Cocktail Party Physics

when satellites collide, it's really a drag

The NASCAR season has started, which means I got to go down to Daytona a couple weeks ago.  Daytona is a 2.5 mile track and banked at 31 degrees, which means that speeds can get high enough that the cars become aerodynamically unstable.  To limit speed, engine power is artificially restricted, which means that minimizing drag - the friction between air molecules and the car's surface - becomes incredibly important.

Unfortunately, I didn't get to watch much of the Daytona 500, since we were back home finishing taping a "Science of NASCAR" project. One of the fun parts of that weekend was dragging The Rocket Scientist (TRS) out to Texas Motor Speedway, where he explained to me in-between takes that drag played an important role in another scientific event that happened earlier in the week.

On Feb 10th, a privately owned US Iridium satellite collided with a defunct Russian military satellite.  The Iridium satellite is one of 66 satellites in a communications network.  The Russian satellite is "space junk" - stuff that is not longer used, but is still in orbit.  Newer satellites are equipped with enough fuel to "make them commit suicide", as The Rocket Scientist puts it poetically, by burning up on re-entry.  Otherwise, you have to resort to something like shooting down misbehaving satellites with missiles.

You would think that someone -- like NORAD, whose job it is to predict possible satellite collisions -- would have noticed there might be a problem, but there apparently were no warnings before the impact.  The Pentagon uses optical telescopes and radar to track more than 18,000 objects. You can find some of the information on space-track.org.  Aerospace analyst T S Kelso, using the Pentagon's public data, says the available data shows the two satellites should have missed each other by 584 meters. 

NASA's chief scientist estimates that there are about 19,000 objects in low Earth orbit and higher Earth orbits.  Only 10% of those objects are useful satellites.  The rest is space junk.  That count includes an estimated 1,000 objects larger than 10 centimeters (4 inches) created by this months' satellite collision. 

In 2004, Dr. Hugh Lewis and collaborators calculated what would happen if an Iridium satellite hit a 1-kg piece of space junk.  They calculated the probability of a collision as one in a few million.  Of course, with all the new debris -- and the fact that the remaining 65 Iridium satellites move in circular orbits that cross each other at the poles (the collision happened over Siberia) -- those odds have probably increased by a few orders of magnitude.

A spacecraft would need 40 joules of energy per gram of its mass to be totally obliterated.  The Chinese missile test was estimated at 250 joules per gram.  The energetics in the satellite collision are even larger.  The two satellites that hit each other were going 42,120 km/h. The Iridium satellite was 1,234 lbs and the Russian satellite was 1,984 lbs. That adds up to about 50,000 joules of energy per gram of satellite.  I'm guessing the insurance adjuster is going to total both satellites.  (Iridium actually has 'spares' in alternative orbits that they can press into service to replace the destroyed satellite, so they won't need to hassle with the insurance company over a loaner.) 

Just because I am compelled to give The Rocket Scientist a hard time whenever possible, I asked him how his "peeps" had managed to let this happen.  His answer?

Sunspots.

Well, they've been correlated to everything from crop yields and energy use to the Dow Jones Average and skirt length, so why not?

I was heartened to learn that sunspots have to do with magnetism (something I actually think I understand); however, these are some pretty large magnets.  A typical sunspot has a diameter of about 37,000 km. The intense magnetic activity of a sunspot affects convection - the rise and fall of gases or liquids.  The inhibited convection on the surface decreases the sunspot temperature to around 4,000-4,600 K.  The photosphere (the outer layer of the Sun) ranges from about 6,000 Kelvin at the inner boundary to 4,500 K at the outside, with an effective temperature of 5,800 K, so sunspots are actually cold areas on the Sun.

Irradiance is the power per area incident on a surface.  If you had a 60-W light bulb shining on a 1 square meter area, the irradience would be 60 W/m².  Sunspots are lower temperature than the rest of the surface, so you would think that sunspots would decrease the irradience.  Surprisingly, the opposite happens:  The irradience increases.  More sunspots means hotter, fewer sunspots mean colder.

