Limited Uranium Supply ?

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Limited Uranium Supply ?

According to the World Nuclear Association, there is effectively an unlimited supply of uranium to power our current and future nuclear power plants. They say that between the use of new technology "breeder' reactor and expanded exploration effort, we can supply a significant portion of future energy needs. Until now, I have accepted the CM site consensus that we have a peak uranium fast appraoching that is similar to peal oil.

I wonder if their conclisions are valid ?

http://www.world-nuclear.org/info/inf75.html

Jim

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Re: Limited Uranium Supply ?
Tuesday, November 17, 2009

The Coming Nuclear Crisis

The world is running out of uranium and nobody seems to have noticed.

The world is about to enter a period of unprecedented investment in nuclear power. The combined threats of climate change, energy security and fears over the high prices and dwindling reserves of oil are forcing governments towards the nuclear option. The perception is that nuclear power is a carbon-free technology, that it breaks our reliance on oil and that it gives governments control over their own energy supply.

That looks dangerously overoptimistic, says Michael Dittmar, from the Swiss Federal Institute of Technology in Zurich who publishes the final chapter of an impressive four-part analysis of the global nuclear industry on the arXiv today.

Perhaps the most worrying problem is the misconception that uranium is plentiful. The world's nuclear plants today eat through some 65,000 tons of uranium each year. Of this, the mining industry supplies about 40,000 tons. The rest comes from secondary sources such as civilian and military stockpiles, reprocessed fuel and re-enriched uranium. "But without access to the military stocks, the civilian western uranium stocks will be exhausted by 2013, concludes Dittmar.

It's not clear how the shortfall can be made up since nobody seems to know where the mining industry can look for more.

That means countries that rely on uranium imports such as Japan and many western countries will face uranium .shortages, possibly as soon as 2013. Far from being the secure source of energy that many governments are basing their future energy needs on, nuclear power looks decidedly rickety.

But what of new technologies such as fission breeder reactors which generate fuel and nuclear fusion? Dittmar is pessimistic about fission breeders. "Their huge construction costs, their poor safety records and their inefficient performance give little reason to believe that they will ever become commercially significant," he says.

And the future looks even worse for nuclear fusion: "No matter how far into the future we may look, nuclear fusion as an energy source is even less probable than large-scale breeder reactors."

Dittmar paints a bleak future for the countries betting on nuclear power. And his analysis doesn't even touch on issues such as safety, the proliferation of nuclear technology and the disposal of nuclear waste.

The message if you live in one of these countries is to stock up on firewood and candles.

There is one tantalising ray of sunlight in this nuclear nightmare: the possibility that severe energy shortages will force governments to release military stockpiles of weapons grade uranium and plutonium for civilian use. Could it be possible that the coming nuclear energy crisis could rid the world of most of its nuclear weapons?

Ref: The Future of Nuclear Energy: Facts and Fiction

arxiv.org/abs/0908.0627: Chapter I: Nuclear Fission Energy Today
arxiv.org/abs/0908.3075: Chapter II: What is known about Secondary Uranium Resources?
arxiv.org/abs/0909.1421: Chapter III: How (un)reliable are the Red Book Uranium Resource Data?
arxiv.org/abs/0911.2628 :Chapter IV: Energy from Breeder Reactors and from Fusion?

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Re: Limited Uranium Supply ?

Is there enough Uranium to run a nuclear industry big enough to take over from fossil fuels ?

by Dave Kimble at www.peakoil.org.au

As supplies of easily recovered oil start to decline, (see Peak Oil ) world oil production will fail to meet world energy demand. This raises the question of which alternative energy supplies can be expanded to cover the increasing shortfall. One candidate is nuclear energy, which in turn raises the question of whether there is enough Uranium resource to fully take over from Oil. Will we run into Peak Uranium before we have coped with Peak Oil ?

Mining production

Current world production of Uranium is around 36,000 tonnes of metal per year, but production is limited by market forces which have a complicated history resulting in large stockpiles, depressed prices and limited interest in mining. Total world consumption of Uranium is 66,000 tonnes of metal per year, with 30,000 tonnes coming from stockpiles, recycling of spent fuel and weapons decommisioning, see below.

