How long can you tread water?

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The new blockbuster disaster movie Noah looks like it might be harmless, if simple-minded, fun.  I want to see it, if for no other reasons than watching Russell Crowe and Anthony Hopkins ham it up, and to see if Emma Watson, a one-time student at my alma mater, can make it big past Hogwarts.  I had to explain to my kids why I kept on yelling “Voopa-voopa-voopa… DING!” and “You want a hint? How long… can you tread… water? Hah hah hah hah hah,” every time I saw the trailer.  (My wife has ordered them to poke me if I try to do this when we see it.)

Why bring this up here? There’s a teaching point which can be applied to any disaster movie:  How reasonable is it from the standpoint of basic science?  The science fiction writer Isaac Asimov already observed that the rainfall rate would been enough to swamp an aircraft carrier, let alone a smallish ship (by today’s standards).  However, it’s fun to think about.

I want to talk about an aspect of such a disaster which Asimov didn’t cover:  where’d the water come from?  And how much energy is involved in putting it where it needs to go?  We can make some simple estimates using energy methods.

Maybe the water came from the oceans.  According to NOAA (no relation) the average depth of the ocean is about 14,000 feet (roughly 4,000 meters.)  Since there is three times as much ocean area as land, we can imagine (somehow) emptying the oceans to cover the land to a depth of three times as much, or some 50,000 feet – more than enough to do the job.  It would take a heck of a lot of energy to do this, however.  This is a very large volume of water: under some reasonable assumptions it’s something like a million trillion cubic meters.  The mass of that much water is a billion trillion kilograms, or a million trillion tons.

Let’s say we evaporate the oceans so that it rises into the sky and falls as rain onto the land.  This doesn’t happen under ordinary circumstances – the Earth  isn’t hot enough to make this happen.    The energy needed to evaporate all of the oceans is about the same as the amount of energy which would be used by our world civilization in 9 million years.  Another way to put this: it rained for forty days and forty nights.  Therefore, the total rate at which this energy would need to be put into Earth’s climate system is some one billion trillion watts – about seven thousand times the total power which the Earth gets from the sun!  A power input that large would destroy all life on Earth by boiling everything alive.

If the water came from elsewhere, say a rain of comets, which are largely water, the problem gets worse.  The comet impact speed would be about the same as the speed of Earth in its orbit around the sun (30 kilometers per second, or 67,000 mph.)  It’s a hefty speed.  The speed is so high because the comets would be traveling around the sun in about the same way in which the Earth does. It could be somewhat higher or lower depending on exactly how the collision happens.  The total impact energy is given by (1/2) x (the mass) x (impact speed ) x (impact speed), or about seven hundred thousand trillion trillion joules. (Yes, I wrote that right – trillion trillion.) The comet or asteroid which struck Earth 65 million years ago killing the dinosaurs had an impact energy about one million times less than this.  With a series of impacts like this, the flooding would be the least of Noah’s problems.  He’d have to worry about mile-high waves each time one of the comets struck, the fact that Earth’s atmosphere would be more water than air after the impacts, the complete and utter darkness shrouding the land due to kicked up dust…  And how do we get rid of the water afterwards?  You need about the same amount of energy to push it back up into space.

Amazingly enough, real disasters like this have befallen the Earth, luckily before any life existed on it.  The best theory scientists have on how the Moon formed was due to an impact over four billion years ago by an object about the size of Mars.  The impactor had a mass a few hundred times that of all of the oceans on Earth, but the impact would have “only” been ten times more energetic that our hypothetical cometary scenario because the collision was a “slow” one (about 4,000 meters per second, or 8,900 mph).  Luckily, there are no more objects that size in the solar system which could collide with Earth.

Two points: 1) Always start with the energy involved if you’re trying to decide if movie “science” is reasonable;  2)  I’m still looking forward to the movie.  Expect a review if it violates still more basic science.