Sunspots are cyclic with about an 11.1-year period.  The period is related to the fact that the solar system doesn't revolve around the Sun.  The Sun is slightly displaced from the solar system's center of gravity (CG), getting up to a million kilometers from the CG at times.  The motion of the Sun relative to the CG affects turbulence in the photosphere and that transition from turbulent to not affects the number of sunspots.

The Rocket Scientist explained to me that sunspots change latitude during the course of a solar cycle.  They form a "butterfly pattern".  Sunspots usually occur in a belt of plus and minus 35 degrees from the equator.  At the start of a new solar cycle, the sunspots form at high latitudes.  As more and more sunspots appear, they start to form at lower latitudes.  During the minimum, they are closest to the equator.  A plot of latitude vs. date looks like butterfly wings.

The 11.1 year cycle is superposed on the total number of sunspots.  There have been periods where the overall number of sunspots was very small.  The most famous of these is the 70-year period called the  Maunder minimum, which was from 1645 to 1715.  During one period where you'd expect 40,000-50,000 sunspots, there were only about 50. 

We're in another low period right now, with 2008 having been declared the "Blankest Year of the Space Age" in terms of sunspot activity.  The minimum in the sunspot cycle probably happened sometime late summer or early Fall of 2008.

Drag becomes important because sunspots affect the temperature and the density of the atmosphere.  During sunspot maximum, drag increases and when drag increases, it slows down satellites and their orbits become smaller.  During a sunspot minimum, drag decreases.

That, The Rocket Scientist thinks, is why the models used to predict satellite collisions may have been off.  The abnormal sunspot activity - or lack of sunspot activity - is great for communications.  But it causes a host of other effects, one of which may have been the satellite collision.

Altitude makes a difference in racing.  The higher the altitude, the less dense the air.  That decreases drag, but it also decreases how much oxygen gets into the engine per volume, which decreases horsepower.

Putting a racetrack at the top of Mount Kilomanjaro, The Rocket Scientist says, would make for interesting racing.  Of course, he's never tried getting out of the Pocono racetrack, or he'd know that mountains are definitely not the best thing when it comes to post-race traffic. 

science, politics, and getting it wrong

One surefire way to panic the heck out of people is to mention nuclear bombs and radical Islam in the same sentence. I dunno about you, but I kinda had a mini-freakout when I read about the amount of enriched uranium the United Nations says that Iran has at its disposal for bomb making. It was hard not to, with the alarming headlines: the LA Times said "IRAN HAS ENOUGH FUEL FOR A NUCLEAR BOMB, REPORT SAYS"; the New York Times was a little more low-key: "IRAN HAS MORE ENRICHED URANIUM THAN THOUGHT." Coupled with our mostly ignorant, media-induced fear of all things Muslim, this was a briefly heart-stopping revelation. But as is true of any story told by any human being, it's the framing that counts. Both reports, in their xenophobia, downplayed the fact that the enriched uranium Iran possesses has only been enriched by 4% (reactor grade), while bomb-worthy uranium must be at least 85% enriched. Even Mother Jones' Kevin Drum was rather alarmist about it, though he at least admits the Iranians have decided both to do less reactor-grade enrichment than they could and not to further enrich what they've got. Then there's the brilliant, anonymous, senior UN official who said ''You have enough atoms' to make a nuclear bomb," according to Drum. Atoms? Huh?

So what does that mean, exactly? How much is "enough" weapons-grade uranium? And how much more work would it be for Iran to enrich that reactor-grade uranium to bomb-making level? And how easy would it be to spot it? Cheryl Rofer over at WhirledView has a great post on most of these questions, in an entry appropriately titled "Whoo-hoo! Atoms of Fissionable Material Everywhere!"

That's right: everywhere.

As Rofer says,

Ah yes. And if you live in Boulder, Colorado, or in Connecticut, or New York City, you have enough U-235 under your house (or perhaps block) to amass a nuclear bomb! Or . . . all that sea water lapping up against the California coast has uranium in it too! I have a call in to the IAEA to inspect your homes!

 Not just random atoms, but enough U-235! Whoa!

