The Shape of Days

I’m not going to mince words here: This post is nerdy. It’s incredibly nerdy. You know all those Web sites out there that are really, really nerdy? With the exception of the ones about Japanese cartoons, this post is nerdier than all of them combined.

Still here? Okay. Let us commence the nerding.

I was talking to a friend of mine tonight. He’d had a little technological problem today. He was trying to make two computers talk to each other — well, more specifically, he was trying to make one computer talk to all other computers everywhere, but from our point of view it’s the same thing. It wasn’t working, and he went through a great deal of swearing and hair-pulling before discovering that his computer wasn’t listening. It’s not that it was unplugged, but it was as close to that as he could get without actually removing the cable.

Understandably this discovery was met with equal parts relief and head-pounding-against-wallism.

Anyway, we were talking about that, and I was trying to reassure him that yes, in fact I have done things as seemingly stupid as that, many times, please don’t ask for details because it’s too embarrassing. Suddenly I got the bright idea of getting his mind off of things by changing the subject.

“Hey,” said I, thinking myself all clever. “This reminds me of that ‘Battlestar Galactica’ show. You know, they’re always talking about how the only way to make their computers safe from the cylons is by physically disconnecting them from each other.”

And then we talked about that for a little bit. Sure, the computers aboard the fictional spaceship are impervious to cybernetic attack because there’s no way for anybody to communicate with them from a distance. It’s like defeating burglars armed with lockpicks by building a house with no doors.

“But,” my friend said after a moment’s consideration, “what about dradis?”

See, on this spaceship from another world, dradis is what they use instead of radar. It looks like radar, it works like radar, it has the same basic characteristics of radar. It’s just called something else because, after all, they’re from another planet. They’ve got their own names for stuff.

My friend wondered aloud why, since this big aircraft carrier in space is constantly scanning its local volume with dradis, the cylons haven’t infiltrated and disrupted the computers that handle that system. Or, for that matter, why they haven’t picked their way in through the communications systems. After all, it’s not like the Galactica is a big, solid box totally isolated from all external signals. They’re transmitting and receiving stuff all the time. And every antenna on the thing is a point of vulnerability to the cylons’ godlike computer powers.

That, it seemed to me, was a valid point. So we chatted about it for a minute to see if we could find a hole in our reasoning.

The communications systems are pretty easy to excuse. Their wireless is analog. It would be no more possible to insert a computer virus that way than it would be to remotely crash your transistor radio. “But surely the signals are encrypted,” my friend said. Except we know they’re not. There was one episode of the show a few years ago where our heroes deliberately sent out misleading messages in the clear in order to lure the cylons into a trap. So their wireless is just plain old analog radio. Nothing computery there.

But what about dradis? I suggested that it, too, was a purely analog system, just like radar was as recently as ten or fifteen years ago. A radio signal goes out, gets reflected back, various analog components — think vacuum tubes and stuff — measure the strength and frequency of the signal to draw a picture of the space around the ship. Easy.

My friend wasn’t so sure. This is space we’re talking about, after all. The distances are kinda crazy. Ships can be so far apart — halfway across a solar system from each other — that radio would be useless for determining direction and range. Even at the speed of light, the signals would take too long to propagate.

That seemed reasonable to me. But it raised a question. In order to make a reasonable guess as to whether dradis could be radar-with-a-different-name, I said, we needed to have some concept of the scale on which the story operates. Are these spaceships miles apart? Thousands of miles? Millions of miles?

We went looking for clues.

Friends, if you thought everything up to now has been nerdy, you’d better go get yourself a nice cup of tea or something, ‘cause we’re just now getting warmed up.

In the show’s pilot episode, a three-hour made-for-TV movie that aired back in 2003, we’re given a few pieces of information. First, we’re told that Galactica is being decommissioned and turned into a museum, kind of like the World War II aircraft carrier Intrepid. This tells us that Galactica has basically been parked somewhere. Second, we’re told that Galactica is a five-hour flight by the science-fiction equivalent of a commercial jetliner from our heroes home planet of Caprica. That’s an important piece of information, because it lets us sketch out a sort of notional sphere, centered on the planet Caprica, where Galactica could possibly be. More on this in a bit.

