Sunday, March 27, 2011

Spaced Out

I'm afraid the skunk cabbage seminar I promised last week has been postponed. Not only did a member of the peanut gallery neglect to use spoiler tags and COMPLETELY RUINED IT FOR EVERYBODY, but the skunk cabbage blog post is traditionally a celebration of the changing seasons, and after this last sucker punch from Old Man Winter I see precious little worth celebrating. Guess this means we'll have to think of another topic for our weekly heart to heart.

Sometimes when I chat with my father about a new astronomical discovery related in some popular science periodical or other, the old man will remark "seriously, how do they know any of this?" It's a sentiment I can appreciate, especially where science news for the layman is concerned. (This is certainly not to suggest that I am much more than a layman.) We'll read an article on about the latest pulsar observations or speculations about dark energy, and the journalist, writing for a general audience, will skip right to the researchers' announcements without going into much detail about the recondite theories, postulates, observations, graphs, stacks of photographs, and walls of calculus from which the scientists produced their new discovery or hypothesis. Incredulous minds like my old man are reluctant to accept the validity of a statement when they can't see the reasoning on which it is based. After all, "because scientists say so" is just as vacuous and dangerous a position to take as "because the Church says so."

Today, in part fifty-seven-point-three-three-three of our ongoing Amateur Astronomy Series (tremendous emphasis on the "amateur " part), we will learn what scientists have deduced about the physical characteristics of a distant object, and more importantly, how they went about doing it. I would like to avoid turning this into another "LOOK AT SPACE AND HOW BIG AND CRAZY AND MINDBLOWING IT IS" piece: I would rather draw attention to the ingenuity the human mind has employed in coming to a more thorough understanding of the universe beyond our little blue pebblet, and in decrypting the code of the cosmic program.

What we're gonna do today is calculate the average density of the planet Jupiter.


Density, as you know, is a measure of how much matter is pressed into a given space. Or to put it more simply:

mass (kg) / volume (m^3) = density (kg/m^3)

So in order to even begin doing this, we need to figure out Jupiter's volume and mass first. Both can be done without too much difficulty, especially since the real scientists have already done all the painstaking measurements and guesswork for us.

Let's begin with the planet's volume. Jupiter isn't quite spherical, but we're going to assume that it is, since I sure as hell don't know how to correct an equation to account for rotational flattening. Anyway, as you surely remember from sophomore geometry class (and as I just looked up on Wikipedia), the volume of a sphere can be calculated like so:


Great! But what the hell is Jupiter's radius?

If you recall from our last scintillating episode, astronomers have long known how to get a very close approximation of a distant object's size using basic geometry. For this, we're going to assume that the Earth and Jupiter are positioned roughly at their closest point of approach (which we'll talk more about in a minute). At this distance, Jupiter's angular diameter in the night sky is 46.8 arc seconds, which comes to about 0.013°. Now we plug it into this familiar equation...

(angular size)° / 360° = (Jupiter's diameter) km / 2π(Jupiter's distance from Earth) km

And we get...

0.013° / 360° = (Jupiter's diameter) km / 2π(Jupiter's distance from Earth) km

Wait. That's no good. We still need to figure out Jupiter's distance from Earth. To do this, we turn to Mr. Johannes Kepler.

Johannes Kepler

Thanks to the trove of meticulously-compiled stellar records left to him by Tycho Brahe and the eighteen years he spent poring over them, crunching numbers, and making observations of his own, Kepler discovered that the planets' orbits obey three basic rules.

Kepler's first law states that planetary orbits are elliptical. Think of an ellipse as a circle with two centers (called foci). In a circle, every point on the circumference is equidistant from the center. With an ellipse, you can pick any point on the curve, measure the distances between it and both foci, add them together, and come to the same sum you would with any other point on the curve.

Anyhow. When considering planetary distances from the sun, standard procedure is to use the semimajor axis, which really just means "one half of the ellipse's width." Kepler assigns Earth's semimajor axis the value of 1 astronomical unit (A.U.).

Kepler's third law establishes the relationship between a planet's distance from the sun and the times it takes to complete one orbital revolution. Put simply:

(orbital period in Earth years)^2 = (semimajor axis in A.U.)^3

Kepler then calculated and published the orbital periods and semimajor axes of the first six planets. Thanks to him, we know that Jupiter has a semimajor axis of 5.2 A.U. Since Earth's semimajor axis is 1 A.U., we're going to assume that Earth and Jupiter are positioned so that the distance between them is roughly 4.2 A.U. (which, again, is about where they are during their closest approach).

But wait: this doesn't do us much good either. We're not looking for a measurement in astronomical units. We need kilometers.

