D H

Nonsense. The two are related in that (1) they're both asteroids, and (2) they happened to come closest to the Earth (a little too close in the case of that Russian meteor) on the same day. Otherwise, there is no relationship. The two objects had vastly different orbits about the Sun, both in terms of eccentricity and orbital plane.

You are still ignoring kinetic energy. Your pressure cooker is not going about 20 kilometers per second. That meteor was. [imath]1/2\,m\,v^2[/imath] makes for a lot of kinetic energy when both m and v are rather large. In this case, 10,000 tons moving at 20 km/s represented a whole lot of kinetic energy, about the same as that released by 30 Hiroshima-type bombs. When that meteor blew up, the rate at which energy was transferred to the atmosphere went up by orders of magnitude because the tiny pieces had a whole lot more surface area than did the meteor right before it blew up. The bulk of that energy transfer was in the form of heat.

What else could it be? It just might be the Door to Hell. Didn't anyone ever tell you not to believe everything on the internet?

It wasn't fire. It was "just" kinetic energy. The cross sectional surface area suddenly increased by orders of magnitude when that rock exploded (no fire needed). That huge increase in surface area meant a huge increase in the rate at which energy was transferred to the atmosphere. Kaboom, and ka-flash.

Apparently it's Norfolk Island, not King Island, where that blue breed of cattle live.

Have you ever gone primitive camping? If you have, you should know that you don't use sedimentary rocks such as sandstone for the fire ring because if you do they might explode. Combustion is not needed. All that is needed is the water that's bound in the rock to be released as steam. The internal pressure that results, coupled with the inherent weakness of those rocks, makes the rocks explode. That is what happened with this meteor. Carbonaceous chondrites make sandstone look downright sturdy, and some contain quite a bit of water and other volatiles. It's answers.com. What do you expect? Answers? Bon jour. You're forgetting about kinetic energy, [math]KE=\frac 1 2 mv^2[/math]. This meteor had a mass of about 10,000 short tons and was going about 47,000 mph. That represents a lot of energy, about 30 times the amount of energy released by the Hiroshima bomb.

From Asteroid 2012 DA14: Observing Prospects and How to See It: A good search strategy to catch 2012 DA14 is to actually to treat it like you’re hunting for a faint satellite. Find the time that it’s crossing a set declination and begin scanning with binoculars in right ascension back and forth until you “ambush” your astronomical prey moving slowly against the starry background. If using a telescope, use the lowest power and widest field of view that the instrument will allow.

Multiplying the quantity of some material obtainable from some source of that material by some unit price does not necessarily mean that that is economic value of that source. That article is false economics at work. By way of analogy, there's a readily accessible supply of gold worth over 41 trillion dollars right here on Earth, the gold that is dissolved in the world's oceans. The reason no one goes after this readily accessible supply is that one would have to process about 77 million liters (20 million gallons) of ocean water to get just one gram of gold. Because of this, the economic value of that supposed 41 trillion dollar supply is zero. Absolutely nothing. The method by which that article arrives at that figure of $195 billion is quite simple: Multiple 130,000 tons by 15% (10% metal, 5% water) to obtain 19,500 tons of recoverable product and multiply that by $10 million per ton. Tada! $195 billion. That's a bogus figure. That 10 million dollars per ton is an intentionally inflated figure. He intentionally used GEO as opposed to LEO because it costs about 10 times more to get a satellite into GEO than it does to get a satellite of the same mass into LEO. (Aside: Note the factor of ten multiplier. LEO to GEO is a delta V of about 4.1 km/s, about 40% of the delta V needed to get from ground to LEO. Cost is a highly non-linear function of delta V.) That $10 million per ton is a cost, a sunk cost. We don't send one 1 ton rock up into geostationary orbit because that makes the rock now have a value of $10 million. We send a one ton satellite up into geostationary orbit because the value returned by that satellite exceeds the 10 million dollar needed in getting that satellite into that orbit. Equating cost with value is bogus economics.