Spot market prices (currently around US$20/pound) are a poor indicator of the true supply/demand situation, as anyone wanting to build a commercial nuclear reactor with a life-span of 30 - 60 years will want to have a long-term supply contract locked in before construction begins. The spot market only handles about 12% of the overall market, and is subject to wild fluctuations. Long-term contracts with power companies are expected to run at US$26 this year.

Correspondingly, suppliers know they will have to provide for long-term supply contracts and this means it can make economic sense to stockpile Uranium while production is up and running, rather than close down a mine because of short-term market considerations.

Over-enthusiastic expectations for increases in the nuclear energy industry have led to large stockpiles and many small and low-grade ore mines have closed. It is possible that if a large-scale swing to nuclear energy was to occur, there might be shortfall in supply, but this would not be what we call Peak Uranium. That only comes when a fully developed mining industry still cannot meet demand.

The mining and milling of Uranium ore to the yellow-cake stage is an expensive business so the grade of the ore is particularly important, while there is a choice.

Recycling Uranium versus "Once Through"

When a conventional nuclear power reactor has used up about 4% of its uranium-235, the resulting contamination of the fuel with by-products slows down the nuclear fission reaction and it is time to change the fuel rods. Usually about a third of the rods are changed every year. What went in as 100% Uranium dioxide (~3.5% U-235), comes out as oxides of 96% Uranium, 1% Plutonium and 3% fission products and Actinides (heavier elements than Plutonium).

For most nuclear power reactors built in the US before the mid-1970s, the intention was for them to reprocess the spent fuel to recycle the uranium which still contains a lot of valuable U-235. A number of reprocessing facilities were built to handle this work. Unlike the reactors which were designed to 'cook' the fuel at relatively low temperatures and produce a relatively pure Plutonium-239 fraction for weapons purposes, the higher temperature cooking in a power reactor produces a significant proportion of Pu-240 and higher isotopes in the Plutonium mix. These isotopes are very difficult to separate, given the highly radioactive and toxic nature of Plutonium. Pu-240 has a shorter half-life than Pu-239 (6,564 years v. 24,110 years) thus it has an increased tendency to fission spontaneously. So it was thought that this made the Plutonium mixture recovered from power reactors unsuitable for bomb making.

However during the 1970s it became clear that although it would be difficult to make a bomb with a reliable yield, a bomb could nevertheless be made from recovered power reactor Plutonium. India's nuclear explosion in 1974 compounded these fears. Worried about the potential for weapons proliferation, and the overthrow of the Shah of Iran (who had a US-supported civil nuclear program) in 1979 President Carter introduced the Nuclear Waste Policy Act which banned commercial fuel recycling in the US, including on behalf of foreign customers of US reactors. This limited the fuel 'cycle' to a 'once through' process.

In the once through process, the spent fuel rods are still broken up and dissolved in nitric acid, and the Plutonium is separated from the Uranium using the organic solvent "Purex" process. But from there on the Uranium component is put directly into storage without being recycled. President Reagan reversed the ban in 1981, but US policy was still to favour 'once through', and the Nuclear Non-proliferation Act of 1978 forbids supporting reprocessing by non-nuclear weapon states. The US nuclear industry has never taken up the recycling option again, partly because the old reprocessing plants were no longer able to meet new safety requirements, and partly because an over-estimation of future nuclear capacity has led to over-investment in mining and processing, resulting in low prices for mined uranium and hence a commercial preference for freshly-mined, rather than recycled, uranium.

The problem goes beyond the depleted savings accounts of the businessmen involved as the US government was affected too. The term "reprocessing" is now often used for both the "recycling" and "once through" processes. Meanwhile France, UK and Russia have always allowed recycling, and Japan also recycled up until 1997, when it sub-contracted the task to the UK's BNFL. A 1997 study by the Nuclear Energy Agency of OECD put the additional cost of electricity from recycled fuel at 10% over that derived from high-quality Uranium ores. Nevertheless these countries have valued the increased security they get from a reduced dependence on imported Uranium.

The resulting Uranium also has a higher proportion of isotopes other than U-238 and U-235 which has the potential to shorten the reprocessed fuel rods' life. However there may be technological solutions to this problem in the future.

