Matters of Gravity

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I was just interviewed on the “Jason Rantz” show on KIRO radio (a Seattle station.)  The interview was much more relaxed than most of them have been – Jason was interested in what I was saying, and seemed a lot more relaxed than most of the other radio talk show hosts I’ve been interviewed by.  The interview will be about ten minutes long, although we talked for about twice as long.  Once there’s a podcast I’ll put a link up for it.

We mostly talked about movies, including the recent movie Gravity.  One thing in the discussion which got me thinking was that Jason was surprised that the chain reaction of satellite destruction which drives the main plot is a real idea.  This got me thinking – most people don’t know about it, so it’s a good idea for a blog.  Three points before I start:

1)    There are spoilers for the movie in this blog, so readers beware!

2)    Neal Degrasse Tyson mentioned this in a tweet about the movie a while ago but I want to treat this in more depth; and

3)    I did like the movie despite what I say below.

As far as the third point goes, I like movies even if they get the science wrong.  I repeat the main point of this blog: thinking about the science adds depth to the movies and enjoyment of them, not detract, at least as far as I’m concerned.  If I had to grade the space science in Gravity, I’d probably give it a B-, which is pretty good as far as movies go.  Here, of course, the gold standard for accuracy in depictions of space travel is 2001: A Space Odyssey, made in 1968.  The depictions of how objects move in space are both highly accurate and beautifully depicted, as one would expect from the pairing of Stanley Kubrick and Arthur C. Clarke.  (If you watch the movie, turn it off once you get to the final 20 minutes and imagine your own ending.)

Gravity wasn’t as good, but it did a better job than a lot of others.  There were no banked turns in space, for example.  I found the final scene hard to believe, and there were a few other points which bothered me.  For example, the parachute seemed to billow when Sandra Bullock was maneuvering the Russian space capsule, which wouldn’t happen in the absence of air.  Also, I think (from a short stint at NASA where I consulted on a project related to it) that fires don’t burn the way they were depicted in the capsule scene.  Fires get fresh oxygen through convection, which doesn’t happen in microgravity situations like on the shuttle or in any free-fall orbit. There’s a Youtube video  which shows how a candle flame extinguishes itself in free fall when dropped down a long shaft – this simulates the same physics as a spacecraft in orbit around a planet.  (The theory behind this is originally due to Albert Einstein!)  However, the movie overall was entertaining and pretty intelligent, even if I was able to guess who was going to die and in which order within five minutes.  (The attractive heroine survives, the senior astronaut played by the big-time movie star dies heroically midway through the movie, and the hapless “red shirt” is killed off asap.  Told you there were spoilers!)

The incident driving the plot of the movie is a chain reaction of satellite destruction.  The Russians deliberately destroy an old satellite (presumably so that it won’t endanger other satellites in similar orbits), but this leads to the debris from that satellite destroying others, leading to that debris destroying others, etc.  That is, the Russians create the very situation they were trying to avoid – the planned destruction of one satellite leading to the unplanned destruction of many others.  The consequences include the downing of GPS navigation on Earth and space debris at high velocities coming in to destroy the shuttle the characters are working from.

OK:  two points.  One, the chain reaction is in fact a real concern.  This is known as the “Kessler syndrome” after the space scientist, Donald Kessler, who first predicted it in 1978.  Two, if it does happen, it will not be anything like in the movie.

Issue one:  Low-Earth orbit (LEO), some 160 to 2,000 kilometers above the planet, is filled with debris from older missions.  According to the Union of Concerned Scientists, about half of the thousand or more currently active satellites are in LEO, and there are tens of  thousands of centimeter size or larger fragments of debris from launches or older, inactive satellites.  The potential is that if there is enough material populating these orbits, chain reactions like the one in the movie may start.  Space is big – really big – but there’s a lot of stuff in that particular region of space.  Given enough time, collisions happen.  The collisions take place at very high speed – collisions will take place at relative speeds of something like the orbital speed at that altitude, or 15,000 miles per hour.  It’ll be higher or lower depending on the exact orbital parameters, but whatever it is will be high enough to completely destroy the two colliding objects.

The tricky part is that anything placed into orbit tends to stay there.  It’s not like on Earth, where gravity will cause the debris to fall out of the sky – when two planes collide, the little bits from the collision don’t race off at high speeds to become hazards to other planes for years or centuries to come.  In space, even in a low-Earth orbit, there is barely any atmosphere to cause friction to make the debris fall back down into the atmosphere and burn up there.  The idea behind the Kessler syndrome is that eventually there will be enough junk that the detritus caused by one collision will lead to more, with an ever expanding circle of destruction which will eventually take out most of the satellites at that particular orbital radius.   The mathematics is almost exactly the same as a chain reaction in an above-critical nuclear bomb core:  in that, one neutron’s fission creates more than one neutron, which leads to more fission processes: one leads to two, two create four, four, eight, for example, and eventually there are enough to destroy a city.  It’s harder to do the calculation for space debris, but according to a 2010 paper by Donald Kessler, several regions above 500 km have the potential for a runaway chain reaction.

