Physics Today, the Flash and project Rosetta

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A random conflation of three separate items for this post:

Physics Today’s Facebook page just added a link to a Q&A session they did with me about my book.  The reviewed it in the last issue of the journal, and it got a very nice review from Edward Belbruno, a physicist I respect quite a lot.

The Flash can run on water!  At least, so says the episode last night.  According to his lab rat friends, he needs to run at 650 mph to do this – is this accurate?  I think the answer’s lower: more like 60-100 mph.  Still an impossibility, but not so impossible an impossible.  The issue is momentum transfer: every step he takes across the water transfers some fraction of his momentum to the water.  The rate of momentum transfer is the force he applies; Newton’s third law says that an equal force is pushing up on him.  A quick estimate says that the speed is about the square root of (g (the acceleration of gravity) times the stride length (maybe 2 meters?) times a fudge factor (which should be somewhere between 10 and 100, in lieu of difficult detailed models)).  Putting all this together, the needed speed is about 50 meters per second, or about 100 mph, maybe even lower.  Running up the side of a building is a different matter: if he tries to run up fast, he’ll just bounce off because of his high speed of approach.  Better he should run up a long ramp and launch himself into the air, except that landing after doing that is a problem…

Of course, the big news today is Philae, the lander for project Rosetta, landing on comet 67P/Churyumov-Gerasimenko.  It may have bounced once after harpoons failed to anchor it to the surface, which worried the scientists, for good cause. The escape velocity of a body like it depends on two things: its density and its mean radius.  Because it’s small and light (most comets are loosely-held conglomerations of dust and ice), the escape speed is going to be very low.  It’s about 4 km across, roughly 1,000 times smaller than Earth; if its density is 1/10 that of Earth, the escape speed will be about 3,000 times less than Earth’s (escape speed goes as size times square root of density.)  This might lower the escape speed to meters per second, making it very possible for it to drift away on a bad bounce.

xkcd, as usual, has an excellent comic covering the landing.

The first images look amazing.

Physics in a Flash

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I saw the first episode of the new CW show “The Flash” last night. Like most shows on the network, it was mindless fun. It has the CW stamp of lightweight actors, cardboard characters, bubblegum philosophy and idiotic science, but it was still enjoyable. The show, of course, centers around the eponymous superhero who can move at speeds impossible for the mundane human, and how he uses this new power to right wrongs and fight evil. It’s very formulaic; one could guess within the first few minutes who fit where into the grand scheme of things: who’s evil, who’s good, who the love interest is, who will eventually betray whom, and so on. But beyond the surface entertainment, the “science” of the show provides even more fun.

I’m a physicist, and like to think about physics in this world and in the magical world of TV land. The Flash provides a good venue for some entertaining ideas: first of all, how fast does the Flash move? It’s a bit hard to tell just by watching the show, but the writers/directors provided an indirect clue when they showed him moving against a graphic of city streets as seen from above. He seemed to move about 10 blocks in about a second. In New York, 10 city blocks is 1 mile, so 1 mile per second seems a pretty reasonable guess; in metric terms, about 1,600 meters per second. This is about 1,000 times faster than the average walking speed of an adult mundane. Hmmm… Well, if he’s going from 0 to 1600 in about a tenth of a second flat, he’s got an acceleration of nearly 1600 g’s! (I’m using the fact that acceleration is change in velocity over change in time, and that 1 g is about 10 meters per second per second in metric units.) He’s got to be made of stern stuff, as even experienced jet pilots will black out at 9 g’s, and get pretty dead if they’re exposed to accelerations of better than 20 g’s for any length of time. Another way to put it is that this acceleration is something like falling from the stratosphere and hitting the ground suddenly. Oww…

This leads to some other things: if he suddenly sped up and launched himself off of a ramp into the air, he could go a distance of about 160 mile before hitting the ground again! (I’m ignoring air resistance here, and the curvature of the Earth, and Coriolis force, and a bunch of other things as well. However, the show itself is hardly realistic, so neener, neener.) What if we don’t ignore air resistance? The force due to drag of the air as he runs around is something like 800 times his own weight; think about lying on a matress with 800 people sitting on top of you. This is what he feels whenever he runs around! The power which it takes to get him to run around like this is something like 10 million times the average metabolic rate of a normal human being, or the total power used in all of the daily activities by all of the residents of a large town!