Before the 20th Century, astronomers used triangulation to arrive at an approximation of the distance between Earth and Venus. Since Earth's semimajor axis is 1 A.U., and Venus's semimajor axis is about 0.7 A.U., they reckoned that the difference between Earth and Venus (in kilometers) would correspond to roughly 0.3 A.U. From there, they could use that value to determine how many kilometers are in one astronomical unit. Since Venus is about 45,000,000 km away from the Earth, 0.3 A.U. equates to 45,000,000 km. Dividing the latter figure by the former gives us 150,000,000 km for 1 A.U. (Scientists experimenting with radar in the 20th Century pegged the value at a more precise 149,597,870 km, but 150,000,000 km is still used for simplicity's sake.)

So! If Jupiter's distance from Earth is 4.2 A.U., and an A.U. is equal to 1.5 x 10^8 km, then Jupiter's distance from the Earth in kilometers is 6.3 x 10^8 (or 630,000, 000).

Back to the equation!

0.013° / 360° = (Jupiter's diameter) km / 2π(630,000,000) km

What we end up with is some huge number with a lot of decimal places that we're just gonna call 143,000 km. So if that's Jupiter's diameter, that means its radius is about 71,500 km. Now, at last, we can figure out its volume:

(4/3)π(71,500)^3 = 1,531,111,204,795,974.7523

Whoa! Let's just round that down to a much more manageable 1,530,000,000,000,000 km^3. And since density (which is what we're ultimately trying to determine, remember?) more often uses meters than kilometers, let's convert it into meters for a final value of:

1,530,000,000,000,000,000,000,000 m^3 = Jupiter's volume

Still with me? I will be inconsolably heartbroken if you are not.

Now that we know how much space Jupiter occupies, we still have to figure out how massive it actually is. I saved this part for last because I think it is very cool. First, let's look at Jupiter's moon Europa.


This icy little fella revolves around Jupiter in a circular orbit that takes 3.55 days to complete and whose angular radius appears as 3.66 arc minutes (0.061° ).

First, we'll calculate the circumference of Europa's orbit. We get its radius through the same trick we used to find Jupiter's diameter, arriving at about 671,000 km. From here, finding the circumference is as easy as:

2π(671,000) km = 4,216,017.341 km

We'll round that up to 4,220,000 km since we're too cool to give a damn. But you wonder: where are we going with this?

So we know Europa travels a distance of 4,200,000 km over a period of about 3.55 days. Now we're going to smash these values together to determine its speed. Since speed is usually more concerned with "per second" than "per day," we convert 3.55 days into about 307,000 seconds. So if Europa moves 4,200,000 kilometers every 307,000 seconds, then its speed must be somewhere in the neighborhood of 13.7 km/s.

Now the ball enters the court of Sir Issac Newton.

Sir Issac Noo-Tun

Europa maintains a speed of 13.7 km/s as it orbits Jupiter. Its velocity, however, constantly changes. Speed only concerns itself with distance and time; velocity also considers direction. By Newton's definitions, since Europa moves in a circle instead of a straight line, the moon is accelerating.
Newton determined that the acceleration of any body moving at speed v in a circular orbit of radius r may be shown to be:

a = v^2 / r

Using this equation (and remembering that Europa's orbital radius is half of its orbital diameter), we find that Europa accelerates at a rate of about 0.00056 km per second per second.

According to Newton's laws of motion, an object accelerates when a force is applied to it. In Europa's case, that force is the gravitational interaction between it and Jupiter. Here is how we calculate gravitational force:

Let's take a moment to define these terms. F represents force, measured in newtons (N). M and m represent the respective masses of the larger and smaller bodies (in this case, Jupiter and Europa) in kilograms (kg). r represents the distance between bodies M and m (in other words, the orbital radius) in meters (m). And G stands for the gravitational constant of proportionality and has a set value of 6.67 x 10^-11 n m^2/kg^2.

This is where it gets wacky and brilliant. We can determine how much gravitational force Jupiter exerts on Europa based on the moon's acceleration. Then we can figure out Jupiter's mass from the amount of gravitational force it exerts on Europa. The key to doing this is lies in Netwon's second law of motion: force equals mass times acceleration, or...

F = ma

Let's go over this one more time. We've got force (F), measured in newtons (N). We've got Europa's mass (m) and Jupiter's mass (M), measured in kilograms (kg). We've got Europa's orbital radius (r) measured in meters (m). We've got Europa's orbital speed (v) and orbital acceleration (a), measured in meters per second (m/s) and meters per second per second (m/s^2), respectively. And finally, we have the gravitational constant (G), which is 6.67 x 10^-11 n m^2/kg^2.