So that part of the movie reflects real concerns.  However, for dramatic effect, the movie showed the debris ripping through the shuttle, causing mayhem, killing off one of the astronauts, and playing havoc with Earth’s communications satellites and GPS in very short order.  Not going to happen.

First off, most of the satellites are in much higher orbits than LEO.  Much, much higher.  Geosynchronous satellites for satellite TV and communications are at about 35,000 km up.  The GPS satellites, supposedly taken out by the cascade, are up at about 20,000 km.  It takes a whole lot of energy to move a particle from LEO into one of those orbits – most of the particles created by the cascade won’t have enough energy, and the laws of probability dicate that a hit by the small number of the ones which have enough energy is enormously improbable.  So our communications networks are safe.

The bigger problem with the movie is that this is a very slow process.  We think of chain reactions as being fast because of devices like the atomic bomb.  However, space is so sparcely populated that even in a chain reaction situation, the average time between collisions will be months, maybe even years.  The point of the Kessler syndrome isn’t that it’s fast but that one collision will lead to more than one collision afterwards.  The chain reaction wouldn’t have posed a threat to the astronauts up there unless they got incredibly unlucky.  There also wouldn’t have been thousands of these particles just happening to be going in the same direction – the collision would have led to them being spread out in all directions.  (This is not quite true, as the particles would tend to be travelling along the trajectory of the center of mass of the two colliding particles, but it’s close enough.)

I repeat: Gravity was a fun movie.  It’s a good example of the impersonal isolated man or woman against nature film.  If I wasn’t completely bowled over by it, it still made an impact (if you’ll pardon the pun.)

 

USA Science and Engineering Festival

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Another quick post:  I’ll have a more substantial one after this weekend.

The St. Mary’s College Physics department will have a booth at the 2014 USA Science and Engineering Festival this weekend. My colleague, Josh Grossman and I will be staffing the booth almost continuously – we will have a number of fun demos, including a (hopefully working) Theremin, a larger-than-life Game of Life, and several optics demos, plus copies of my book on display (not for sale, alas).  We’re in booth 5642.  Even if you don’t want to see my ugly mug, please come by – the Festival is huge, with thousands of booths and loads of special presentations and demonstrations.  They Might Be Giants, my favorite band, among a lot of other celebrities, will be there.

As I think about it, a post on the science fiction sound of the Theremin might be interesting…

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.

For the budding science fiction writer: More local color

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The third in our sequence of posts for those who are starting to write science fiction.

So now you’ve picked your world and the star it circles.  You’ve figured out how far away it should be.  What should the world look like?  How can you make it distinct?

There are limitless ways in which you can pursue this.  Exotic fauna is one way: make the animals different from those on Earth.  We’ll explore this in an upcoming post.  I’m going to concentrate on the flora in this one: what should vegetation look like on your planet, assuming it has vegetation at all?

Flowers come in all shapes and sizes and colors.  The local quality of light may make some differences, but you are pretty much free to choose what you want in this regard.  However, leaf color is probably going to be determined by the star you’ve picked.

Stellar spectra

Light curves from three types of stars

The figure shows a schematic diagram, representative only,  of the spectrum of different classes of stars.  This shows the relative amounts of power which the star emits as a function of the wavelength of light.  Human eyes are insensitive to most light: our eyes are most sensitive in the wavelength region in which our sun emits the most light.

On Earth, leaves are green because Earthly chlorophyl absorbs blue (shorter wavelength) and red (longer wavelength) light predominantly.  Why this is so is a little bit tricky.  The chemical pathways by which plants absorb light and convert it into energy are complicated, and involve no less than about 8 photons per reaction.  Red light has low energy photons but can be used directly for photosynthesis.  Blue light has high-energy photons, but can be “down-converted” to lower energy to make them useful for photosynthesis.  Because of this, photons of wavelengths which appear blue and red to our eyes are used for photosynthesis on Earth and are absorbed, while middle wavelength photons, i.e., green light, is reflected,  leading to leaves being green.

Vegetation under different stars is probably going to look different.  Dr. Nancy Kiang and her colleagues at NASA have investigated the most likely chemical pathways for energy uptake for vegetation on planets circling other stars.  Note that the M-class star emits less light in toto than the sun does.  Dr. Kiang and her group theorized that plants on worlds circling M-class stars would need every available photon; if they absorb all light, they would appear black.  On the other hand, planets circling F-class or brighter stars would have too much light, especially in the short wavelength spectral region.  They might have to reflect the blue light, leading to blue-looking leaves.

These are just a few of the details which the science fiction writer needs to keep in mind.  In the next post, we’ll discuss how the distance of the planet determines the length of the year.