Later, we’re told that it will take Galactica three days to make the trip from wherever it was parked to a space station in orbit around the planet Ragnar. Ragnar is described as being a big, cold, inhospitable gas giant planet. Think Neptune.

All right. That’s all the information we need to start making some back-of-the-napkin guesses as to just how fast Galactica is capable of moving, and by extrapolation, make more guesses about how far away ships are from each other on this show.

It takes about three days to make what’s called a minimum-energy trip from Earth’s orbit to the Moon. But that’s, as it says right on the tin, a minimum-energy trip. It’s the equivalent of pulling your car out of your garage and idling in first gear all the way to San Francisco. It’s possible, sure, but wow, does it ever take a long time.

How do you make the trip go by faster? You step on the gas.

We have to assume that the characters on the TV show in question aren’t making any minimum-energy trips. Actually, that’s a lie; in the pilot episode, two characters do in fact inject their spaceship into a minimum-energy transfer orbit to get back home, but that little scientific detail is neither elaborated on nor particularly important to the story. But the story does provide us with evidence that, in that setting, getting from place to place by coasting is unusual. That’s not normally how they do things.

So if it takes five hours to get from Caprica to wherever Galactica’s parked, how far could that plausibly be?

My first instinct when my friend and I discussed this was to say lunar orbit. It’s not clear that Caprica even has a moon in this story — although a Phobos-scale body near Galactica is visible during an early special effects shot in the pilot episode — but let’s say they parked it around a quarter of a million miles above the planet. High enough to be in a long-term stable orbit, close enough to be convenient for school trips.

My friend raised an objection. From lunar orbit, the Earth is highly visible. It’s huge and bright, dominating the sky. But in no exterior shot of the parked Galactica do we see Caprica hanging there. Sure, maybe all those shots were composed with Caprica behind the cameraman, okay, fine. But remember, the central plot point of the pilot episode is the massive nuclear bombardment of their home planet. From lunar-orbit range, the people aboard Galactica would have been able to crack a window — if they had any windows — and see the detonations back home. But nobody ever talks about this. So from a storytelling point of view, it’s unlikely Galactica was in lunar orbit around Caprica.

Okay, if not there, then where? Assume the “Battlestar Galactica” equivalent of a commercial jetliner would smoke a 747 in a race. Assume it can go fast, like on the order of solar escape velocity. Where could that kind of a plane go in five hours?

How about the L4 and L5 points in Caprica’s orbit?

This is gonna get a little obtuse, so bear with me. If you set a small object orbiting a much larger object, there are a handful of points of gravitational stability, places where you could put an object and have it stay there all by itself. One is along the line between the two orbiting bodies, where the gravitational attraction between them is balanced. Think of that point as being on top of a hill between two valleys; you don’t go anywhere, because the forces are balanced.

There’s a point like that, called a Lagrangian or libration point, sixty degrees ahead of the smaller body in its orbit. That’s called the L4 point. Another point, the L5 point, is sixty degrees behind the smaller body. If you put an object at either of those points with no proper motion relative to the rotating system, that object will stay there. These are points of gravitational stability.

Sometimes the L4 and L5 points of a two-body system are called the Trojan points. See, a long time ago some guys looked up in the sky and discovered that there are two bunches of asteroids all clumped together that are moving in funny ways. These astronomers named the asteroids in one group after ancient Greek soldiers, and named the asteroids in the other group after Trojan soldiers, the idea being that each clump represents one of those ancient armies. Collectively, those asteroids are now called the Trojan asteroids. What the astronomers eventually discovered is that these asteroids are all clumped together and moving oddly because they’re not actually orbiting the sun at all. Instead, they’re orbiting two invisible points along the orbit of Jupiter, the L4 and L5 points. Those points in space are so gravitationally stable that they just naturally attract stuff, like corners attract dust bunnies.

If you want to hang something up in space in such a way that you won’t have to worry about it for a long, long time, the L4 and L5 points are darned fine places to put it. So why wouldn’t our heroes park Galactica at one of those two libration points along Caprica’s orbit? Close enough to home, gravitationally stable, yet far enough away so as not to interfere with existing shipping lanes or whatnot. Brilliant.