What you are about to see is some serious algebraic ninjutsu, courtesy of Sir Issac Newton. Don't blink or you'll miss it:


All that's left is to plug in the values and solve. (Remember: even though we used kilometers for Europa's orbital radius and speed, we're converting them to meters now.)

M = (671,000,000 x 13,700^2) / 6.67 x 10^-11

And so, we get:

M = 1.9 x 10^27 kg


M = 1,900,000,000,000,000,000,000,000,000 kg

And so, having determined Jupiter's mass and volume, we can at last figure out its average density:

1.9 x 10^27 kg / 1.53 x 10^24 m^3 = 1.242 x 10^3 kg/m^3

Jupiter's average density would appear to be 1,242 kilograms per cubic meter by our reckoning. According to NASA, Jupiter's average density is actually more like 1,326 kilograms per cubic meter, but remember: they've corrected their equations to account for the planet's rotational flattening and use much more precise measurements than we did. But all in all, we came pretty close.

As far as the accuracy of these methods and figures are concerned, you need look no further than the unmanned probes that have visited Jupiter over the last thirty years for verification. It would be pretty hard getting a satellite in orbit around a planet 400,000,000 miles away without having a damned good idea of its mass and gravitational force in advance. And do note that these same probes were what ultimately confirmed the old "Jupiter is a gaseous planet" hypothesis, which was originally established on the grounds of the same average density calculations we just performed.

Monday, March 21, 2011

This week's episode: "Misc. Rally Reflections" or "MONEY FOR JOBS AND EDUCATION / NOT FOR WAR AND OCCUPATION!"

On Saturday morning my friend James and I sped down to Washington, DC to catch an anti-war demonstration at the White House. The aspiring shutterbug James wanted to take pictures, while I was just looking for an excuse to drive ten hours in one day. Not that I'm unsympathetic to the cause -- but there's no surer way to end up a pessimist than to have been an idealist in youth.

The demo was held in Lafayette Square, just across the street from 1600 Pennsylvania Ave. 200-300 people showed up by my reckoning, though I should not be relied on in any matter concerning numbers. This approximation takes both groups into account, since there were two demonstrations occurring simultaneously. One was the anti-war rally that James and I came for, while the other was a "DOWN WITH QADDAFI" gathering occupying a stage toward the other end of the park. Standing between the two and opening both ears, you could hear and appreciate why the traditionally Democratic constituencies have such trouble getting their shit together long enough to effectively concentrate on a single target. While the anti-war group chanted "LIBYA IS THE NEW IRAQ / PEOPLE UNITE, STAND UP, FIGHT BACK!" the Libyan crowd was shouting "FREE, FREE, LEEB-YAH!" To the south, a potbellied kid with a beard lambasted America and its imperialist intentions masquerading as humanitarianism, and breathlessly listed every conceivable parallel between 2003 Iraq and 2011 Libya (including the ones that didn't make sense when you thought about them). To the north, a professional-looking middle aged woman speaking into microphone thanked and praised Sarkozy for having the stones to spearhead the military operation against the insane dictator massacring his own people to cheers and flourishes of the Libyan and French flags.
Despite the dissimilarities between the crowds and the dissonance in their messages, one could infer an awful lot about the demonstrators and the broader situation by looking back and forth between them.

Let's start with the anti-war faction. The heavy majority of the demonstrators could be sorted into one of two generational brackets: the 18 to 29-year-old college kids, graduate students, or career activists/couch-sleepers, and the 45 to 60-year-olds upon whom the Vietnam years had stamped an indelible brand. Most of them were white.

The most intense and dedicated demonstrators formed a cluster in front of the police barricade on the sidewalk, leading hoarse chants over bullhorns and delivering extemporaneous addresses about the military industrial complex and how American pretenses of altruism are never to be trusted. In this pocket were six or so ringleaders and their two-dozen followers; they contributed about 90% of the event's noise and enthusiasm. But once you went outside the activist nucleus, you saw a rapid decline in the crowd's density and energy. Demonstrators stood around like they had come to watch a show in the park. The organizers chanted slogans on and off for hours, but there were rarely more than 15-30 voices joining in. People let their "FREE BRADLEY MANNING!" and "STOP OCCUPATIONS AND TORTURE FOR EMPIRE!" signs falls onto the grass and didn't bother picking them up. Every now and then, some of the ballsier protesters (mostly middle-aged folks) who had parked themselves by the White House fence got put in handcuffs by the police and ushered into a police van or public transit bus. Some of the demonstrators closest to the police barricade cheered them as they passed. Most of us just watched.