The moral: thinking about Physics makes shows like this much more fun.

A quick note:  One thing which I had forgotten (shame on me!) is that if my estimate is correct, he’s running at several times the speed of sound.  My estimates for the forces acting on him are low.  I was assuming that he wasn’t compressing the air ahead of him to any significant extent.  Running this fast,  he’s going to generate a shock wave because the compression of the air in front of him can’t get out of the way fast enough.  Someone watching him as he runs by will see him first, then hear the noise of his passage, as he is outrunning the sound waves he generates…  It’s like watching a supersonic jet pass overhead.

Bright the Hawk’s Flight

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This Saturday was a beautiful day where I live, so I decided to take a walk down to the end of our street. It was about 75 F outside, and there wasn’t a cloud in the sky. There’s a big osprey nest on one of the docks near our house, and as I was walking the female took wing; I had my camera, and was able to snap a shot of the bird as she flew across the sky.Osprey

The picture reminded me of the lines from one of my favorite fantasy novels, A Wizard of Earthsea. For my readers who haven’t read this book, read it! It’s the first book in a trilogy: it centers around a young wizard, Ged, who goes to a magic school and… If it sounds familiar, remember it was written twenty-four years before the first Harry Potter novel. It’s better than the Potter series in a number of ways; for someone like me, the fact that Ursula Le Guin created consistent rules of magic and stuck to them in the series enhances the enjoyment tremendously.

The lines are from the “Creation of Ea”, which is the creation story among the inhabitants of the Archipelago, the loosely-bound confederation of islands in which the stories are mainly set. These lines begin the epic:

“Only in silence the word,

Only in dark the light,

Only in dying life;

Bright the hawk’s flight

On the empty sky”

They frame the book, and indeed the series, as they are a succinct expression of the philosophy of the Equilibrium which pervades the books. One problem, though: look at the picture. The flight of the hawk is dark across the empty sky!

Why is it dark? The osprey has brown wings with some gray and white feathers, and a white breast. If anything, one would expect it to be light when seen from below. However, this isn’t how our eyes work. Vision is complicated – it’s not just the optics of the eye. Yes, the eye focuses images from the outside world onto the retina, and the retinal cells sense the light and transmit the information to the brain, but how the information is transmitted is very complicated. The cells don’t simply send the “pixel levels”, so to speak, to the brain directly. There’s a lot of processing, much of it taking place in the nerves in the eye. They are all linked together in a complex manner.

The optical system of the brain is hooked together in such as way as to enhance contrasts. Dark areas appear darker when adjacent to lighter ones. This takes place at a very low level: each ganglion which transmits light level information to the brain is hooked up to the ganglia surrounding it in such a way that if the cells around it are illuminated, its own response decreases, but the reverse is true if the cells around it are dark. The net effect is that our eyes enhance contrasts. The wonderful book “Seeing the Light” explains this in more detail, plus much more on how the visual system works.  (It’s interesting that photographic film enhances contrast as well because of how film is developed.  Digital cameras are built so that their images are usually processed to imitate film and the eye.)

This is why the osprey looks dark. Even though the osprey is mostly light colored, the brightness of the skylight around it makes it appear dark by contrast, not on an absolute scale. This makes me wonder about the creators of the epic. The epic itself is about contrasts: light against dark, silence against the word, life against death. However, the brightness contrast against the sky makes the hawk’s flight dark in a quite literal sense.

Le Guin meant the lines metaphorically, of course, but it is strange that the metaphoric sense is diametrically opposite the literal one.  Epic poetry can often be read on both levels:  Dante’s Divine Comedy, for example, has a number of places where Dante deliberately invokes the cosmology as known in his day, or other scientific tidbits, to explain or complement his theology.  (There is some optics: he discusses with Beatrice the fact that a candle seen in a distant mirror looks smaller but not darker than the original.)  I still enjoy the lines, of course, and find them deeply moving, but if I ever write a book on optics in literature, those are going straight into it.

The science of The Europa Report

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I just watched The Europa Report, a 2013 movie about a crewed space mission to look for life on Europa, the smallest of Jupiter’s Galilean satellites (the four moons of Jupiter found by Galileo in 1610).  The movie was recommended by a friend, who was wondering if the science in the movie was accurate.  This is my attempt to answer her question.  To cut to the chase, I enjoyed the movie a lot, although there were a few problems with the science.  They weren’t big ones, however.  Spoilers follow, so be warned.

