Resonant Constellation

I have gmail for my personal email, and as such, I often get unobtrusive ads on the side of my email messages relating to the subject of the mail. Since I’m going observing this weekend, I was corresponding with my colleagues about certain technical details of our impending observations. I saw a link on the side near the bottom-one I’m sure most people out there have come across once or twice-a service claiming to be able to sell you the ‘rights’ to “name a star!” Oh boy.

Since I had just discussed how idiotic just such a practice is with my friend Pete a few hours ago, I decided to click the link to remind myself of the idiocy. They claim that there is only one star registry which is copywrite protected with the US patent office (theirs, of course). The go on to further claim that the International Star Registry has allowed thousands of people to name their own stars. The price they charge for this is between $50 and $500. What do you get for this? A certificate and a star chart. The different framing options make up the order of magnitude price difference.

Okay, first of all, I hope I don’t have to tell you that this so-called ’star registry’ is completely bogus. It is entirely meaningless and certainly not worth $50 (much less $500). Secondly, there are only a few thousand stars which are visible to the human eye. Most of these have popular names, and all of them are named in more than one catalog (names like GL 436, LHS 310, 2MASS J11421096+2642251, etcetera. By the way, those are all the same star, which has at least 30 different catalog designations). I’ve got to assume that they’re going just a bit deeper into the magnitude scale and assigning people stars that they can’t actually see. Fair enough, I can see no fault with that, but most people (especially ones gullible enough to fall for this) will probably be expecting to be able to look up and point at “their” star.

My favorite part of this idiocy, however, was their last sentence:

There are still a few stars left to be named but you must act quickly to secure a good one before they run out.

(emphasis in original)

They run out. Nevermind that there are more stars in just our galaxy than there have been humans who ever lived, more stars than you could possibly imagine-roughly a hundred billion. Clearly, stars are a limited commodity. Sometimes, I feel like time spent educating people might be better spent banging the instructor’s head on the wall. At least they’d have a big bruise to show for it.

If you REALLY want to name your own stars, do what my friend Dave did before he learned the names of the stars and constellations. He went outside, looked up, and made it all up himself. If you really want, you could make your own certificate and draw a star chart of what you see to remind yourself of where the stars you named are. In all honesty, though, I’d simply suggest leaving out the naming stuff and just stargazing. To paraphrase Feynmann, names don’t tell you anything useful about the object, they sometimes just get in the way.

I was supposed to be up on Mt. Bigelow, observing right now. Instead, I am at home, impotently shaking my tiny fists at the sky. Why, you ask? Because of my arch-nemesis, clouds. We still accomplished our most important goal, which was to get certified to operate the telescope on our own. Basically this involves learning how all of the systems work, how they break, and what to do when they do break. Most of the instruction seemed to actually be tips on quirks of the system and ways to get around them. In fact, most of the operating procedures seem to be clever/desperate ways to get around the fact that most of the equipment doesn’t, in the strictest sense, work. There’s a hell of a lot of components that make a big telescope run, and keeping them all straight was a significant task.

As we were driving up, Jared and I heard and saw lightning, which already made us doubtful about our night of observing. While the rain and thunder moved on, the cloud cover refused to lift and with the prediction of thunderstorms in the morning we decided to stow the telescope and take emergency lightning precautions before leaving (this includes airgaping every single electronic device on the premises, which takes about a half an hour to complete). We were back down by 9:30.

Oh well, at least I’ll get some sleep now.

Every once in a while, I entertain myself by learning about random math stuff. A recent example is my foray into Fibonacci sequences which I mentioned in a previous post. This time, my friend Pete mentioned a peculiar number, called Graham’s number. As far as I can tell, this is the largest number to ever be used in a serious mathematical proof.

I know what you math-nerds out there are thinking: larger, even, than a Googol? (), or a Googolplex? (). Yes, my friends, Graham’s number is inconceivably big. It makes a Googolplex look like a mere handful. Interesting note: when I was little, no more than five, I remember writing out a Googol on an etch a sketch and trying to explain it to my grandparents. I was a weird kid.

Graham’s number is so absurdly large that there are not enough particles IN THE UNIVERSE to express it via any standard notation. Think about that-go outside to a high place and look around. Then think that everything you can see is made of inconceivably tiny particles which are so small, they cannot be seen by the human eye, nor any optical magnifier that has ever, or will ever, be made. Look at your hand-there must be millions, perhaps billions of particles in your hand alone. And yet including everything you can see, much less the entire friggin’ universe, there aren’t enough of these unfathomably tiny particles to write out this number, even using a series of exponents. Wow.