Thoughts on Project Orion

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I did an interview a few days ago with Michio Kaku on his radio show “Science Fantastic”. It’ll be broadcast sometime this weekend.   It was a strange conversation, at least from my point of view.  I’d never given a long radio interview before and the whole thing seemed rushed and stressful.  Kaku wanted to emphasize the weirder and more outré aspectes of science fiction; fitting, perhaps, from the program title, but most good science fiction rests on a firm basis of known science.

One good thing did come from the program.  Kaku and I were discussing starships.  I, perhaps unwisely, told him that my personal favorite idea for a starship was Project Orion, the truly audacious suggestion that we could propel spacecraft using nuclear bombs as propellants.   Dr. Kaku raised a very good objection to this, which is what I want to write about here. (As an aside, there is a new NASA program to develop a crewed rocket propelled by conventional engines called “Orion” – don’t get the two confused!)

Before I go on with this topic, let’s discuss nuclear rockets in general:  spaceflight enthusiasts have always wanted rocket fuels which have higher energy density than chemical propellants.  This is because it takes a lot of energy to get a rocket moving at the high speeds it needs (25,000 mph or more) to reach destinations like the moon or farther.  Chemical propellants like combinations of liquid hydrogen and oxygen work, but just barely. From the 1950’s through the 1970’s nuclear energy was seen as a viable fuel alternative – the Nobel laureate physicist Richard Feynman may have been the first person to realize this, but a number of science fiction writers including Robert Heinlein also came to this conclusion.

The problem is that harnessing the large amounts of energy, millions of times higher per kilogram than chemical energy, is difficult.  The simplest way to do it is to take a gas (usually hydrogen) and heat it to very high temperatures and pressures using the reactor.  The gas escapes through a nozzle and the spaceship is pushed forward.  However, materials science limits this.  If the temperature gets too high, you start melting the nuclear fuel itself.  This limits the fuel ejection speed to about twice what chemical propellants can do.

Project Orion wanted to get around this by building a big spaceship with a “pusher plate” separating the crew from the engines.  Nuclear bombs would be ejected behind the ship and blown up.  The resulting explosion propelled the ship forward.  It seems daft, but a team led by two very good scientists, Ted Taylor and Freeman Dyson, worked out many of the practical details.  The effective fuel ejection speeds which you could get were five or six times, maybe even more, than you could get from conventional chemical fuels.  It also seems that you could keep the crew safe from radiation, and keep the explosions from destroying the ship.

You can’t build a spacecraft based on this principle today.  Trying to make it work would probably violate the 1963 treaty banning above-ground nuclear testing.  Dr. Kaku made the very good point that Ted Taylor himself stopped working on bomb design because the small hydrogen bombs which the ship would use would make very good terrorist weapons.  This caused me to stop and think things over.

I’m of two minds about Orion.  On the one hand, I am very worried about the prospects of nuclear terrorism.  I grew up in the DC suburbs, and was terrified as a teenager by the prospect of nuclear war with the Soviet Union.  Today isn’t much less scary, as smaller nations have gotten the bomb, and mounting pressures due to the world economy and the environment seem to make war and terrorist acts more and more likely.  Developing small nuclear weapons seems foolish in this light.

On the other hand, the Orion idea is the only feasible method using current technology to move a payload at very high speeds – perhaps at speeds of up to a few percent of the speed of light.  People have discussed other methods of powering starships, for example fusion reactors and matter-antimatter annihilation. (Yes, people have studied this seriously – it’s not just from Star Trek!)  However, neither could be done now: antimatter has an equivalent cost of  several trillion dollars a pound, and can only be produced in microscopic quantities today.  No one knows how to make a fusion reactor on Earth, let alone put one in a spacecraft, although recent developments may be promising.

If humanity wanted to send a space probe to the Alpha Centauri system, four light years away, the only conceivable means to do it using today’s technology would be something like Orion.  It wouldn’t be easy or cheap, and it wouldn’t happen any time soon.  It might not be possible, but this method would be the one with the best chance of success.  It would also take decades for the spacecraft to reach the system; any government funding a project like this would need to be farsighted in a way which most aren’t today.  Whether it would be worth doing is something which our society, or perhaps our society fifty years from now, would have to decide for itself.