That's not what happened. That's not what a physicist generally means by "ignore" in this context. The sun converts about 4 billion* kg/s into other forms of energy, which is eventually radiated away at c. In the volume inside the earth, that's 500 s of travel, or the equivalent of 2 x 10^12 kg. The mass of the sun is 2 x 10^30 kg. Ignoring the effect of the light gives an error of a part in 10^18 in terms of effect on the earth. At that point you ignore it, unless you are doing an experiment where a part in 10^18 matters. Not including in a calculation is not the same as refusing to consider. The immediate effect is significantly smaller than one part in 10^18. The solar system is nearly Newtonian in behavior. One way to account for relativistic effects is a parametric post-Newtonian formalism, which models relativistic effects as perturbations of Newtonian gravity. The light that is still in transit from the Sun to the Earth is essentially indistinguishable from mass at the center of the Sun. It is completely indistinguishable in a Newtonian context thanks to Newton's shell theorem. There's a slight relativistic effect, but now we're looking at a tiny perturbation of any already tiny perturbation. The same applies to the light that was emitted more than eight minutes ago. In a Newtonian context the contribution of this older light is identically zero, once again thanks to Newton's shell theorem. There once again is a slight relativistic effect, but once again this is but a tiny perturbation on top of an already tiny perturbation. There is a cumulative effect due to the Sun losing mass. The Sun also loses mass in the form of the solar wind. Both of these effects are very small, less than 10-13 solar masses per year. This mass loss should change the orbits of planets slightly, but the effect is negligibly small (i.e., much less than measurement error).

Why should they? That light is subject to gravitation, sure. Astronomers see this in eclipses and in images such as this: That's the Einstein cross. That light gravitates, why should they? The effect is incredibly small, much smaller than observational errors, and much smaller than numerical errors in the case of a simulation. There's no reason to include this effect.

Stop calling it "rest mass". It's just a name, and you are getting far to hung up on that name. Use the term "invariant mass" instead, where "invariant" means "the same in all inertial frames of reference."

That is a key issue that needs to be resolved. Consider the following scenario. Suppose that, contrary to what I posted earlier, Naive Space Mining, Inc. does manage to develop this mythical 2500 kg precious metal mining machine and sends one each to a dozen or so candidate asteroids. Suppose the rocket doesn't have the necessary oomph to bring the mined material back to Earth. The mining machine instead builds up a pile of mined precious metals for later recovery, something to be done a decade or so later. Next suppose Teach Space, LLC (Teach as in Edward Teach, aka Blackbeard) secretly develops a recovery vehicle well in advance of the work by Naive Space Mining, Inc. They send recovery vehicles to all of those mining sites, pick up the precious piles, and come home. Did Teach Space, LLC violate any laws? That's the "group hug" theory of international space law, and it doesn't make sense. No space faring nation is a signator to the (failed) Moon Treaty, which would have made this "group hug" point of view into international law. The problem is that there is no concept yet of what ownership rights in outer space are, or even what they should be.

Try again, but this time Don't use an Isp of 450s. That's hydrogen. Nobody uses hydrogen for the upper stages. It doesn't make sense. SpaceX doesn't use hydrogen, period. They know hydrogen as a fuel doesn't make sense, period. Take into account that when you increase the size of a rocket you are increasing the size of the rocket. You apparently just doubled the fuel quantity. Rockets don't work that way. I wouldn't. Thinking of mining metals in space, any kind of metals, is a pipe dream for now. Thinking of mining precious metals and rare earths is beyond the pipe dream stage. What we can do in the next ten or twenty years (i.e., now) is to mine easily attainable and very common stuff that nonetheless is valuable if used in space. Water. Methane. Water is not just water, it's also a very portable source of oxygen. Methane is an easily managed, non-cryogenic fuel. Mining these two is feasible and economical, or close to it. It's still using some very low TRL concepts, and that will have to be addressed.

Ultimately, yes, we are. Why? I'd say it's more dangerous to think that our children's children's children will have to get by on a lot less than we have. We should be looking for ways to make the world of those future generations an even brighter and better world than ours. You are presenting a false dilemma. Yes, as we marshal ever more power we do have to be ever more careful of the consequences. "With great power comes great responsibility." When we have an exawatt on our hands we will have to be even more responsible shepherding that than we are now. I agree, but not because of the reasons you cited. I agree because that is the path that will eventually let our children's children's children bring the plunder home. Right now, and in the near future, mining asteroids for precious metals to bring home for profit does not add up economically or technologically. Mining asteroids for common stuff, water and methane, comes much, much closer to being technologically feasible and economically viable. It's a matter of picking the low hanging fruit. Water and volatiles are the low hanging fruit. Non-precious metals such as iron and nickel are a bit higher hanging fruit on that plunderable tree of space resources. The key problem with precious metals and rare earths is that they are rare. Plundering those bounties will take a good amount of well-established infrastructure. Our children's children's children will exploit those resources (or so I hope!), but it will take a while to get to the point where doing so is technologically feasible and economically viable.