Several radioactive isotopes of uranium exist in nature, but in very small concentrations (2-4 parts per million), and decay very slowly. Although U-235 is the only naturally fissile (fissionable by low kinetic energy neutrons) isotope, it occurs in such small concentrations that it's not dangerous. In fact, naturally occurring uranium salts (uranium dioxide), which are a vivid yellow, were frequently added in small amounts to glass to give it a characteristic and unique fluorescence sometimes called Vaseline glass. Yes, it's radioactive, but the radioactivity is approximately equivalent to what occurs naturally in the human body. Even a collector's houseful of it isn't dangerous. And it glows beautifully under black light (UV radiation).

U-238 is also fissionable, but it takes higher energy particles to set it off. It's U-235 that's most often used in weapons. There are some high concentration (up to 70% uranium oxide) ore deposits in Canada, but much of the ore that's mined is low-concentration (0.01 to 0.25%). Once the ore is crushed, leached with acid, and precipitated it becomes something called "yellowcake," which contains at least 75% uranium oxides (see picture at left). Further purification involves halides of uranium (a compound with halogen), which are reduced with alkali earths and by thermal decomposition, or through electrolysis in a molten salt solution. What you're left with at this stage is a quite pure chunk of radioactive metal. This is still not enriched uranium. That's a whole other process.

Enrichment begins with uranium hexafluoride, or "hex" as it's known to the nuke people, obtained by taking yellowcake through a multi-step process that starts with dissolving it in nitric acid and involves further steps with ammonia, reduction with hydrogen, the addition of hydrofluoric acid and finally oxidation with fluorine to produce hex. Hex is highly toxic, violently reactive with water, and corrosive to metals, so if it's going to be enriched it's often stored in glass, in a vacuum, as in the picture at right, where you can see the gray-white crystals it forms at room temperature.

From this stage the hex, at least in Iran and much of U.S., goes to a gas centrifuge, or a "cascade" of centrifuges (left). These aren't the table-top kind you see in a chem lab, though the principle is similar. Heated slightly, the crystalline form of hex, still under vacuum, evaporates and the spinning of the centrifuges separates out the heavier molecules of U-238 and the lighter ones of U-235 until you're left with a very dense heavy metal composed of at least 20% (called weapons-usable) but more often at least 85% (wepons-grade) enriched or highly enriched uranium.

The less enriched the uranium, the higher the critical mass, or gross amount, required to sustain a sufficiently powerful chain reaction. For example, you'd need, at minimum, about 110 lbs. (50-52 kg.) of highly enriched (85%) uranium to arm a nuclear weapon. (The LA Times, I'd like to point out, got this number wrong, mixing kilograms with pounds.) You'd need far more than that of 20% enriched, which would make a very (physically) large (even though the payload is small), very crude bomb unless constructed with sophisticated techniques, all of which are classified by experienced bomb-making nations, and most of all, extremely costly. (Remember, it was, in part, the cost of the nuclear arms race that toppled the U.S.S.R.)

According to the UN report, Iran has approximately 2,200 lbs. of low enriched uranium (LEU). It takes approximately 2,200-3,700 lbs. of LEU to make enough Highly Enriched Uranium (HEU) for one bomb. Although Iran now has enough LEU for the task, it does not yet have the facilities to do so, a fact the doesn't appear in either story until well down the page. It would take more high-speed centrifuge cascades than are currently online or in the works, not to mention an actual bomb-construction facility. Although Iran has barred UN inspectors from some of its facilities (claiming that none are currently ready to receive nuclear material and thus not subject to inspection), satellite imagery would surely spot any new facilities constructed for bomb-making purposes.

It's hard to say what any individual's intentions are, let alone a whole nation's. But it also doesn't help to scare monger with misleadingly constructed news reports that make it sound as if Iran has plenty of weapons-grade uranium at its disposal. It doesn't; nor does it seem to be interested in producing any. The biggest issue, in other words, is not the uranium Iran has declared, but the uranium the U.N. Security Council doesn't know about—if there is any. Sound familiar? Weapons of Mass Destruction, anyone?  We jumped to disastrous conclusions with Iraq; it would be wise not to do the same thing with Iran.

You can read the 5-page report to the Security Council here. It's worth the time to get the straight story without the media frame.

[Hat-tip to Will Shetterly for drawing my attention to this factual distortion.]