Before long it occurred to me that James and I weren't the only people who had come to check out the scene and take some snapshots. Looking through the crowd, it seemed that most of the people beyond the primary noisemakers and activists hadn't come here for a strenuous exercise of their First Amendment right: they were to watch, just like us.

Kneejerk observation: holy shit -- this is exactly the problem. We are a generation of observers. OH MY GOD I'M DOING IT EVEN NOW

That might be the most easiest answer to produce and accept. But I am not totally sure if it is the most accurate.

Let's consider this. We have a demonstration organized for the purpose of making a twofold statement: 

A.) We need to end America's foreign wars and 

B.) redirect the billions we spend on military occupations toward repairing our busted economy, educational system, infrastructure, etc.

Next: who are the beneficiaries of this event? Which branches of the population theoretically stand the most to gain from what this group proposes? 

1.) The battered working class and crumbling middle class, who could use a little help in the form of government initiatives, which we can't afford. Our national finances arrived at this sorry state from a slew of causes, but spending billions upon billions to maintain two military occupations for nearly a decade is one of the main culprits. 

2.) The servicemen and veterans of the United States armed forces. Since this is a volunteer army, we can safely presume that most of these folks come from families belonging to the first category.
But there were relatively few anti-war demonstrators that fit either profile. Several veterans (of various ages and wars) attended the rally, and a few working-class slobs (such as James and myself) showed up. But the anti-war, anti-imperialist, pro-Wikileaks crowd overwhelmingly consisted of white college students and middle-aged folks who clearly had families and jobs. Should we try to guess why this might be? 

Guess #1: It is hard to spur oneself into a righteous frenzy over the indirect and abstract. The Tea Partiers can channel their outrage toward liberalism, multiculturalism, intellectualism, gun control, etc. toward Barack Obama. Osama Bin Laden's goat-face became the symbolic purpose for American's initial invasion of Afghanistan. But the military industrial complex and disaster capitalism are not sentient entities that can be recognizably depicted on homemade placards, nor are they ideas we can easily tether to a familiar figure. There are a hundred thousand reasons why these things are hurting America, but the human mind has a harder time recognizing and responding to threats it can't attribute to a singular, physical source. A particular ideology can indirectly kill hundreds of thousands more people than a tiger might maul by itself, but evolution has made us a whole lot better at responding to the tiger. Side B of this guess is that students likely have more time, inclination, and energy to express their outrage toward concepts and descriptions than the rest of the general populace. 

Guess #2: The people most harmed by the war economy (not to mention the Right's all but declared siege on the lower and middle classes) probably don't have the time or money to spend hauling themselves to DC to spend their Saturday afternoon chanting slogans toward Barack Obama's empty, unresponsive windows. They've got shit to do. Second jobs to work. Bills to pay. Families to feed. Want ads to search. Ironically, the people most affected by the subject of the protest are also those with the least ability to participate. 

Guess #3: It is very easy to become desensitized to war when it's been in the news nonstop for the last decade, especially when nobody you know personally has been affected by it. This is the huge difference between the most recent American wars and Vietnam. When you have an all-volunteer military, most of its members will be coming from the lower-income, less-educated brackets of the populace. (Let's be honest here -- you don't see many NYU sophomores deciding to put their Art History degrees on hold to serve their country's interests in Afghanistan for the sake of patriotism.) The people suffering most from the war are largely members of an isolated economic class. During Vietnam, everyone was fair game. If it were the sons, brothers, and husbands of the bankers, board members, doctors, and lawyers getting conscripted at random to have their limbs blown off in the Middle East, you can bet your ass the post-2003 anti-war movement would have more traction. Look at the clique of yuppie tourists walking down the sidewalk, bemusedly snickering at the scene and whipping out their cell phone cameras. If one of their boyfriends or buddies had his number called last year and his guts pumped full of shrapnel last month, I doubt they'd approach a war protest with a "hey check out these freaks" attitude.

But let's look at the Libyan demonstrators for a moment. Most of them seemed to be Libyan immigrants or first-generation Americans. Though its numbers were fewer than the anti-war group, its members exhibited a far more conviction and solidarity. They clustered tightly together, participated in every chant, listened raptly to every speaker while they cheered and raised their Libyan flags. Entire families had come out for this -- husbands, wives, children. While their parents participated in singing (what I presume was) the Libyan national anthem, their kids played soccer off to the side.

Why such a difference? Three more guesses... 

Guess #1: Their countrymen -- friends, neighbors, relatives -- are actively being slaughtered. The situation isn't matter of people being indirectly harmed as the result of government policy; it's a matter of people being directly blown the fuck up as the result of government policy. 