So let’s say, for sake of argument, that Galactica is at Caprica’s L4 point, orbiting our heroes’ sun sixty degrees ahead of their home planet. It takes five hours to get there on their version of a 747. How fast is that, really?

Take the distance from the Earth to the sun. Don’t worry about how many miles it is; just imagine it in your head like a really long yardstick. That distance is called one astronomical unit, or AU. It’s about 90 million miles. Because Caprica is described in the show as a very Earth-like planet, let’s assume that Caprica also orbits its sun at a distance of about 90 million miles, or one AU. It doesn’t have to, but there’s no reason given in the story why it couldn’t be.

The L4 point, where Galactica is, is also exactly one AU from Caprica, as the crow flies. So our heroes have to be able to traverse one AU in five hours. If you do the math, that comes out to about eighteen and a half million miles per hour, or about three percent of the speed of light.

Fast? You bet your ass it is. But not unreasonably so. That’s only about a hundred times faster than the fastest thing human beings have ever built, a space probe called Helios. Given that science fiction all too often describes ships crossing trillions of miles in hours, or even minutes, this is refreshingly plausible.

But that’s just our heroes’ version of a jetliner. Surely a warship would be able to do better than that, right? Maybe Galactica can go much faster than that.

Well, we have everything we need now to figure out just how fast Galactica can go. Remember, it can make the trip from the Caprica L4 point to the orbit of Ragnar in three days. That’s gotta be a hard minimum, since they’re in the middle of an all-out shooting war; if they could go faster, I’m sure they would go faster.

So how far is it to Ragnar?

Well, remember that Ragnar is described as being a gassy planet way out at the edge of our heroes’ solar system. Like Neptune, I said. Okay, let’s say it is Neptune. That should at least give us some numbers to start with. Neptune — i.e., Ragnar — orbits the sun at a distance of about 30 AUs. Sometimes a little less, sometimes a little more, but it averages out to about 30 AUs. If Ragnar is all the way over on the other side of the solar system from Galactica at the time our story takes place, then Galactica is 31 AUs away; if it’s on this side, then Galactica is 29 AUs away. Again, it averages out to 30 AUs.

And our heroes said they can make the trip in three days. That ten AUs — roughly 900 million miles — in a day, or thirty-nine million miles an hour. That’s really fast, but wait. That’s only about twice as fast as our jetliner goes. That’s not unreasonable at all for a ship of war!

So now we have decent back-of-the-envelope figures of Galactica’s top speed, plus a pretty decent picture of our heroes’ solar system to boot. And it’s all consistent, and while none of it is strictly realistic, it’s all plausible. Plausible enough to tell a story, anyway.

But wait.

Wait just a second.

Thirty-nine million miles an hour? From the Earth to Neptune in three days? That’s insane! Not because the speed itself is all that high, but because the acceleration must be ridiculous!

Everybody knows what acceleration is. If you’re not moving and you want to be moving, you have to start moving. And if you want to be moving fast, you have to start out slowly and get faster and faster until you reach your target speed.

Say you needed to win a drag race. A very specific kind of drag race. It’s exactly 300 feet, and you can’t just cross the finish line. You have to stop at the finish line. Like right on it. It’s quirky as hell, but the hot chick who came up with the rules says she’ll go home with the winner, so you decide to play along.

Furthermore, assume just for sake of argument that your car is specially tuned so that it can go from zero to sixty and from sixty to zero in exactly the same time. In other words, slamming on the brakes stops your car at exactly the same rate that stomping on the gas accelerates it.

How do you win the race? Well, it’s obvious. You stomp on the gas and accelerate until you’re halfway to the finish, then you slam on the brakes. Because you slow down exactly as fast as you speed up, you’ll screech to a stop with your front tires kissing the finish line. Hot chick, here we come.

That’s how you get from point A to point B in space in the minimum time. You stomp on the gas until you’re halfway there, then you turn around and stomp on the gas again until you stop. If you did your math right, where you’ll be is where you intended to be.