So how do you write it down? Well, mathematicians are relatively creative people (if not entirely practical), and they’ve come up with intriguing ways of expressing large numbers. One way is called “Up-arrow notation,” in which the number is expressed by a series of rows including numbers and arrows which signify computational steps to arrive at the number itself. Each higher row is predicated on how many arrows are in the last row. This is the only way to express Graham’s number. To show just how depressingly large this number is, you still can’t even express just the first row of up-arrow notation with all of the particles in the universe. There are 64 total rows.

What I can tell you about it is that it ends in the string “…262464195387″, where the … represents a whole lotta other numbers. So why would anybody in their right mind need such a comically large number? Were these mathematicians perhaps compensating for something (say, the budget differential between their department and a useful department like Astronomy)? From wikipedia:

Graham’s number is connected to the following problem in the branch of mathematics known as Ramsey theory:
Consider an n-dimensional hypercube, and connect each pair of vertices to obtain a complete graph on 2n vertices. Then colour each of the edges of this graph using only the colours red and black. What is the smallest value of n for which every possible such colouring must necessarily contain a single-coloured complete sub-graph with 4 vertices which lie in a plane?
Graham & Rothschild [1971] proved that this problem has a solution, N*, and gave as a bounding estimate 6 ≤ N* ≤ N, with N a particular, explicitly defined, very large number; however, Graham (in unpublished work) revised this upper bound to be a much larger number. Graham’s revised upper bound was later published — and dubbed “Graham’s number” — by Martin Gardner in [Scientific American, "Mathematical Games", November 1977].
The lower bound was later improved by Exoo[2003], who showed the solution to be at least 11, and provided experimental evidence suggesting that it is at least 12. Thus, the best known bounding estimate for the solution N* is 11 ≤ N* ≤ G, where G is Graham’s number.

Wow, that’s so useful (/sarcasm). It must have been a profoundly depressing result: “So, Ronald, how’s that proof you’re working on coming? Did you ever get a result?”
“Yeah, it’s somewhere between 11 and wharrgarbl.”

Even as an astronomer (a field which is known for large numbers, even coining the term ‘astronomical’), I’d probably just call it “effectively infinite for all foreseeable/sane purposes.” No wonder it was published in “Mathematical Games.”

In all honesty, stuff like this is probably good for the math departments-it will keep them at their desks during the inter-departmental war. I for one know that the physics department has long desired to vaporize the chemistry department with a large laser array. The mathematicians will likely be too busy coming up with crazy stuff like Graham’s number to be bothered by such events.

Last minute note:
I have just discovered that there is a larger named number, called TREE(3). It is part of a sequence of numbers: TREE(1)=1, TREE(2)=3, TREE(3)=Makes the word big seem hackneyed. Apparently, Graham’s number is “unnoticeable” next to a lower bound to TREE(3), which is itself unnoticeable next to TREE(3). I hear TREE(3), will anybody go to TREE(4)? Sold to the man in the straightjacket.

There are even bigger numbers yet, obviously, including “Totally Indescribable Cardinals,” (yes, that is the formal name), Transfinite numbers, and all sorts of made up names (Bajillion, Frumptillion, etcetera). For an incredibly humorous article on made up, unspecified numbers, look here.

Of course, infinity puts all of these so-called large numbers to shame. Compared to infinity, they might as well be 0. Maybe you should be careful next time you use the word “infinite” in casual conversation. You probably doesn’t mean that many.

Well, it’s finally over, and aside from a slight headache and severe sleep deprivation, I’m not too much worse for the wear. Just before the semester ended, however, fun things began to occur. The first was that my name is now on a submitted paper, which you can find here. It is not yet accepted to the journal, and we’re still waiting on referee’s notes.

Also on the research front, I have a new job, researching the stellar population around the light-echo source V838 Monocerotis. This is a really interesting star, and my research is aimed at determining if it is part of a young or old population. This could tell us a lot about how the outburst event occurred, and even what it was.