The movie is set five minutes into the future, after remote probing of Europa has revealed the possibility of under-surface life on Europa.  It’s been known since the Voyager probes that the moon’s surface is principally water ice at a temperature ranging from 50 Kelvin (-223 C) to about 125 Kelvin (-150 C), at least according to Wikipedia.  This is wayyyy too low for life as we know it, but cracks running through the surface indicate that there might be liquid water underneath the crust, raising the possibility that life might exist there.  The presence of water became more probable when water vapor (probably caused by plumes of water breaking through the crust) were detected in December, 2013.

First, a bit of science:  how can such an icy place have warmth enough for water underneath?  In one word: tides.  Really, tidal friction.  As Europa orbits Jupiter, the massive gravitational attraction which Jupiter exerts on the planet stretches it in the direction of Jupiter, and squeezes it along the other two directions.  This stretching and squeezing leads to heating of the moon as it orbits the planet.  Europa is an icy ball – it’s covered by an “ocean’’ of ice which is probably several hundreds of kilometers thick, and a water ocean underneath that, with a relatively small rocky core.  Therefore, it seems that one of the conditions for life (liquid water) exists on the planet.

This has been a staple of science fiction stories since its discovery in the late 1970’s.  The first novel I know of which featured Europan life was 2010: Odyssey 2 by Arthur C. Clarke, the sequel to the 1966 novel and movie 2001: A Space Odyssey.  In the novel, the mysterious aliens responsible for the Monolith turn Jupiter into a star to allow the Europans to develop beyond their primitive life forms and become a technologically advanced species.  The Europa Report owes a great deal to 2001 and its sequel: it has a very similar look and feel to 2001, and of course it is based on a mission to find life on Europa.  In a conscious homage to the older movie, NASA plays Johann Strauss, Jr.’s “Blue Danube” waltz as the mission is starting, in reference to the space station docking scene from 2001.

The movie is very different from 2001, however, although the sound track is nearly as good (very high praise from me…)  It is a “found footage” movie (although in this case, “sent footage” is more accurate.)  It concerned a crewed mission to Europa, sent there because the  plumes of water and other evidence indicate the possibility of life.  The movie includes Neal deGrasse Tyson discussing how he wants to go ice fishing on Europa (I think it’s real footage), and some pretty accurate discussion of the motivation and science of the expedition.

The first point to make is that the movie science is very good, by Hollywood standards.  It’s one of the most accutate I’ve seen in a while.  I’m going to nitpick about the science, but my readers should keep this overall point in mind.  Let’s start with the space travel:

First off, it takes the spaceship 22 months to reach Jupiter and its moon system.  Why 22 months?  Probably because that’s how long it took the Voyager spacecraft to reach Jupiter from Earth.  I don’t know this for a fact, but my suspicion is that the writers and director just used values from a handy mission which already went there instead of trying to do the rather difficult job of estimating the mission time.

It’s not a crazy estimate.  Jupiter has an average distance of 5.2 AU from the sun (5.2 times the average distance of Earth from the sun).  The spacecraft won’t travel on a straight line from Earth, so it’s hard to say exactly how far the spacecraft will have to travel.  However, if we assume something like 5 AU total distance, the average speed is about 14 kilometers per second (very roughly 30,000 mph).  This isn’t crazy, but there will be difficulties with doing this.

The ship flies by the moon and Mars while en route, so it’s reasonable to assume that the ship was using a gravitational assist speed boost from both bodies.  Again, not a crazy idea, but only very detailed calculations would show if that’s feasible or not.  Unfortunately, the movie never mentioned if that was part of the plan.  One issue which I had with the movie was tha the cast seemed remarkably blasé when passing Mars.  Also, if you’re going to pass it, why not drop off a probe while you’re doing so, or at least spend some mission time getting data?  The crew doesn’t seem to have too much else to do.