Guess #2: Qaddafi. Unlike the anti-war crowd, the Libyans demonstrators had a singular, assailable human being at which they could direct their anger and blame. 

Guess #3: Their problem has (or had) a seemingly viable, realistic solution: U.S. military intervention in Libya. The anti-war demonstrators wanted nothing less than a total overhaul of America's economic and foreign policy -- something that is easy to demand, but not so easy to do. Not only was the Libyan crowd addressing a problem with a much clearer solution, the solution was already likely to happen. People are more willing to focus their time and energy toward reasonably feasible purposes than pipe dreams.

But that last guess brings us to the most curious and noticeable thing about the idealists and young liberals representing the anti-war crowd. It seems like they're waiting for something -- for a solution or a savior. All of them believe that America is in need of seismic social and political changes -- a sentiment certainly shared by far, far many more people than just the kids distributing socialist literature and protest flyers. The people James and I talked to all talked about revolutions. They want a revolution to happen, but nobody's sure how to strike the match as a certain Tunisian youth did last December (both figuratively and literally).

Or maybe they're just not willing to do it. They aren't desperate enough. Revolution is a risky venture -- the only ones who can afford it are either those with too little to lose or too much to worry.
Uncertainty. Unwillingness. One's as good as the other, really. If you were to ask Count Tolstoy (hey remember that guy?), he would say that it's not so much a matter of desire or will: it will only happen when the circumstances become such that nothing else is possible.

Coincidentally, as I thought about all this on Sunday morning and sat down to read the next chapter of The Doll, I turned the page and had this statement leap out at me: 

For human nature is odd: the less we tend to martyrdom ourselves, the more we require it of our neighbours. 

But I do go on in my old age.

What say we cap the verbiage and I show you some souvenirs? First, a few of the snapshots James took. (He has a Shutterfly page you can visit; several friends and well-wishers are trying to convince him to switch to Flickr instead.) Click to enlarge!
And now for a sampling of the literature we collected! Again, click to enlarge.

Tune in next week for a discussion about the magical properties of skunk cabbage!

Friday, March 18, 2011

Quick Midweek Oddments

I got my new binoculars a couple days ago.

I implore you not to pay any attention to the cluttered state of my living area/workspace. Please focus on the binoculars and how sexy they are.

For $150 or so (plus a tripod and free shipping!), this wasn't a half-bad expenditure. They're about as strong as a smallish telescope -- I definitely won't be able to make out anything too distant or dim, but they're real nice for a beginner who's still getting a handle on where everything is. It seemed best to play around with a relatively inexpensive pair of noks for the time being and invest in something bigger and better down the road. A telescope is not something I can half-ass; it's either a $900 piece of equipment that can resolve the gas planets' bands and brew hot cocoa (for those lonely winter nights) or nothing at all.

Sadly, because of a waxing moon and overcast skies, I haven't had a chance to see very much. Got a real nice look at the Orion Nebula, though. It'll be even better once there's less haze and background light.

Speaking of stars, I should correct something I mentioned in that last post. Since it's been persistently cloudy for the last week or so, I couldn't go outside and check my work on that last post -- I was pretty much going from memory, and the skies change quicker than you might think. A lot of it's accurate, but the father west the stars drift, the more they get skewed downward, toward the horizon. (Remember, they path they "travel" along through the sky is circular.) I had mentioned that you could find the Pleiades at about two o'clock of Aldebaran, but when I went outside this evening at around nine, they were more like three o' clock instead. (I just thought I would mention this in the extremely unlikely event that somebody went outside to look and cursed me for lying to them/not knowing what I was talking about).

Final tidbit: managed to dig up a few email addresses belonging to people in Sendai I met during that summer study abroad program I attended five (five!?!) years ago. Their replies to my "OH MY GOD ARE YOU OKAY?!" messages are so delightful and so endearingly, inimitably Japanese I almost want to share them here. Not to disparage them, of course -- reading them makes me feel a half-forgotten fondness and nostalgia, and reminds me how totally different our cultures are and how funny they both seem in the context of each other. Everyone everywhere is screwed up and hilarious and lovely.

I really hope everything works out over there.

Sunday, March 13, 2011

Star Stuff

I recently began an internship at a small publishing outfit in New York because my professional life is going nowhere and I reckoned it would be at least a few cents cheaper than a semester of graduate school. Two mornings a week I hop a train to Manhattan, take the subway to Brooklyn, then walk ten minutes to the gallery building where the office is situated. On the two evenings that correspond to these two mornings, I exit the building and walk ten minutes, take the subway to Manhattan, and hop a train back to Jersey.