The issue here is that any propulsion system for any spacecraft is a weapon in disguise.  Conventional rockets are made from highly explosive materials, as we saw in the Challenger disaster.  The higher the energy density, the worse it gets: in the extreme case, if you somehow could make a rocket propelled by antimatter, simply turning the engine on too close to Earth could sterilize it!   You can’t deweaponize a starship.

The best science fiction investigates the problems created or issues raised by new discoveries or new technologies.  I’ve never read a story or seen a movie or TV show which really looks at the societal problems which would be caused by the development of the Orion concept into a truly workable spacecraft.  Perhaps it’s time to write one.

PS  If you like what I write, or even don’t, please leave a comment!

For the budding SF writer, part 2: Local color

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Now that we’ve fixed where the planet is going to be, we need to think about what life is like on the planet – quite literally.  There are milions of details to consider – let’s just pick one to start out with.  Let’s think about the star and how that’s going to affect what you see when you look around.

Everything starts with the star.  Luckily for the writer, stars are all pretty simple in some respects.   The star’s luminosity determines its color, which will determine how things look on the planet — at least, to any human visitors to it.  Remember, if we have an Earth-like planet at some distance D from the star, how bright the star is relative to our sun (L) will be about D*D, although there will be some adjustments for atmospheric composition and albedo (see my previous post.)

Here’s a table summarizing the information  on stellar coloration as a function of luminosity:  this is only data for what are called “main sequence” stars, that is essentially middle-aged stars which “burn” hydrogen into helium in their cores.  If you want to use a star in its old age, or a newly forming protostar in a story, you have to dig a little deeper.

L Color
.01 Red
.1 Orange
1 Yellow
10 White
100 Blue-white
1,000 and higher Blue

As stars get increasingly dim, a larger fraction of their light will be in the infrared spectrum, that is in long wavelengths which we can’t see.  As they become increasingly bright, more of their light will be in the ultraviolet – still invisible to they eye, but at shorter wavelengths than we can see.  (This can also lead to obvious complications for humans visiting such planets.)

There’s a lot of room for play when you start thinking about the color of different things on the planet.  Let’s start with the sky.  Earth’s sky is blue because light from the sun is scattered by air molecules.  They scatter short wavelengths (that is, bluer light) more readily than longer wavelengths (i.e., red light), which is what gives the sky its characteristic blue tint.  When you look at the sky, you’re seeing light which has been scattered.Because of this, the coloration of various features of sky light should more or less mimic the properties of the star: skies on planets with reddish stars should be blue, but less blue than our own sky – maybe greenish blue or green?  Detailed computer simulations could show if this were true.   Particles in the atmosphere due to smog, pollen or volcanic eruptions will change the sky color; for example, fire from smoke or volcano can make the sun or moon appear green or blue when seen through it (hence the phrase, “once in a blue moon”, which doesn’t mean the second full moon in a month.)  Atmospheric refraction warps the appearance of the rising sun and moon: thicker atmospheres will warp them more, thinner ones less.  It’s again something to have fun with when thinking of story details.  The green flash is due to atmospheric refraction and layering of the atmosphere when the sun sets over a flat landscape like the ocean: an ocean planet with the right atmosphere could have an extended green flash every night…Now that we’ve gotten the sky colors, let’s go on to the landscape, and think about what plant life and ground cover will look like, in the next post on this subject.

For the budding SF writer, part 1: Where to put your planet

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Note: What I write here was covered in Poul Anderson’s 1960-something essay, “How to build a planet”, plus other sources.  However, it’s worth restating.