Remember, Galactica is a ship of war, and those evil cylons just bombed the holy hell out of our heroes’ home planet. They’re not gonna take the scenic route to get to Ragnar. They’re gonna get there in the absolute minimum time. That means accelerating to a truly hellish speed, then turning ass-first and running the engines to the red line until they coast to a stop. Their speed will average thirty-nine million miles an hour, but they’ll either be speeding up or slowing down the whole way.

Just how fast will Galactica have to accelerate?

Acceleration is measured in g’s, where one g is the force of gravity you’re feeling right now. If you were in outer space, floating around weightless, and your rocket began to accelerate at one g, you’d be pulled down into your seat with exactly the same force you’re current feeling. Two g’s means you’d be pulled down twice as hard. And so on.

I did the math on this. In order to make that trip to Ragnar in three days, Galactica has to accelerate constantly at twenty-seven g’s.

The math is boring, and not even that complicated. The formula for the distance traversed by an object under constant acceleration for a given time is ½at² where a is the constant acceleration and t is the duration of your trip. Rearranging the terms, we get a = 2s/t², where s is the distance traveled. In other words, if you know how far you have to go and how long you have to get there, you can figure out the acceleration you’ll experience.

I plugged in all those numbers from before — twice — and got twenty-seven g’s.

For comparison’s sake, human beings black out when subjected to sustained acceleration of between five and ten g’s, and anything from 20 to 40 g’s is be fatal. If you want a more visceral analogy, imagine sitting in your chair right now, just as you are … with twenty-six identical twins sitting on top of you. Cause that’s what it would feel like.

But wait. We’re not done yet. If we know how fast Galactica can accelerate, then if we knew the ship’s mass, we could estimate how much thrust the engines have to put out.

Of course, estimating the mass of a totally imaginary thing is no easy task. Everything up to this point has been pretty reasonable, numbers extracted from real-world analogues of fictional things like planets. But when it comes to guessing the mass of this spaceship, we have no choice but to make a totally wild-assed guess.

Well, not totally wild-assed. See, we have at least a scale reference. See, Galactica is built like an aircraft carrier, and like an aircraft carrier it has runways for recovering returning fighters. Real aircraft carriers have only one runway, but Galactica has two, one along either side of the main hull. Visually, these runways look to be oh-more-or-less-something-like as long as the flight deck of a Nimitz-class aircraft carrier. Overall, these runways comprise about half the length of Galactica, making the whole ship about twice as long, stem to stern, as a Nimitz-class carrier.

Having absolutely nothing else to go on, I decided to give the Galactica a mass ten times larger than a Nimitz-class carrier. I know, I know, that’s probably absurdly low. Galactica is a heavily armored ship, capable of withstanding a nuclear explosion right up against her hull with significant but hardly crippling damage. There’s gotta be a lot of mass there to absorb the radiative energy of an explosion like that. But we’ve got to start somewhere, and ten times the mass of an aircraft carrier sounded like a decent beginning.

A Nimitz-class carrier, fully loaded, has a displacement of about 100,000 tons. Displacement is a fancy way of saying that’s how much the ship weighs. If you had a scale big enough to hold an aircraft carrier, that scale would tip at about 100,000 tons.

So Galactica, being ten times more massive, weighs about a million tons. That’s convenient, because round numbers make math simpler.

The force — i.e., thrust — you have to apply to accelerate an object is equal to the mass of that object multiplied by how much acceleration you want. I multiplied the entirely made-up mass of a million tons by the derived acceleration of 27 g’s … and then I erased everything and started over. Because the answer I got couldn’t possibly be right.

I did the calculation three times. In order for a ship with that mass to accelerate at that speed, it would need to put out fifty-four billion pounds of thrust.

Want a comparison? That’s nearly eight thousand Saturn V rockets.

As I said to my friend, “They need magic engines.”