During my commute last week I was kicking around ideas for a new blog post, since the last two were such cop-outs -- one was an excerpt from someone else's novel, and one was an excerpt from my novel.* Turning to observations made on the four train rides I make during a day at the internship for material, I was all set to to squeeze some more out water of the "ways in which technology is making our lives worse instead of better" stone, but then I entered the subway after leaving the gallery and realized I still had the office keys in my pocket.

Up the escalator, through the turnstile, back to the street. Ten minute walk to the office to return the keys to the boss. By now it was nearly 7:00 PM and the urban twilight settled in. As I headed south, uphill along Washington Street, I spotted a bright yellowish star almost directly ahead.

Jupiter? I scanned its surroundings. No -- not Jupiter. Not with Orion at two o' clock. This would have to be Sirius. There was Jupiter -- above Manhattan in the west, blinking behind the arches of the Brooklyn Bridge.

Then I thought fuck it -- this week I'm just gonna write about stars.

Tonight we'll go over a small stretch of the winter sky that should be visible just after dark around this time of year (provided your latitude is in the same ballpark as Manhattan). Since the stars "revolve" along a curve, assume that we're looking at the stars around 7:00 pm (8:00 for daylight savings) in early March when I cite an o'clock as a direction from one star to the next.

Let's begin in the south, as I did the other night. All you need to do is face the direction in which the sun set and turn about 90 degrees counter-clockwise. Search the sky for a bright star. It won't be hard to find; it isn't that high up, and you'll probably know it when you see it. This would be the dog star, Sirius (α CMa): the second-brightest star in the sky (outshone only by the sun) and the centerpiece of the constellation Canis Major.

Believe it or not, Sirius is actually a binary star, composed of two individual stars (Sirius A and Sirius B) orbiting each other. Sirius A is the really massive and bright one, while Sirius B is an unassuming white dwarf, formerly a red giant and the larger of the two. Squint as hard as you like; unless you've got a real nice telescope and a great vantage point, you'll never resolve the two separately.
Moving along: at about two o' clock from Sirius stalks Orion, the hunter of the winter sky:

The three stars forming his belt (center) are nearly impossible to miss. From left to right, they're often listed by science types as ζ (Zeta) Ori, ε (Epsilon) Ori, and δ (Delta) Ori. The Greek letters come from the Bayer Designation, a system devised by astronomer Johann Bayer to catalog stars by constellation and brightness.

Fun fact: though the stars of Orion's Belt appear to be arranged in a neat row, this is only a trick of our terrestrial perspective. According to stellar parallax measurements collected by the Hipparcos satellite during the early 1990s, the distance between each star and the earth varies more than you might suspect:

Earth to ζ Ori: 800 light years (approx)
Earth to ε Ori: 1300 light years (approx)
Earth to δ Ori: 900 light years (approx)

The "belt," then, is actually a group of distant, unrelated stars arranged in a zigzag. Only because of our particular vantage point do we perceive them as sitting in a line.

At any rate, Orion is very recognizable, easy to find (even in areas with a lot of light pollution), and full of neat stuff. We'll begin at the hunter's left shoulder with the red supergiant Betelgeuse (α Ori).

Betelgeuse is another hard star to miss, thanks to its brightness and distinct hue: simply lift your gaze straight up from the belt's leftmost and middle stars and look for the orange-red star. Again, you'll know it when you see it.

Many astronomy books and educational materials like using Betelgeuse to demonstrate the relative sizes of stellar bodies, and I intend to follow suit -- but first, let's play with shapes.

If you think back to our November adventure and observation of the Andromeda Galaxy, you might recall a method of calculating distances using simple geometry. The same trick can also be used to get an idea of a distant object's size as well -- provided you already know its distance.

To begin, here's the Earth.

Now we draw a circle around the Earth. This represents the celestial sphere -- an imaginary construct representing how we perceive the heavens. Think of it as a huge hollow ball with stars painted on the interior. The Earth floats in the center, remaining still while the sphere rotates around it.

Since every star occupies a small but measurable width on this spherical plane, it is possible to quantify their perceived sizes as angular measurements. Betelgeuse probably isn't the best example we could be using, since observations of its angular size tend to vary (for a number of reasons). But if we just use the median of some measurements given by an uncited Wikipedia article (0.0545 arc seconds) and convert it to degrees using the Calculator application in my System Tools folder, we might hope to guess that of the 360 degrees in the sky, the red supergiant Betelgeuse occupies some 0.00001513 degrees (or so). Phew!

Now we draw a second circle around the first and mark off a section proportional to Betelgeuse's angular size on the first circle. This represents the star's actual width.