Uranium from decommissioning ex-Soviet weapons

Another complicating factor in Uranium supply is the Highly Enriched Uranium Purchase Agreement signed with Russia by the Clinton administration in 1993. This agreement provides for the US purchase of 500 metric tons of Russian highly enriched Uranium (>90% U-235) resulting from the dismantling of 20,000 nuclear warheads. This uranium will be blended down to low-enriched Uranium (~3.5% U-235) in Russia over a 20-year period that began in 1995. The cost for this agreement is $12 billion over the 20-year period. The payments to Russia will compensate for the Uranium content and the enrichment services as well as provide funds for the increased security of fissile material in Russia. Overall, the net effect should be to provide for a budget neutral agreement, that is no profit, no subsidies.

The value of the low-enriched Uranium on the commercial market should equal the payment to Russia. To date, the Agreement has succeeded in converting in excess of 111 metric tons of highly enriched Uranium, enough for 5,000 nuclear weapons. According to US nuclear safety regulators, this has resulted in the Russian low-enriched uranium supply representing approximately 50% of the Uranium supply for the nuclear power industry in the United States. South Africa has never admitted to building nuclear weapons, but they have given evasive answers to IEAE inquiries. In October 1992, Nucleonics Week reported that IAEA inspectors had found machinery that had been used "to shape spherical fissile cores for a nuclear explosive device" at their Pelindaba site. That year they began talks with the US over de-commissioning stockpiles of highly enriched Uranium and selling the low enriched uranium to the US on similar terms to the Russian program. The current state of this program is unknown.

Re-enrichment of depleted Uranium

The element Uranium can exist as 22 different isotopes, ( http://chemlab.pc.maricopa.edu/periodic/U.html ) with half lives ranging from 1 microsecond (U-222) to 4.4 billion years (U-238). Naturally occurring Uranium consists of three isotopes: U-238 = 99.2745% ; U-235 = 0.7200% ; U-234 = 0.0055% Despite its tiny proportion of the total by weight, U-234 produces ~49% of the radioactive emissions. The standard enrichment process for pressurised water reactor (PWR) fuel converts this mix to: fuel stream : U-238 = 96.4% ; U-235 = 3.6% tailings stream : U-238 = 99.7% ; U-235 = 0.3% However the concentration of U-235 left in the tailings stream is a commercial decision, based on the type of enrichment technology used and the cost of process energy.

Since 1996 tailings from the British-Dutch-German consortium Eurenco have been sent to the Russian company Minatom's plant at Novouralsk, where it is re-enriched back to U-235 = 0.7% and returned to Eurenco for standard enrichment. 6,000 tonnes of tailings were processed in this way in 1996. It has been suggested that Minatom cannot be charging the full cost of processing in this scenario, but it has a large excess enrichment capacity and perhaps can afford to neglect capital costs on the deal. Another suggestion (by a consultant to Uranium Exchange Co. in Nuclear Fuel, 19 October 1998) is that Minatom is stripping the tailings further than contracted, and keeping the extra U-235 for itself. Given the Russian excess stocks of highly enriched Uranium from redundant weapons stockpiles, this latter scenario seems improbable.

Other factors

All of these factors have an important bearing on when Peak Uranium occurs. Total known Uranium ores of good quality are only sufficient to supply 3 years worth of total world energy needs, although it needs to be remembered that there is probably a lot of ore left to be discovered, and that electrical energy is only ever going to be a part of the overall energy mix. Complicating matters still further, so much energy is spent in processing poorer ores, that on current technology, ores of less than 0.01% purity are uneconomic and have EPRs of less than 1. This doesn't stop nuclear spin-doctors from gloating about the zillions of tonnes of Uranium to be found in rocks (at concentrations of 0.0004%) and in seawater (at concentrations of 0.0000002%).

If that is not complicated enough, it is possible to run most power reactors on a fuel containing up to 30% MOX, which is a mixture of Uranium and Plutonium oxides. The Plutonium comes from the recycling process, and the Uranium can come from either recycling or fresh mining. This reduces the amount of Plutonium that has to be either permanently stored (and potentially diverted to weapons production), and so indirectly reduces costs for the nuclear industry.

However conventional reactor designs cannot utilise all the Plutonium produced, so this does not solve all the problems. As at the end of 1995, about 970 tonnes of Plutonium had been created in the 180,000 tones of spent fuel Of this, about 185 tonnes had been separated, and 50 tonnes recycled as MOX fuel. Other methods of using all this Plutonium for thermal energy purposes are thought by the industry to be at least 30 years away.

