoogleNauts' most recent post;<br /><br />Going back to my previous post, let's now look at propellant expended!<br /><br />We found that the total velocity increment in two impulses would be around 12,778 m/s.<br />Now bringing back the orginal mass of the asteroid as 750,000 tons (I will assume this to be metric tons, so asteroid mass is 7.5*10^8 kg.)<br /><br />Let's start with Konstantine Tsiokolvsky's rocket equation:<br /><br />dV=Ce*ln(Mi/Mf) (1) where dV=the velocity increment, <br />Ce=the exhaust velocity, <br />Mi is the initial mass of the rocket, <br />Mf is the final mass of the rocket.<br /><br />Just to get a first order of magnitude solution, just to see how big of a rocket we'll need, we can do something which seems completely illogical: neglect the rocket!<br /><br />Taking equation one, and rearranging algebraicly to the useful form:<br /><br />Mi/Mf=e^(dV/Ce) (1a) where e is the base of natural logorythms and is about <br />2.7183<br /><br />But we can identify another useful quantity called the Mass Ratio usually denoted by<br /><br />MR = Mi/Mf (2) or similarly:<br />MR=e^(dV/Ce) (2a)<br /><br />The Mass Ratio is really important because it relates the empty mass of a vehicle to its fully fueled mass. Now we can do some useful computations. First, I want to use a NERVA style engine with a nominal specific impulse of 1000 seconds. The specific impulse is an interesting way to measure a rocket's performance: what it means is that with 1000 seconds of specific impulse, a rocket engine will generate 1000 lb of thrust (force) for every pound (mass) of propellant consumed each second. To sustain a thrust of 100,000 pounds requires consuming 100 pounds per second of propellant! Anyways, it is related to the exhaust velocity in meters per second (sorry about mixing units, I usually work in MKS) by the relation:<br /><br />Ce=Isp*g (3) where Ce=exhaust velocity m/s,<br />Isp=specific impulse in seconds,<br />g=9.80665 m/s^2, the acceleration due to gravity at<br />Earth's s <div class="Discussion_UserSignature"> <font color="#993300"><span class="body"><font size="2" color="#3366ff"><div align="center">. </div><div align="center">Never roll in the mud with a pig. You'll both get dirty & the pig likes it.</div></font></span></font> </div>

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#### spacester

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<font color="yellow">Doing the substitutions I get a Va=2733.8 m/s. So in order to put this asteroid into an elliptical orbit, we must capture it. To do this we must shed: 15,000 m/s-2733.8 m/s=12,266 m/s! In other words, the asteroid is moving faster than the escape velocity of Earth, so we must bleed off about 81.8% of its initial velocity! </font><br /><br />No. <br /><br /><font color="yellow">Asteroid wrangling isn't going to be easy! </font><br /><br />Yes. But your first dV (12,266 m/s) figure makes it look worse than it is. Actually, the second figure is way too low so in the end, that total number may be close.<br /><br />That's a very nice effort; I've not the time to offer a better answer, and I am very much not inclined to slow down the discussion here, but I can't let this go unanswered either. <img src="/images/icons/crazy.gif" /><br /><br />Velocity is a vector quantity. Note that the solution is pure algebra and no Calculus is required. It <b><i>is</i></b> rather advanced Algebra, but technically speaking, solving this problem is a matter of algebra and vector arithmetic. Euler's equations for an ellipse and related formulae are the heart of the analysis.<br /><br />This particular asteroid is not a good target, for both analysis and actual execution. In a way, this is almost an example of worst case for an NEO.<br /><br />The orbit is highly elliptical, which means that one cannot even use Lambert's Solution effectively. Lambert's is for transfer between any two circular orbits. It's what you use for ALL fastest trajectories between objects in circular orbits, even Star Trek class propulsion capability ('impulse', not warp <img src="/images/icons/smile.gif" /> ). <b>Hohmann is minimum energy, it can also be called 'the two-tangent solution'; to go faster, you employ 'the one-tangent solution'. To go faster than that, you use 'Lambert's solution'.</b><br /><br />These solutions are all based on transfer between <b>circular orbits.</b> AFAIK general <div class="Discussion_UserSignature"> </div>