Sorry, the Fukushima disaster already took that option away from you. The three big nuclear power plant disasters, Chernobyl, Three Mile Island, and Fukushima, have collectively spelled the end of the nuclear power industry. The industry was at best moribund prior to Fukushima. Now its dead. We humans aren't rational. Nuclear power is safe, far safer than any other form of electrical power generation -- even if you include those anomalous and curable disasters in the equation. Coal power plants kill coal miners by the thousands and are extremely hazardous to the environment. Hydropower has had a number of disasters that have killed more people than have been killed by the nuclear power industry, and hydropower is not near as green as most people think.

Of course you did. You used crackpot numerological tautological physics. You used numerology by labeling [imath]\frac{\alpha c}{2\pi}[/imath] as [imath]V_a[/imath]. You used crackpot physics by pretending that this [imath]V_a[/imath] represents something real, "the aether's tangential velocity", rather than just a numerological string of symbols that happen to have units of velocity. You used tautology in that the Compton radius is defined in terms of the fine structure constant, the electron mass, the speed of light, and Plank's constant. Your first equation simplifies to [imath]h=h[/imath].

Nonsense. The rocket equation is a nasty, brutal thing. Here's one version: [imath]\Delta v = v_e \ln(m_0/m_1)[/imath], where [imath]\Delta v[/imath] is the change in velocity, [imath]v_e[/imath] is the effective exhaust velocity, [imath]m_0[/imath] is the initial mass of the vehicle, including fuel, and [imath]m_1[/imath] is the final mass (all fuel consumed) of the vehicle. Here's another: [imath]m_f = (m_s+m_p)(\exp(\Delta v/v_e)-1)[/imath], where [imath]m_f[/imath] is the mass of the fuel needed to achieve the desired [imath]\Delta v[/imath] given a payload mass of [imath]m_p[/imath] and a vehicular structural mass of [imath]m_s[/imath]. Notice the natural logarithm in the first form, the exponential in the second. Either way, the rocket equation is exponential. Costs are anything but linear with respect to [imath]\Delta v[/imath]. In fact, the rocket equation is worse than exponential. Naively applying the rocket equation quickly leads to a vehicle that is initially 99% or more fuel. We don't know how to build such a vehicle. At some point you need a bigger rocket. That means even more fuel, even more vehicular structure, even more costs. There's yet another problem that gets in the way, which is the cube square law. Making a rocket whose initial mass is 99% fuel is not a big problem if the rocket is rather small. Make the rocket as a whole bigger and the cube square law demands that that initial fuel load decrease as a percentage as vehicle mass increases. For an extremely large rocket the upper limit on the initial fuel load is closer to 90% than 99%. Using a multistage rocket is one way to somewhat contravene the nastiness of the rocket equation. It's still exponential, however, and adding stages increases costs by a non-linear factor. A multistage solution also increases structural integrity issues. The initial stages have to have enough structural integrity to bear their own weight under thrust plus all of the loaded weight of the stages above. A prime example: The Apollo moon missions. The Gemini missions which preceded the Apollo missions were about halfway to the surface of the moon (and back) in terms of delta V. Doubling the delta V did a whole lot more than double the cost. Had we stopped with Gemini the costs of the 1960s human space program would have been an order or magnitude smaller than they were, or even less. No, we should agree that his numbers are ridiculously optimistic, economically and technologically naive, and omit a significant number of costs. Precious metals will be amongst the last things mined in space, not the first. The first will be water and volatiles such as methane. Then (maybe) we'll go after common metals such as iron and nickel. Regarding that parenthetical "maybe": We won't do any of this if we focus only on the immediate return on investment. Space mining will be a loss leader rather than a profit center for a long, long time. Only with a vibrant space mining economy will we have the massive infrastructure in place to go after the very small quantities of precious metals and rare earths that are present in mineable quantities in a small percentage of the asteroids. Even then, our space-faring successors will have to be careful not to flood the market and turn those precious metals and rare earths into semi-precious metals and not-so-rare earths. Those large bucket excavators are just a tad more massive than 2500 kg. There any many different kinds of machines involved, many of which are gargantuan compared to that mythical 2500 kg mining machine. Those large bucket operations eat through parts at a phenomenal rate, consume immense amounts of energy, and rely heavily on dynamite. The uniform distribution is not a feature. It's a misfeature. Those large bucket operations are only economical where the target metals are concentrated by some fluke of nature.