This weekend, I have been in Phoenix at the invite of my friend Pete (you can find his website to the right in my links) attending a blog bash and the NRA Convention. I went to this event as a member of the media and as such, felt obligated to take pictures, investigate things, and write interesting things down. In all honesty, I did feel a bit out of place at this convention (Star Trek conventions are much more my speed). There were quite a few people there, and the overwhelming majority of them live by the de-facto catchphrase of the convention: “Guns, Family, and God.” This is obviously not the usual crowd that I hang out with, hence the slight uncomfortableness, but we did meet up with several other bloggers who are anything but stereotypical NRA members. In fact, I believe I was the only non-member in that group. I channeled my inner journalism nerd (high-school paper) and wrote down many fascinating observations. I’m still mulling over these, but expect to see my reaction here within a couple of days.

Tomorrow, before leaving Phoenix, we plan to visit Luthier Walt Kuthman of Gypsy mandolins. I’ve been in contact with Walt about the possibility of him building me a custom Bouzouki. At the moment, this seems unlikely due to financial concerns, but I’m still hopeful about the future. Also musically, I just got a new CD by 2Duos, which includes Claire Mann and Aaron Jones, whose album I reviewed in one of the first posts for this blog. I may post a review of this new album here when I get home.

Every summer, I have a project-this is a tradition I have going back at least…well, about three years. This project invariably involves building something. For example, last summer one of my projects (there were two) was building and painstakingly painting a model of the U.S.S. Reliant, Khan’s ship from Star Trek II: The Wrath of Khan. My other was constructing a custom prop-lightsaber. These were very entertaining. At the moment, I am considering several things for this summer’s project (or projects). First, I have designed a system for focusing many laser rays into a single beam. This would involve wiring the lasers to power supplies, and making or otherwise obtaining an optics system. So far, this is my best idea, but if anybody out there has any suggestions, I’d be glad to hear them.

The best thing, of course, is that I survived another year, becoming one of the approximately 6 astronomy majors out of 100 beginning in our freshman class to make it to senior year on schedule. 6% made it. I’m going to need this summer to recuperate a bit.

]Michel Mayor and his exoplanet hunting team have done it again. Gliese 581e weighs in with a minimum mass of . For the technical details, followthis link to the pre-print paper. Of course, this is a pre-print (though accepted for publication in A&A), so it’s not in publication state yet, just out to show that this group discovered it first. The paper will likely be revised before it is finally published, but in my (admittedly short) experience, this is the only copy most people will read.

Most of the time, the inclination angle for these systems isn’t known (unless the planet transits the host star, in which case it can be derived from the impact parameter of the transit, b via a relatively simple formula), so the masses of most known extrasolar planets are listed as lower limits. In this case, however, the system has three other low mass planets, and since it is a stable system, it can be dynamically modeled and upper limits can be placed on the planet masses. In this case, the upper limits on all planet masses in the system is at 1.6 times the minimum, so the maximum mass for this newly discovered planet is only -still a significant discovery. The planet is, however, too close to the star to support life at 0.03 AU and has an orbital period of roughly days (3.14942 to be more exact).

The other planets in the system are worth mentioning as well. Gl581b, the first discovered is at least 15.62 earth masses with a semi-major axis of 0.04 AU, Gl581c is only 5.36 earth masses with a semi-major axis of 0.07 AU, and Gl581d is 7.09 earth masses and orbits at a distance of 0.22 AU. This last is particularly interesting because the planet lies in the habitable zone around the host star.

This remarkable system is only 20 lightyears distant from earth (it is actually the 87th closest known star system), and the host star is likely visible in relatively small (say, 6-7 inch) amateur telescopes. You can find it in the constellation approximately 2 degrees north of beta libra (’commonly’ called Zubeneschamali or Zuben el Chamali). For those of you who want to look for it yourselves, here’s a starchart centered on the location that should help you find it. Of course, libra isn’t up high in the sky until late these days, so you’ll have to stay up late to catch it.

I just found out the results of NASA’s node 3 naming contest and I must say, I am a little disappointed. The suggested name Colbert supposedly won by quite a large margin, but in second place was the name I backed, Serenity. NASA, being NASA, decided to name the node Tranquility.
What? Seriously, guys, why did you even have the vote if you were just going to totally ignore it?

On Monday, NASA brought out a mockup of its new Orion spacecraft to the National Mall for public viewing. This vehicle is pretty damned cool: it’s supposed to bring people back to the moon and perhaps to mars. This, however, is supposed to occur in the 2020s and 2030s, in other words 10-20 years from now. Now, I understand the rationale behind NASA’s long lead times-there’s not much money to go around, so they need to develop and build stuff when the money is around. This leads to truly ridiculous situations (example: the Orbiter’s computers compared to, say, my laptop and the obsolete, though awesome equipment on the Cassini probe).