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Eureka!!! <br /><br />In the last posts, I looked at what it might take to capture and manipulate a small 750,000 metric ton rock into an earth orbit given an inbound relative speed of 15 km/s. This led to a very large propellant consumption (2.68 times the combined asteroid and dry vehicle mass as propellant.) However, this situation is a bit over simplified. By stepping back and taking a look at the bigger picture we see that in order for this situation to happen, the asteroid must be in a very highly elliptical orbit about the sun because the relative closure speed is so high. Earth orbits about the sun with an average orbital speed of 29.2 km/s. An asteroid in an approximately similar speed, or in a slightly elliptical earth orbit crossing configuration will have just about the same speed relative to the sun, say anywhere from 28-30 km/s, but relative to the Earth the actual speed may infact be only about 0.5-2 km/s. The actual speed of course will depend on the actual asteroid, the precise orbital elements, the precise moment when interception or Earth Orbit Insertion Occurs, etc. And this is where it gets dicey, mathematically speaking...<br /><br />Interestingly, this leads us to the conclusion that inbound impactors must have predominantly been moving rather slowly with respect to earth, with a few moving much faster (in highly elliptical orbits) and with a tiny fraction of impacts really smokin' (impacts of 60-65km/s) because of the retrograde solar orbits. Let's hope we don't get any 5km diameter retrograde visitors!<br /><br />O.K., if we tailor our capture scenario so that we have a Near Earth Orbit crossing asteroid that, say, crosses the earth orbit with a heliocentric speed of say 30.5 km/s, if at that same point Earth's heliocentric speed is say 29.3 km/s, then the velocity we need to 'get rid of' is only about 30.5 km/s - 29.3 km/s = 1.2 km/s. The actual deficit requires intimate knowledge of the actual interception angle (the angle the asteroid's traject <div class="Discussion_UserSignature"> <font color="#993300"><span class="body"><font size="2" color="#3366ff"><div align="center">. </div><div align="center">Never roll in the mud with a pig. You'll both get dirty & the pig likes it.</div></font></span></font> </div>

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#### spacester

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LOL, we were writing at the same time, it cracks me up when that happens.<br /><br />I'll just repeat that delta V calculations need to be done using vector arithmetic.<br /><br />30.5 km/s in a direction at an angle to Earth's path around the sun at 29 km/s is a lot of km/s. (Google 'law of cosines') <br /><br />'uplink will close in a few minutes . . .' yikes, posting this, more later <div class="Discussion_UserSignature"> </div>

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Looks like NASAis thinking about this too.<br /><br />NASA May Use Ares/Orion To Visit NEOs <br /><br /><br /><br />Aviation Week & Space Technology, 09/25/2006, page 21<br /><br /><br /><br />Edited by Frank Morring, Jr. <br /><br /><br /><br /><br /><br /><br />Near-Earth objects (NEOs) are potential objectives for NASA's planned new generation of human space exploration vehicles,<br /> along with the Moon and Mars. Jeff Hanley, manager of the Constellation Program overseeing development of the exploration<br /> fleet, says a comet or asteroid in Earth's neighborhood could be a worthy objective for the Orion crew exploration vehicle<br /> (CEV) and its Ares I launcher, even though the Ares/Orion stack is being developed for a lunar return.<br /> "We're getting a study going on looking at using the Constellation architecture to send a CEV possibly to a near-Earth<br /> object, rendezvous with one and stay in proximity and gather readings, possibly gather samples, investigate those bodies<br /> and then return," Hanley says. "The performance requirements are very much within reach of this architecture we're building.<br />" He stresses that a NEO visit is only one potential application for the new human spacecraft that NASA has turned up as it<br /> polls the scientific community, and not a "design reference mission" like lunar return. "We're saying 'look, we're building <br />these big rockets. What can we do with them?'"<br /><br />http://www.aviationweek.com/publication/awst/loggedin/AvnowStoryDispla y.do?fromChannel=awst&pubKey=awst&issueDate=2006-09-25&section=In+Orbi t&headline=Space+industry+intelligence <br /><br /><br /><br /> <div class="Discussion_UserSignature"> <font color="#993300"><span class="body"><font size="2" color="#3366ff"><div align="center">. </div><div align="center">Never roll in the mud with a pig. You'll both get dirty & the pig likes it.</div></font></span></font> </div>