Conclusion

There are a number of other factors affecting the economic viability of nuclear energy. The long-term storage of high-level nuclear wastes may have a technical solution, but it has not yet begun in a practical way, and almost all spent fuel rods are sitting in cooling ponds located at the power stations that created them. The complete decommissioning of old reactors has scarcely begun, and improving safety standards make the economic burden of compliance almost impossible to calculate. Perhaps the best indication of the state of the reprocessing industry is this story from Asahi Shimbun, 7th January 2005: The proliferation of uranium enrichment facilities around the world has recently led the head of the IAEA, Mohamed ElBaradei, to call for a global five-year moratorium on new enrichment and reprocessing facilities. This proposal will be discussed at the conference on the Nuclear Nonproliferation Treaty in New York in May 2005.

In conclusion I think that the number of variables in the possible strategies for fuelling nuclear reactors means that discounting the future of nuclear power on the basis of Peak Uranium is not yet proven. The nuclear industry uses lots of fossil energy in the mining, milling, enrichment and fabrication of nuclear fuel rods, so it may well be that Peak Oil makes the mining of sufficient Uranium to keep the nuclear industry going impossible. The real solution to energy resource depletion is demand side management - using less. But given the ever-lasting growth paradigm we are almost universally engaged in, I cannot see an outcome other than a miltary struggle for control of the world's diminishing oil resources, such as we are currently seeing in Iraq. As supplies get tighter still, this will lead to World War 3.

Dave Kimble March 2005

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Re: Limited Uranium Supply ?

A Japanese spacecraft found uranium on the moon:
http://www.telegraph.co.uk/science/space/5711129/Uranium-could-be-mined-...

And from previous posts:

The  Chinese already have plans for moon mining:
http://www.dailygalaxy.com/my_weblog/2007/10/chinas-new-moon.html

And asteroid mining may not be too far off.  From BBC Sci/Tech:
http://news.bbc.co.uk/2/hi/science/nature/401227.stm

Quote:
n the 2,900 cubic kms of Eros, there is more aluminium, gold, silver, zinc and other base and precious metals than have ever been excavated in history or indeed, could ever be excavated from the upper layers of the Earth's crust.

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Re: Limited Uranium Supply ?
r wrote:

A Japanese spacecraft found uranium on the moon:
http://www.telegraph.co.uk/science/space/5711129/Uranium-could-be-mined-...

And from previous posts:

The  Chinese already have plans for moon mining:
http://www.dailygalaxy.com/my_weblog/2007/10/chinas-new-moon.html

And asteroid mining may not be too far off.  From BBC Sci/Tech:
http://news.bbc.co.uk/2/hi/science/nature/401227.stm

Quote:
n the 2,900 cubic kms of Eros, there is more aluminium, gold, silver, zinc and other base and precious metals than have ever been excavated in history or indeed, could ever be excavated from the upper layers of the Earth's crust.

 

The orbital velocity of an object in a stable circular orbit is given by
v² = G*M / r
where G is the universal gravitational constant
and M is the mass of the object causing the gravitational field (the Sun in this case)
and r is the radius of the orbit
note the mass of the orbiting object doesn't matter.
 
For the Earth, r = 1 AU (Astronomical Unit) by definition,
and v = 108,000 Km/h from Wikipedia
For the asteroids r is 2.3 to 3.3 AU, say 2.8 AU
so v is 64,500 Km/h
 
The kinetic energy of a moving object is
E = m*v² / 2
so to move 1 gram of asteroid from asteroid orbit to earth orbit
is going to take 
( ( 108 * 10^8 * 3,600 )^2 / 2 ) - (  ( 64.5 * 10^8 * 3,600)^2 / 2 ) gram.cm²/sec²
= 486 * 10^24 ergs
= 13.5 trillion KW.h
 
Which only goes to show - the most difficult place to get to in the Universe is the Sun.
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Re: Limited Uranium Supply ?

If you replaced your calculations for an asteroid with the moon I'm sure you'd get another large ergs number yet we moved more than one gram of moon rock to earth in 1969.  I honestly don't think that I'll see asteroid mining in my lifetime yet there are primary and secondary benefits to such a large investment, such as the development of in situ mining processing and advanced robotic technologies.