For once, the problem is not NASA’s, it goes back to the Federal Government (as most problems do these days). In the 60s and early 70s, this country managed to go from never having sent a person into space to landing two on the MOON in just eight years (1961-1969). They had to develop all of the technology, the physics, the methods, the equipment, all of this incredible stuff with the severely limited technology of the time all from scratch. Nobody had done it before. Now the exact same agency, using the same technology (even though we’ve had 40 years of incredible development), the same methods, doing the exact same task is going to take two years longer. This is comically ridiculous, bordering on absurd.

So, I’ve gotta say: if the government wants to set these lofty goals for the space program, they should actually put some funding behind their words. At that point, the problems would all become NASA’s, and based on that institution’s intriguing history, I’d bet we’d have even more fun and dangerous problems. But at least they’d be working on them.

People should really pay attention to the words they’re using, sometimes what they say doesn’t make sense.

A good example is this recent article from the New York Post is about a small asteroid that was just discovered on Friday and passed within 65,000 kilometers (40,000 miles) of the Earth today at about 9 AM (EST)-about twice as far as most communications satellites.

2009 DD45 is about 30 meters across and (I assume) silicate-based like most asteroids, so it would hit the Earth with about as much energy as a relatively large atom bomb. If it were iron, of course, this force would quite a bit larger. The article above says that it would have hit somewhere around Tahiti, but I’m not sure if this is entirely correct-that was the point of closest approach. If it had hit, it probably would have hit beyond that point (as the closest approach would have been at distance=0 and it would have moved over Tahiti by then).

Also, it irks me that the article says:

Astronomers said the asteroid is likely to return for another series of near misses since it’s somehow drawn in by our planet’s gravity.

“Somehow drawn in?” What exactly are they saying here? Bah.

Anyway, what peeved me most about this article was the opening line:

Talk about a near miss!

Not so. As my personal hero and general go-to guy, George Carlin said: It’s not a near miss, a collision is a near miss. “‘*Crunch* Look! They nearly missed!’ ‘Yes, but not quite!’” It was really a near hit-it nearly hit us. Ah, well, maybe I’m too much of a stickler for correct language use. This is probably why I only have friends as weird as I am.

There’s a new smallest exoplanet in town, COROT-Exo-7b. Even better, it’s a transiting exoplanet (a type of planet outside of our solar system that moves across the disk of their host star from our point of view to block some light), a special type of object that I actually know quite a bit about (I’ve been on two projects observing these).

This is actually quite a lucky find, it is difficult to impossible to find out much about most extrasolar planets (which don’t transit their host stars). Since the technology to directly image them hasn’t really developed yet (notable exceptions are the recently imaged Fomalhaut B and HR 8799 B, C and D which are special cases), all we know about them comes directly from the changes they can induce in the host star. This includes the wobble back and forth caused by the planet’s mass (this method of finding planets can be called astrometry or radial velocity-they both exploit this motion in different ways), the sudden magnification and brightening of a background star caused by gravitational microlensing, and a few other less frequently used methods. These methods allow you to approximate a mass and orbital solution for the planet but nothing else. Transiting, however, not only helps to narrow down these parameters, but it also allows you to measure the radius of the planet, the eccentricity of the orbit, and in one special circumstance, map the surface of the planet.

COROT-Exo-7 is a K0 type main-sequence dwarf star about 140 parsecs away (that’s about 460 light years). It has an apparent visual magnitude of 11.7 (to put this into perspective for non-astronomers, the absolute dimmest thing a human can see in the best conditions is about magnitude 6.5. Magnitude is a wacky scale invented by the ancient Greeks, so it’s backwards and logarithmic, all of which is to say that you can’t see this star). It’s a relatively young star at an age of 1.1 billion years (+1.1 -0.4).

The planet itself is about 1.7 times the diameter of earth but about 11 times more massive. Since we know both of these quantities, we can figure out the density of the object and the density can tell us something about the composition. It has been suggested that this planet could actually be half rock and half water, which is a very interesting mixture indeed. Unfortunately, this planet has an orbital period of 20 hours and is practically burning up at nearly 2700 degrees Fahrenheit because it is exceptionally close to the host star. So even though it’s the first planet you could actually walk on, you probably wouldn’t want to.

This discovery is just the beginning of a whole new era for extrasolar planetary science. One of my dreams when I began studying astronomy was to discover an earth-like planet and COROT-Exo-7b is a major step on the road to this goal.