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#### mdodson

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If y'all want some math fun, "Space Resources and Space Settlements" NASA SP-428, 1979 leads into the fun of getting gravity assists from the earth, Venus, and the moon as a way of reducing propellant required. Some of the purely ballistic trajectories (1977 HB and 1943-1973 EC) show smaller trajectories than capturing the monster that Boris started off on. The tables used there unfortunately don't show any NEO's that have been discovered after 1977.

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Do you have a link? <div class="Discussion_UserSignature"> <font color="#993300"><span class="body"><font size="2" color="#3366ff"><div align="center">. </div><div align="center">Never roll in the mud with a pig. You'll both get dirty & the pig likes it.</div></font></span></font> </div>

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#### ebub

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too expensive. much cheaper to get it down here and mine it. Only one space trip, as opposed to hundreds.<br /><br />Bringing it down wouldn't be as much of a problem as landing it safely.

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#### brellis

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How about blasting some decent-size chunks off a NEA and into a trajectory that settles them into a Lagrange Point with earth? If we could manage that, perhaps we could do the same thing on Mars, have a gigantic sample-return payload waiting to be studied, mined, etc. <div class="Discussion_UserSignature"> <p><font size="2" color="#ff0000"><em><strong>I'm a recovering optimist - things could be better.</strong></em></font> </p> </div>

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#### mdodson

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"How about blasting some decent-size chunks off a NEA and into a trajectory..."<br /><br />I don't think we know the form of any asteroid well enough to plan where to place charges, and how to sequence them. Blasting might also blow away the water and other volatiles that are a large reason for fetching them in.

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#### mdodson

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"Much cheaper to get it down here and mine it."<br /><br />My interpretation was that the original premise of the thread was to get it in orbit for use in future missions, as opposed to sending it up from Earth at \$3000 / lb

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#### inventorwannabe

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I'm all with you Boris61! The asteroids is the starting point for human presense in space in a larger scale. OK, if I now have the technology - would it be allright for me to fly up and excavate any asteroid that I find interesting? Would no one object or would everybody stand up screaming "Very well done Mr InventorWannabe!". Sorry, this was my dark side showing up, I don't really believe in humanity when it comes to money and power! So keep tight on your ideas if you want to be a part of the future! There is no such thing as ownership if you can't prove it, they will steal it from your very hands if they can. I have done my homework, I have shown my ideas for people who will testify that it is original work.<br /><br />When it comes to your question - I don't know how much thrust it would take, it sounds to expensive. I would as others have written excavate it in situ, build a rotating colony around it to get gravity for the Bosses (thats all stakeholders working there). The rest is provided from the Earth or through the mining process. Solar power is my first choise for the energy need, nuclear is my second. To get things exported I would use a maglev to shoot goods to a collecting area near whereever the goods are ordered to, there my technology brakes the container and another incarnation of the technology collects it for further transport to earth, moon or whatever other construction site that ordered the goods!<br /><br />A Boss or stakeholder in my future Asteroid Excavation Plant is anyone who has given up all claims against the AEP, in return he or she is a partowner in the AEP and recieves a part of AEP's income. This is by no means a socialistic site though, it's more like first in - most out! The Boss can in turn hire others to do the work needed for retaining the Boss status. The claims put forward from the ones hired is the Boss responsibility to take care of, none the AEP's. So no claims can be put on the AEP form the hired ones and the Boss can only cl