No, you can't. You're halfway there in terms of delta V. The problem is that cost is not a linear function of delta V. It's exponential at best. Oftentimes it's worse than exponential. The ideal rocket equation is brutally exponential, and reality, which is worse than idea, is even more brutal.

I don't agree with his assumptions, either. He is wildly overoptimistic, is rather ignorant both economically and technologically. His baseline platinum concentration of 0.3% is highly unrealistic. The best targets for platinum are the LL chondrites and the iron-nickel asteroids. A concentration of 0.006% is optimistically realistic. That's the 98th percentile concentration in iron nickel asteroids. A concentration of 0.3%? That's straight out of science fiction woo-woo land. His alternate 4.1% figure is beyond science fiction. A mere 2500 kg mining machine -- that's roughly what we have on Mars right now. The Mars Curiosity rover recently drilled a 2.5 inch deep, 0.63 inch diameter hole into a nice soft sedimentary rock. It took a while. That factor of 100 is pretty much useless if this 2500 kg machine of his eventually does mine 100 times its weight but takes five billion years to accomplish this task. Time is of the essence. My full-size pickup weighs more than his 2500 kg mining machine, and no matter how well equipped, it would take a long, long time for it to rip through 2,500,000 kg of rock. My pickup is powered with gasoline, a much more concentrated energy source than solar power. When it runs out, I drive to the nearest gas station. There are no nearby gas stations on an asteroid. Where is this 2500 kg mining machine going to get the energy needed to rip through 2,500,000 kg of rock? Where is this 2500 kg machine going to get the drill bits that have been worn smooth? Where is it going to get dynamite so it doesn't have drill through every bit of the asteroid? How are they going to pack drilling equipment, hauling equipment, refining equipment, and lots and lots of spares into 2500 kg? How are they going to get the mined material back to Earth? There's no budget for and no mention of that expense, and it's not little.

No. No. No. The treaty bans military use of environmental modification techniques. It does not prohibit non-military uses such as seeding clouds in an attempt to stop a drought. There's no complaint to be lodged. Take off your tinfoil hat.

Yes, it is just that, a name. If that name is too confusing, consider calling it invariant mass or intrinsic mass. If that's still too confusing, just call it mass. There's no need for any qualifier. You've already been told that. We observe energy and momentum.

You don't need a calculator to verify this. It's a trivial tautology. What you wrote is just a convoluted way of saying [imath]\pi=e^{\ln \pi}[/imath], or even more succinctly, [imath]\pi=\pi[/imath].

That's what I do, too. The code based editor is not quite WYSIWYM (what you say is what you mean). The primary editor is not quite WYSIWYG (what you see is what you get). Between the two you can more or less minimize the surprises that appear after you hit the "Add Reply" button. It pretty much sucks that this is the only way to get something reasonable.

This doesn't make sense. What it means is that every correct equation must be dimensionally sound. Dimensional analysis is a handy scheme for rejecting expressions such as 1 kilogram + 1 meter as nonsense. However, that an equation or expression is dimensionally sound does not necessarily mean that it is correct. Think of it in terms of the difference between "if" and "only if".

The poles are the two places where the Coriolis effect is strongest. There are a whole slew of places where you won't get a Coriolis effect: Anywhere on the equator will do. The scientific explanation is simple: It's a tourist scam. There is no Coriolis effect at the equator. On the reporter's part, it's just sheer stupidity. "Never attribute to malice that which is adequately explained by stupidity." (Hanlon's razor). This is not BBC's finest hour. The sad fact is that BBC has fallen for this scam multiple times. It's been debunked as a tourist scam, the BBC has been told that it's a tourist scam, and yet they still report it is something fantastic. It isn't. On the part of the people demonstrating this fantastic effect: Yep. It's fraudulent.