This is the first in a series of posts for non-scientists who want to use science in their science fiction stories effectively.  I’m going to start with a venerable one, how to design a planet suitable for Earth-like life.  There’s a simple rule which makes it very easy to begin, although you have to tweak it (nothing’s ever too simple.)  Imagine you have a planet circling a star.  Let’s say that the star is L times as bright as our sun, and the planet is D times as far away from the star on average as Earth is from our sun. For example, since Mars is about 140 million miles on average from the sun, and Earth is about 93 million, D for Mars is about 1.5.  (I’m rounding)  In order for the planet to be roughly the same temperature as the Earth (which is to say, suitable for Earth-like life) there is a relation between D and L:  L should be approximately equal to D*D (that is, D-squared.)  That is, if D=1, L=1*1=1.  If D=2, L=2*2=4; if D=1/3, L=(1/3)*(1/3) = 1/9.

People usually start the other way, by picking a star and then calculating the distance, but doing it this way makes the math something you can do in your head.  The reason for this rule is that the light from the star (the main source of energy warming the planet) spreads out in all directions, and decreases as the square of the distance from the star.  If you have two planets in orbit around the same star, and one is twice as far from the star as the other, then the illumination of the second is 2*2=4 times less than the illumination that the first one gets.  By using the rule that L=D*D, we compensate for that.

This is a good place to start when you’re thinking about where to put your planet, but a bad place to stop.  There are many caveats to the simple rule.  First of all, it assumes that the orbit is roughly circular – the orbits of many planets aren’t.  Secondly, it ignores planetary albedo, the average amount of light which the planet reflects back into space.  Earth’s averge albedo is about 30%, meaning that it absorbs about 70% of the light from the sun.  Planets with higher albedos need to be moved closer to compensate.

Finally, it ignores the effect of the atmosphere.  Earth’s atmosphere traps heat due to a mild greenhouse effect due to a number of gases in the atmosphere; it warms up the planet by about 30 degrees Celsius on average.  Venus has a runaway greenhouse effect because its atmosphere is 95% carbon dioxide; its surface temperature is about 450 degrees Celsius, far, far warmer than it would be if position is all we needed to worry about.  Take the advice given to any starting writer: pay attention to your story’s atmosphere!

In the second post in this series we’ll discuss how L determines the type of star which the planet circles.

Why “Star Trek: Into Darkness” Isn’t Good Science Fiction, part 1

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The hallmark of good science fiction isn’t necessarily good science.  If it were completely scientifically accurate, it wouldn’t be science fiction; it would be a NOVA special.  I would claim that the hallmark of good science fiction is self-consistency.  You break the laws of Physics? OK, but you still need to play fair with your readers or your watchers.  That is, if you hypothesize some grand new technology or scientific breakthrough, don’t ignore the implications when it’s inconvenient…

By this criterion, the second of the Star Trek reboot movies, Star Trek: Into Darkness, fails utterly.  Here are only a few of the problems; I’m not even going to discuss issues involving acting and the plot. Be aware that BIG spoilers follow.

The transwarp, part 1:  In an early scene, Sherlock Hol… I mean, Smau… I mean, Khan/John Harrison, “transwarps” from Earth to the main planet of the Klingon Empire.  The transwarp was Scotty’s invention from the first movie, a combination (somehow) of the transporter with the Warp Drive.  Well, stars are many light years, meaning at least trillions of miles apart.  Even if the Klingon empire is located in the next-nearest star system, it’s a distance of about 65 trillion miles.  He has to transwarp there with an accuracy of a few feet in order to avoid falling off the big cliff he appears on top of.  This is an accuracy of about 1 part in 50 quadrillion (a quadrillion is a thousand trillion.)  To put this into context, if we knew the Earth’s diameter to that accuracy, we would know it to the size of one atom…

The transwarp drive, part 2:  OK, let’s assume we have this phenomenal accuracy.  A large part of the plot is the Federation’s anxiety over going to war with the Klingons. If you have the transwarp and the Klingons don’t, why worry?  Just transwarp an antimatter bomb on them if they make too much trouble.  (If they have transwarp as well, then everyone is in trouble…)  More things suggest themselves: with transwarp, why have starships?  Transwarp is faster, really accurate, and portable.  Maybe it’s not cheap, but starships aren’t either.  (My book estimates antimatter production costs starting at billions of dollars…)

These are only a few of the problems with the movie – stay tuned for more!