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#### scottb50

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Anatoly Perminov, the head of Russia's space agency , said today that Russia will consider deflecting the near-Earth asteroid Apophis from its present path, according to news reports. After all, Apophis's orbit periodically brings the 270-meter asteroid uncomfortably close to Earth, and it has long been on the watch list of nearby bodies that pose a threat (however slight) to Earth. The only problem is that Perminov seems not to have done his homework on the subject.

http://www.scientificamerican.com/blog/ ... 2009-12-30

They must have some good Christmas parties in Russia! While I have to agree we can't stick our heads in the sand and ignore what has every possibility of becoming a reality, to go off on such a tangent, especially for someone who seems to be in a position where understanding the Apophis odds would not be going on like the sky is falling.

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#### cyclonebuster

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Boris,
I am betting a solar powered rail gun can shoot the iron deposits off the asteroid with tremdous reaction forces in the right direction over time to slow the roid down to capture it in Earths orbit. That's the theory now we work the math! 16% iron is a lot of mass we can use to our advantage. :mrgreen:

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#### EarthlingX

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scottb50":ew3ti1l7 said:
Anatoly Perminov, the head of Russia's space agency , said today that Russia will consider deflecting the near-Earth asteroid Apophis from its present path, according to news reports. After all, Apophis's orbit periodically brings the 270-meter asteroid uncomfortably close to Earth, and it has long been on the watch list of nearby bodies that pose a threat (however slight) to Earth. The only problem is that Perminov seems not to have done his homework on the subject.

http://www.scientificamerican.com/blog/ ... 2009-12-30

They must have some good Christmas parties in Russia! While I have to agree we can't stick our heads in the sand and ignore what has every possibility of becoming a reality, to go off on such a tangent, especially for someone who seems to be in a position where understanding the Apophis odds would not be going on like the sky is falling.
If they use this as an excuse to properly finance Angara, i see no problem with that
As to the New Year (i wouldn't be so sure about Christmas) parties there, some live to tell

It is also an initiative to combine world efforts against a common threat, real or only potential, which i find good and welcome.

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#### EarthlingX

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Here is another initiative to combine forces:
Panel calls for global 'asteroid defence agency'
The world should organise its defences now in case an asteroid is found on a collision course with Earth, says a group of US scientists.

There are huge numbers of asteroids that come close to Earth's orbit, called near-Earth asteroids (NEAs). Millions of them are large enough to do serious damage in an impact, including the asteroid Apophis, which has a small chance of hitting Earth in 2036.

And
Experts Chart Steps For Global Asteroid Warning Network
A group of international experts has outlined steps to establish a global detection and warning network to deal with possible asteroid threats to Earth.

from the conclusions:
"We are fully aware that there is a lot of resistance to creating new bureaucracies and massive new institutions," said SWF Technical Advisor Brian Weeden.

"So the objective of the workshop and future discussion is not to create a new United Nations function or entity, but to try and use existing capabilities already being provided by States or institutions and adding other necessary capability. There needs to be a coordinated, global response to asteroid threats, and we are working to find the most efficient and effective way of doing just that," he said.

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#### HopDavid

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Re:

What would it take to relocate a 100-meter diameter asteroid to Earth - Lunar L1 orbit, or GEO? The asteroid pictured is about 3 million tons, or 100,000 Shuttle payloads. It is in an Aten orbit, & approaches to within 2,000,000 miles of Earth orbit once every 3.6 years, traveling 1% out of the ecliptic.
After we have captured it what could we do with it.
Our asteroid is, 33% silica, 24% magnesium / sulfur, 16% iron in the form of chunks, pebbles & granules, 6% H2O 3% carbon, 2% aluminum, & 16% trace element & minerals.
. Never roll in the mud with a pig. You'll both get dirty & the pig likes it.