FWIW, here are some sites discussing the possibilities:

The technical and economic feasibility of mining the near-earth asteroids
M. J. Sonter
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V1N-3TDH483-1...

Scenarios that may lead to the rise of an asteroid-based technical civilisation
Csaba Kecskes
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V1N-44SK2XS-1...

Mining the Sky: Untold Riches from the Asteroids, Comets, and Planets
John S. Lewis
http://www.nss.org/resources/books/non_fiction/NF_011_miningthesky.html

How Asteroid Mining Will Work
http://science.howstuffworks.com/asteroid-mining2.htm
Kevin Bonsor

Mining Asteroids And Getting Rich (Or Not)
Greg Fish
http://science.howstuffworks.com/asteroid-mining2.htm

Mining Asteroids: Not At Those Overheads
Ian O’Neill
http://www.astroengine.com/?p=5795

Permanent
http://www.permanent.com/
“We can do this NOW with present-day technology and a philanthropic investor”

The scientist Stephen Hawking believes humanity's only hope is space exploration:

http://www.dailygalaxy.com/my_weblog/2009/09/stephen-hawking-manned-spac...

 

 

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Re: Limited Uranium Supply ?

Moving material from the Moon to Earth is a completely different scenario. The asteroid problem is billions of times more energy-consuming. The "How Stuff Works" website is a good example of being totally wrong. They also suggest that all you need for fuel is to split water into Hydrogen and Oxygen, and then use that. Simple - the only problem is that it takes 4.41 KW.h of energy to crack a litre of water, and when you burn it in a rocket, you only get 4.41 KW.h of energy back (if you're lucky). So where does the energy come from to crack the water ?

They gloss over the energy problem because that is what makes asteroid mining impossible, and that spoils the story. It doesn't matter how many websites you come up with that say it is a great idea, it is impossible without the energy to make it happen, and the quantities are literally out of this world.

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Re: Limited Uranium Supply ?

Thanks everyone for your responses -- it appears to me that the "World Nuclear Organization" & the "America Nuclear Society" hold  overly optimistic views and  information all the way from 200 years uranium supply at current consumption rates to optimistic views of the early use of fast neutron (breeder) reactors. Their opinion that our current world nuclear output of around 370 GW will increase to  2000 GW (minimum) and 10,000 GW (max) this century paints a rosy picture to say the least -- and even they only predict sizable increase after 2050

While it is clear that  we need to expand the use of all feasible non-fossil fuel sources of energy, we are well advised to not expect a significant contribution beyond current energy generation rates any time in the near future. 

 

Jim

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Re: Limited Uranium Supply ?
DaveK wrote:

Moving material from the Moon to Earth is a completely different scenario. The asteroid problem is billions of times more energy-consuming. The "How Stuff Works" website is a good example of being totally wrong. They also suggest that all you need for fuel is to split water into Hydrogen and Oxygen, and then use that. Simple - the only problem is that it takes 4.41 KW.h of energy to crack a litre of water, and when you burn it in a rocket, you only get 4.41 KW.h of energy back (if you're lucky). So where does the energy come from to crack the water ?

They gloss over the energy problem because that is what makes asteroid mining impossible, and that spoils the story. It doesn't matter how many websites you come up with that say it is a great idea, it is impossible without the energy to make it happen, and the quantities are literally out of this world.

The number of web sies is a red herring: of course how many there are doesn't prove anything.  It does show, however, an active discussion, and out of that discussion are some good points and good ideas.

Here are the misunderstandings:

The asteroids in the Van Allen Belt are too far away but there are near-earth asteroids which are our closest neighbors after the moon.  For example, "The giant asteroid we call Toutatis passed us by at a distance of less than 994,000 miles. That is only about four times the distance from the Earth to the Moon."

The ergs calculation made by DTM above assumed an asteroid in the Van Allen Belt.

Nearly all the energy spent by space travel is due to leaving and entering the earth's gravity.  In the weightlessness of outer space 1000 Kg is the same as 1 g.

I also read about scientists turning water into rocket fuel.  See:

http://www.independent.co.uk/news/science/how-to-turn-water-into-rocket-...

I'm more open minded about this because out in space the solar panels should be much more efficient.  So I think it is possible to use the asteroid materials to build the mining and processing equipment and process the ore into the fuel needed for the return trip.