Astronomical voodoo places Betelgeuse's distance at something like 643 ± 146 light years from Earth. (This number was also pinched from Wikipedia, but at least we got a source.) For the sake of convenience, let's just use 643 light years (6,083,119,760,000,000 km) as our distance. Can you guess the equation yet?

(Betelgeuse's angular size) degrees / 360 degrees = (Betelgeuse's actual width) km / 2π(distance) km
0.00001513 degrees / 360 degrees = X km / 2π(6,083,119,760,000,000) km

Please feel free to add up the numbers yourself and let me know if I made a mistake (which isn't unlikely), but the value I got for X was something like 1,606,359,190.

By this measurement, we get a rough estimate of 1,606,000,000 kilometers for Betelgeuse's width. That's about 998,000,000 miles.

Betelgeuse is a seething, belching nuclear orb with a (very loosely) approximate diameter of 998,000,000 miles. Just for comparison's sake, the sun's diameter is only a measly 870,000 miles, and the diameter of Earth -- the planet on which you and I and six billion other humans live -- comes to an infinitesimal 7,926 miles.

Think about that for a moment, please.

Anyhow, we see variations in measurements of Betelgeuse's apparent size because of the star's instability. Its actual size fluctuates; the stuff it spits out into space make it hard to tell where the "exhaust" ends and the star begins. But astronomers are pretty certain that Betelgeuse is shrinking. If anything we've guessed about stellar life cycles is accurate, this means Betelgeuse is fixing to go supernova. (I don't think there's any proper terrestrial analogy for an event like this. Comparing it to the detonation of a billion mile-wide thermonuclear device probably doesn't even come close to the reality of it.)

We don't know when this is going to happen. It could be next year (though probably not). It could be a million years from now. But when information of the event reaches Earth, it will be very difficult for us (or whatever species survives us) not to notice. The last recorded supernova (1054 A.D.) is reported to have been visible during the day and brighter than the moon at night. More on this later.

Now! Let's move on from Betelgeuse at last and return to Orion's Belt. Hanging below the leftmost star of the belt (and its cute little neighbor) is the "scabbard." My city-dwelling friends might be out of luck where this is concerned -- maybe it was because the sun still hadn't completely set, but I couldn't make out any other stars between Orion's belt and Rigel in the Brooklyn sky.

Quick Rigel Fun Fact #1: Its Bayer Designation pegs it as β Ori, even though it's very perceptibly brighter than α Ori (Betelgeuse).

Quick Rigel Fun Fact #2: Kang and Kodos from The Simpsons claim to originate from the (fictional) fourth planet orbiting Rigel.

Anyway, on to the scabbard. What we're looking for now -- depending on the clarity of the skies -- is either the first or the second star from the top. (If conditions are good, you'll see three stars in the scabbard. Often, you'll only spot two.) Even without a telescope, if you look closely you can discern that it's not a tiny point, like most stars -- it actually looks more like a luminous smear. This is because what you're looking at isn't a star, but a cloud. This would be Messier Object 42, better known as the Orion Nebula.

All you require is a halfway-decent pair of binoculars and a clear evening to get a nice glimpse of it. What you see probably won't look quite as impressive as the above Hubble image, but it's a beautiful sight nonetheless.

Moving on at last from Orion! If we look at Betelgeuse and direct our gaze about two o' clock or so (or one o' clock from the rightmost star in the belt), we stumble into the constellation Taurus. What we're looking for is α Tau -- the orange giant Aldebaran (Arabic for "the follower"), sometimes colloquially referred to as the red eye of the bull.

Here's another stargazing opportunity in which my city-dwelling friends sadly get shortstrawed. If you've got either a very clear night or a pair of binoculars, direct your gaze to about four o' clock of Aldebaran and behold the Hyades star cluster.

From where I live, they're barely visible with the naked eye. With a pair of hand-me-down birdwatching binoculars, I can spot nearly a dozen of them. They're quite a sight -- like little gems sown across the firmament -- but the Hyades are a bit like the Jan Brady of star clusters: everyone pays more attention to their more noticeable and prettier sister(s), whom we'll get to in a sec.
If you look at Aldebaran and move to about ten o' clock, you bump into ζ Tau, the tip of the bull's lower horn. This star doesn't shine as brightly as the other ones we've looked at and can be difficult to find. It often helps to use both Betelgeuse and Aldebaran as signposts:

Right in Zeta Tau's vicinity sits Messier Object 1: the famous Crab Nebula.