One concern of a crewed mission is that of coming home.  For that, you will need fuel to return home at the end of the mission.  To estimate the amount of fuel you need, you have to calculate what are called “Delta v” costs for the rocket – more or less the changes in rocket speed needed to go to Jupiter, maneuver in the system, and return home.  The rocket equation is unforgiving: for chemical fuels, every “delta V” change of about 4 to 5 kilometers per second requires a multiplicative factor of about three in rocket fuel mass to payload mass. (The exact value depends a bit on the type of rocket fuel). Getting the ship away from the gravitational attraction of the Earth and into an orbit headed for the outer solar system is far and away the most difficult problem – it requires a “delta v” change of some 13 kilometers per second, including the effects of air drag.  We can probably assume another six or seven for getting to Jupiter, maneuvering and return, even with any hypothetical gravitational assists from the moon and Mars.  An overall “delta v” budget of about 20 kilometers per second seems right.  20 is 5×4, meanind that the ratio of fuel to payload will be between about 80 and 240 times the payload mass. To put this into perspective, the Voyager spacecraft was launched from a Saturn III rocket; the total mass of the Saturn was about 60,000 kg, while the mass of the Voyager payload is 770 kg (information taken from Wikipedia).  Not all of the Saturn III rocket was fuel, of course; the fuel to payload ratio was probably no better than about 50.  (I can’t find the specific information on this, however, and the fact that the Saturn is a multistage rocket complicates things.)  A Saturn III rocket wouldn’t be big enough– at least, so long as the rocket for the Europa mission is using chemical fuels, which it seemed to be.  The footage used to show the liftoff was clearly of a smaller rocket carrying an uncrewed satellite payload.

It gets worse because a crewed mission is by neccessity much higher mass than an uncrewed one.  There were six crew.  The Apollo 11 Command and Service Module had a total mass of 28,000 kilograms to house half the number of crew for a few days rather than several years (including the return voyage.)  You’d probably need a much larger craft for this mission.  This in a nutshell is why crewed spaceflight is tough.

On to some other issues:  as the ship moves farther from Earth, it will take longer and longer for messages to go from Earth to the ship and back again because of the finite speed of light.  It takes 8.3 minutes for light to go a distance of 1 astronomical unit.  Even as close as the Moon, there should have been a noticeable 1.7 second delay between a crewmember speaking to NASA and the response.  As they pass Mars (closest approach about 0.5 AU), the delay in communication should have been at least 8 minutes – 4 to get to Earth, and 4 to return.  I never saw this mentioned, and it never seemed to take the crew any time to talk to mission control.

(Spoiler alert) Another issue is that the crew never returns – all are lost on the voyage out or due to a series of disasters on Europa.  Some of these disasters seem avoidable, especially (part of) the first tragedy, in which a crewmember is lost en route.  I will only say this about it:  under current NASA regulations, astronauts never attempt a space walk unless there is some means to get back to the spacecraft: either a line or an all-axis maneuverable harness.  This was the kind of problem which could have been avoided with 20 cents of rope from the hardware store…

More nitpicks: on Europa, someone says that the temperature outside is absolute zero.  It’s not – the average Europan temperature is about 50 above absolute zero, warm enough for hydogren to be liquid.  Scientists are pretty picky about this; I can’t imagine any trained scientist making this goof.  Also, you can clearly hear the drill cutting into the ice from outside the ship, despite the surface being in vacuum.  This is something that really bugs me  — sound waves are vibrations in matter.No air, no sound.  If the sound was traveling through the ice and into the ship through the hull, it should have been very faint and distorted.

And now to my final two points:  first off, all of the tragedies were avoidable with the simple expedient of sending a robotic mission to Europa to explore the moon.  Yes, it’s not as glamorous or dramatic (Jerry Pournelle has rather famously said that nobody ever gives a robot a ticker-tape parade), but it could be done at a tiny fraction of the cost of a crewed mission, and no danger to anyone.  The narrator of this  “documentary” defined their end as successful in the face of tragedy, but I’m not inclined to agree no matter how great the discovery they made before dying.  It could have just as easily been made by robot.  Of course, you probably couldn’t make a movie about the dramatic robot mission to Europa to discover life there.

Secondly, it’s a sad commentary on science fiction in the media that movies like this, where there is at least some attempt to get the science right, come around only about once every decade.  I think it is possible to have drama and accurate science at the same time, as this movie and movies like Avatar and 2001 show.  I don’t dislike things like Star Wars or superhero movies with their flagrant disregard for the laws of physics – if nothing else, it’s grist for the critics mill.  But it’s too bad that the right stuff comes along so little.  Oh, well – Sturgeon’s law, I guess.

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.