But come on. Let’s put this in perspective. Say “TV show about a spaceship” to most people and they’ll think “Star Trek.” A whole book has been written about science and “Star Trek”, but as much as the author tried to wave his arms, he couldn’t escape the inevitable conclusion: It’s ridiculous. When judged on the scale of simple physical plausibility, “Star Trek” is ridiculous. For that matter practically all stories about spaceships and traveling between planets are ridiculous. The distances between things in the solar system are just mind-defying — there’s a reason they call it outer space, after all. And traveling between stars is even worse. And between galaxies? Just forget it, okay? Never gonna happen, ever.

But generally speaking, we don’t care. The people who like stories about spaceships and planets are happy to overlook those kinds of implausibilities, and the people who don’t like them aren’t tuning out because the writers got their math wrong. When you’re telling a story, little things like the laws of physics give way to the tale you’re trying to tell. That’s what separates stories from real life.

The interesting and, in my opinion, captivating thing about “Battlestar Galactica” is the fact that the writers consciously chose to hew closely to not scientific fact but back-of-the-envelope scientific plausibility because it lets them tell more interesting stories. It’s hard to tell an interesting story when your characters are galavanting about the cosmos more easily than you drive to the grocery store. By seasoning their plots with just a bit of the reality about how vast, empty and inhospitable their setting is, the “Battlestar Galactica” guys are able to tell more complex, interesting stories without having to resort to tired plot clichés like space aliens and inscrutable beings with god-like powers.

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Wow. That was even nerdier than I thought it would be when I started.

Let’s not tell anyone about this, okay? Let’s just keep this between us.

D’oh

Too late. Tom, the friend I was talking about all through this mess, already spilled the beans. In fact, he saved the whole log of our chat about it and posted it as a PDF, just in case you’re into raw materials.

More

Okay, so I’ve gotta do a little update to this post. This whole thing has been pretty personally embarrassing to me — I don’t normally like my geekier tendencies to be exposed quite so publicly — but it seems incomplete somehow not to tell the whole story.

After I wrote this post Friday night, Tom and I talked a bit more about this stuff. We’d run through the basic storytelling facts of the pilot episode, and how they added up to a fairly plausible and amazingly consistent picture of just how grounded in reality “Battlestar Galactica” is.

But the one thing we’d never settled is just what scale these stories operate on. Sure, we see the big wide shots of the rag-tag fleet drifting through space, and for cinematic purposes a whole lot of ships are crammed into a really small space. That’s just practical; if the fleet were arranged in anything like a realistic fashion, we’d either see just one ship in the middle on a big field of black with little specks of light behind it representing other ships tens of miles away.

But when the cylons appear out of nowhere — the faster-than-light propulsion system is a storytelling conceit — and threaten our heroes, just how far away are they? Do our heroes detect them a million miles out?

We can make an educated guess about this by going back and viewing the episode “Pegasus.” In this episode, the fleet picks up a dradis contact at extreme range and sends the alert patrol out to see what’s up, meanwhile scrambling to prepare for a hasty escape. The twist, of course, is that it’s not the cylons at all, but rather another battlestar that had managed to survive the holocaust.

The pre-credits sequence of that episode is edited more or less in real time. And from watching, we can see that it takes about two minutes for the alert vipers to depart Galactica airspace and do a flyby of Pegasus.

So how far could a viper go in two minutes? Remember, these pilots are on an intercept mission in a time of war; if they were flying F-16s, they’d have the throttles firewalled to full afterburner. They’re going as fast as they can possibly go. How fast is that?

In space, speed is less of a relevant factor than acceleration. There are pilots aboard these things, and that puts a hard limit on how fast the vipers can accelerate. As we discussed, a pilot will black out at between five and ten g’s of vertical acceleration; that is, acceleration that’s parallel to the spine. But pilots in vipers are seated, just like pilots in airplanes. So acceleration along the velocity vector would be perpendicular to the pilots’ spines, not parallel to it. The human body is tolerant of a lot more perpendicular acceleration than parallel acceleration. NASA says even untrained pilots, without the benefits of pressure suits, can handle as much as about 15 g’s of perpendicular acceleration without losing consciousness.