I agree possible is not the same as probable.  So it is not probable but not impossible.  And my point is that when civilization realizes it has run out of the resources it needs to keep going it will, probably someday, turn to outer space as the solution.

Some of he  reasons why Stewart Brand, Whole Earth Catalog author, is behind nuclear energy are the large footprint of solar arrays and wind farms and the infrastructure that must be built from the farms to cities.  So there are big problems with non-fossil fuel technologies also.

 

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Re: Limited Uranium Supply ?
If the asteroid is in an elliptical orbit which brings it close to Earth,
that means it will be going very fast (relative to the Earth)
when it is in the region of the Earth's orbit.
So the problem is not then strictly one of crossing a gravitational field,
but one of needing to be sped up or slowed down
while staying in the same general space
This requires lots of acceleration, which requires lots of fuel.
 
This means the solution is exactly the same as before.
If it is an asteroid, it must be in an asteroid orbit,
so the problem is still one of a gigantic energy requirement.
 
Dave
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Re: Limited Uranium Supply ?

In 2001 the Shoemaker spacecraft landed safely on Eros and took pictures so I know it can be done....

PS - the asteroid belt beyond Mars is not the Van Allen radiation belt around the earth.  Sorry.

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Re: Limited Uranium Supply ?
r wrote:

In 2001 the Shoemaker spacecraft landed safely on Eros and took pictures so I know it can be done....

PS - the asteroid belt beyond Mars is not the Van Allen radiation belt around the earth.  Sorry.

BUT did it come back, and more to the point, bring anything back?

Don't understand the last comment.. (?)

Repeat three times:  With Fossil Fuels you can do ANYTHING!

Mike

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Re: Limited Uranium Supply ?
DamntheMatrix wrote:

BUT did it come back, and more to the point, bring anything back?

Don't understand the last comment.. (?)

Repeat three times:  With Fossil Fuels you can do ANYTHING!

Taking off from Eros is a lot easier than taking off from Mars or the Moon, obviously. But you are rignt that getting there was easier because the rocket scientists used the gravitational attraction of other objects to propel the craft to its destination.

But rocket fuel is hydrogen not oil.  And I have a link above to an article about the manufacture in space of hydrogen as a by-product of generating electricity with solar panels. 

Therefore it's the manufacture of the craft and, therefore, the manufacture of wind turbines and solar arrays that also require fossil fuels, that is a problem.  Therefore we should be back to the stone age soon enough and this awful stressed-out violent civilization will finally be dead.  Thanks!

The other comment I was apologizing for mistakenly naming the asteroid belt beyond Mars the Van Allen belt.

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Re: Limited Uranium Supply ?
Damnthematrix wrote:

BUT did it come back, and more to the point, bring anything back?

Don't understand the last comment.. (?)

Repeat three times:  With Fossil Fuels you can do ANYTHING!

Japanese Hayabusa probe returns from a tiny asteroid, 3 billion miles away:

http://www.smartplanet.com/technology/blog/thinking-tech/japanese-hayabu...

Japan launched the Hayabusa (Japanese for peregrine falcon) probe back in 2003, aimed at a small near-earth asteroid named Itokawa. The probe was designed to land on Itokawa, a mile-long bean-shaped asteroid, gather samples, and return home, which it did, this past weekend.

Japanese space probe finds unique asteroid dust:

http://www.reuters.com/article/idUSTRE65C0EA20100614

The Hayabusa probe blazed a spectacular trail over Australia before slamming into the desert at around midnight local time, ending a journey to the near-Earth asteroid Itokawa that began in 2003.

A spokesman for the Japan Aerospace Exploration Agency (JAXA) told Reuters the first image available indicated the capsule carrying the precious cargo had survived.

After sunrise, Australian defense officials flew local Aboriginal elders to the site by helicopter to verify that no sacred sites had been damaged. A defense spokesman said the indigenous leaders had cleared the way for the capsule to be recovered later on Monday.

Hayabusa, which means falcon in Japanese, landed on the irregularly shaped asteroid in 2005 and scientists think it managed to pick up a small sample of material. If successful, it would be the first time a spacecraft has brought such a sample back to Earth, other than from our own Moon.

....

Asteroids like Itokawa and Eros have escape velocities on the order of 22 miles per hour...

 

 

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