Boris, if you want to find the nicest asteroids in terms of delta V, go to
http://neo.jpl.nasa.gov/cgi-bin/neo_ca

You can sort by V-infinity. V-infinity is the asteroid's speed with regard to earth when it's in earth's neighborhood, but not so close it's been sped up by earth's gravity.

On this page I usually choose "future only" and leave the other pull down menu options alone, but you might want to use it differently.

If you do it early enough, I believe just a slight nudge can substantially alter the asteroid's periapsis altitude during hyperbolic fly by.

The asteroid's speed at periapsis is sqrt(Vesc^2 + Vinf^2) where Vesc is escape velocity at the altitude of periapsis.

I whomped up a spread sheet where you can type in the asteroid's V infinity. You can also type in altitude of periapsis and apoapsis of the earth orbit you want to park it in.

The delta V needed to park it in the orbit you set is given by insertion burn from periapsis

If you play with this, you will find it takes a lot less delta V when your parking orbit has a very low periapsis and very high apoapsis.

And if your periapsis is low enough to be atmosphere grazing, aerobraking can provide delta V. However this is very dangerous. I would use this technique for small payloads from an asteroid but certainly not an entire asteroid as this might cause a Tunguska or even Chicxulub impact.

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#### Valcan

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Here you might live this book if you like the idea.

http://www.webscription.net/p-1108-live ... r-die.aspx

I think mining and developing NEO's for materials and to develop them into stations. For resources, research, industry. Hell even for food eventually.

Step one to conquering the solar system, shipyard.

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#### scottb50

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Step one to conquering the solar system, shipyard....

Step one is getting off the planet.

Step two and three are pretty straight forward. If an asteroid or Comet could be a resource won't be known until we are there. It might be easier, and cheaper, to send rovers first.

Mars and the moon both need manned stations and exploration and exploitation. Huge antennas and optical telescopes on the dark side would come to mind. Hubble II, on the surface of the moon, manned, could be an idea. Mars would entail years of exploration which would require a number of people over an extended period.

Other places don't offer much, Mercury might have heavier metals, or more of the same heavy metals Earth has, and beyond Mars is a one way trip. Within those bounds is a pretty huge area though.

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#### HopDavid

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scottb50":ut2sakwx said:
Step one to conquering the solar system, shipyard....

Step one is getting off the planet.

Step two and three are pretty straight forward. If an asteroid or Comet could be a resource won't be known until we are there. It might be easier, and cheaper, to send rovers first.

We've used radar to find subterranean water on Mars. I'm hoping we could make fly by probes that will five us info about an asteroid's interior as well as exterior. Because fly bys would be considerably cheaper than landers and rovers.

After relatively inexpensive prospector probes have found resources, then it might be worthwhile to send more expensive infrastructure to an asteroid.

Initially, the most valuable resource won't be platinum, gold, diamonds, etc. It will be water and other hydrogen compounds. That is because propellents outside earth's gravity well can reduce cost of space flight.

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#### Valcan

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scottb50":3njk6btk said:
Step one to conquering the solar system, shipyard....

Step one is getting off the planet.

Step two and three are pretty straight forward. If an asteroid or Comet could be a resource won't be known until we are there. It might be easier, and cheaper, to send rovers first.

Mars and the moon both need manned stations and exploration and exploitation. Huge antennas and optical telescopes on the dark side would come to mind. Hubble II, on the surface of the moon, manned, could be an idea. Mars would entail years of exploration which would require a number of people over an extended period.

Other places don't offer much, Mercury might have heavier metals, or more of the same heavy metals Earth has, and beyond Mars is a one way trip. Within those bounds is a pretty huge area though.

Yea i understand what your saying and mostly agree its just i usually get rather long winded in this subject and im trying to break a bad habit.

Would be great if we could figure out how to build cheap robust asteroid probes that could be mass produced to find the best ones.

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