But how much acceleration the body can stand isn’t the only factor. These pilots also have to be able to stay in control of their planes. At 15 g’s, you’d have absolutely no chance whatsoever of manipulating a joystick or pushing down on a rudder pedal. Realistically, under any acceleration a lot heavier than about 2 g’s, it’s hard to imagine our pilots continuing to function.

So okay. Let’s use that as our guideline. How far would a viper go if you pushed the throttle to the firewall and took off in a straight line at 2 g’s for two minutes?

The answer is about 90 miles. To be specific, 87.6 miles. Which means when Galatica detected her, Pegasus was about 90 miles away, not counting whatever distance she might have traversed in the time it took the alert vipers to intercept her.

Is this consistent with the story as told on screen? Well, when Pegasus appeared on Galactica’s scopes, she was beyond visual range; no, Galactica doesn’t have windows, but it certainly does have optical telescopes for navigation and such, and those telescopes weren’t helpful in identifying the other ship. Second, Pegasus was inside dradis range, and we’re operating on the assumption that dradis is nothing more than old-fashioned analog radar. A contact the size of a battlestar at 90 miles would produce a most adequate radar return, thank you very much. So yeah. Putting Pegasus 90 miles from Galactica is entirely consistent with what we’ve seen on screen.

Except for one microscopic, almost irrelevant detail. During the episode, there’s a tight close-up on one of the dradis displays. The space around Galactica is delineated by range circles, and those range circles are numbered. The blip for Pegasus is more or less halfway between the circle labeled “70” and the one labeled “80.” Around 76 or so.

Okay, so our heroes don’t measure things in miles. Just like they use a different name for radar, they have their own units of measurement. Heck, all of us live on one tiny planet, and we can’t all agree on one set of units of measurement. Expecting people from a distant world to use statute miles is pretty ridiculous.

Except … I had a little brainstorm. The writers of “Battlestar Galactica” make no secret of the fact that what they’re really trying to do is tell a Navy story that happens to be set in outer space. In fact, if you wanted to adapt the “Battlestar Galactica” story to a different setting and put it on an aircraft carrier patrolling the open seas, there’s not a whole heck of a lot of rewriting you’d have to do. You could lift a lot of the scenes, even whole story arcs, unchanged.

So what if … I got out my calculator.

Yup: 87.6 statute miles is about 76 nautical miles. Which is perfectly consistent with what we see on the dradis display.

Does this mean our heroes measure distance in nautical miles? Well, actually it could, without even bending much less breaking credibility.

See, unlike a statute mile, a nautical mile is a unit with a very simple geometrical definition: It’s the length of an arc of the Earth’s surface subtended by one minute of longitude, or ¹⁄₂₁₆₀₀ of the circumference of the Earth.

Why does this matter? Because our heroes could live on an entirely different, but similar, planet and start with an entirely different notion of geometry and still come up with a basic unit of length that’s pretty close to one nautical mile. That’s not at all implausible. And since everything we’ve talked about so far is surrounded by pretty wide error bars, we can say with confidence that vipers accelerate at about 2 g’s, and that our heroes measure distance in units that are about a nautical mile.

Coming back to reality for a second, of course none of this means anything. It’s a television show, for crying out loud. I’m absolutely certain that some guy in the art department said, “Eh, I think I’ll put the dot for Pegasus about halfway between the 70 ring and the 80 ring, that looks pretty good” with absolutely no thought given to what that really means.

I just happen to think that it makes the show more enjoyable when almost everything we see is basically plausible and basically consistent. When something comes along that’s just silly, or that seems to break a previously established precedent, there’s a little “Hey” moment that snaps the viewer out of the show. Like when they replaced Dick Sargent with Dick York — or was it vice-versa? — on the old “Bewitched” show. It left the audience at least momentarily aware that they’re watching television, rather than being captivated by a well-told and emotionally engaging story.

That’s not to say “Battlestar Galactica” doesn’t have pull-you-out-of-the-story moments. Of course it does, some bigger than others. It’s just kind of nice that they don’t manage to squeeze one into every single scene.

• Unsolicited advice to blogger wannabes from a cranky old man
• Why not this? Why not that?
• Thanks to all them watcher-type people, and also the Princeton Public Library for some reason