Remember that 1054 A.D. supernova I mentioned earlier? This is the remnants -- a visible, tangible echo of the big KABOOM. To save you the trouble of looking it up and converting the units, the Crab Nebula's radius is somewhere in the neighborhood of 32,000,000,000,000 miles, and it seems to be expanding at about 900 miles a second -- which means, in a sense, that the explosion from 1054 A.D. is still happening.

I'll wait a moment while you try to wrap your head around that. Lord knows I can't.

The star wasn't quite massive enough to collapse into a black hole after the supernova, but somewhere in its billowing corpse spins a pulsar. I won't even pretend to know enough about neutron stars and pulsars to provide any facts, so I will direct you elsewhere for that. (The universe is full of very wonderful and frankly terrifying things.)

It is possible to glimpse the Crab Nebula from Earth, provided you have sufficiently clear skies and sufficiently powerful optics. Apparently I have neither, because I CAN'T FIND THE DAMN THING. (I can't quite pin down the location of the constellation Cancer, either. Strange that interstellar crustaceans should prove such elusive critters.)

To conclude our brief cosmic stroll and to wrap up this not-so-brief blog post, look at Aldebaran again and direct your gaze one or two o' clock or so. What you'll see is a star cluster that more than one inexperienced and clueless stargazer (including myself) has mistakenly assumed was the little dipper because of its shape. This is one of the most famous and renowned sights of the night sky: it so evoked the imagination of Arabic astronomers that they named a prominent orange star "the follower" because of how it appears to wander after it across the celestial sphere. You're looking Messier Object 45, the seven (well, six) sisters -- the Pleiades.

The Pleiades don't appear quite so bright (or blue) with the naked eye, though I have yet to view them through a good telescope. Even without any optical enhancements, they appear a lovely little jeweled tadpole in the winter night. If any of my New York-dwelling friends or readers are reading this, please look for them when you have a chance. I couldn't spot them during my walk to the subway the other night, though it very well could have been that my vision was obstructed by buildings. Let me know: does the tadpole wriggle in Manhattan's skies?

Yeesh. When I start waxing pseudo-poetic like that, it means I've spent too much time typing and not enough time sleeping. I hope this has been entertaining and informative for you, and I doubly hope it encourages you to spend a bit more time exploring the skies in the nights to come. (And I triply hope I've managed to trick you into thinking I have any idea what I'm talking about.) Stargazing can be an addictive hobby -- soon as you learn to "read" part of the cosmic tapestry, you find yourself more curious and eager to decipher more of it. (Also, strong circumstantial evidence suggests that pointing out stars and constellations when you're on a date doubles your chances of getting laid.)

Remember, these are all winter stars -- in another month or so, they'll be out of sight. Find them while you have the chance!

* Yeah, about that novel: in an epiphany, I realized that the only way I can possibly make it work is by rewriting 80% of it. I'm thrilled to have discovered a way out of the impasse, but at the same time...

Sunday, March 6, 2011

Dreams, Environs

[Conversation between two people in a car on the westbound lane of Route 119, ten miles outside Boulder, Colorado.]

"What I'm saying is that there is something in the city, every city -- in particular the long-established metropolises: your Philadelphias, New Yorks, Seattles, and San Diegos -- that seems deeply tangled up in the surreal. Waking, moving about, working, resting, watching the sun rise and set in such a place, you can't help feeling a sense of the uncanny. A kind of déjà vu, displacement -– a psychic itch. As though a doppelganger were staring back at you from every street lamp, crossing sign, and turnstile. It's like an altered state of consciousness. A pre-lucid dream that never gives itself away, but never totally fools you into supposing it's real, never jostles you awake. I’ve lived in many cities....and it never stops. It never leaves you. Am I dreaming? Is this place for real? Because it is a dream. To live in the city is to be within a composite sculpture of humanity's soul -- a vision of our secret self that understands only desire and geometry, rendered in brick and steel, glass and garbage. Every constituent piece of your surroundings was devised by a human mind, wrought by human means, crafted to facilitate human purposes and interests. Man's perception, intelligence, experience, and understanding of what is possible, incarnate as a landscape. That's what the city is. But then -- what's all of this? These mountains, these forests? Where is the artificer? Involuntarily conceived across eons, collected into cohesion and form through currents operating independently of intent or intelligence...such things would be inconceivable to us were our terrestrial existence not shared with theirs -- but they are still fundamentally alien, outside of us, independent of our nature. Malleable at best, hostile at worst. And yet we are profoundly bound to it, shaped as we were by the same inscrutable engine of action, reaction, cause, and effect..."

"I suppose it follows that it isn't our dream, but --"

"We are part of its dream. Or of the dream containing it."

"So our cities are dreams within a dream."



"What isn't?"