Dream big, young scientists

Looking back through old journals for something entirely different, I found the following research proposal that I wrote in Oct-Nov of 1996, shortly before I got awarded my PhD scholarship. It was a pretty good scholarship I got, so I'm repeating this in case anyone else wants to aim high in the planetary science field: 

Knowing the chemical and isotopic composition of the whole Earth would help constrain the mechanics, timing, and efficiency of differentiation and core formation, as well as give valuable information on the partitioning of siderophile elements into the core. Unfortunately, directly sampling the core is impossible using current technology. Many substitutes of this have been explored, including the analysis of the undifferentiated chondrites and the study of iron-nickel meteorites thought to be pieces of a demolished differentiated planetary body. 

Sadly, oxygen and other isotopes show that these objects formed in a region of the solar nebula different to the Earth, and thus their compositions cannot be directly compared to that of the Earth-Moon system without extrapolation. Since the Moon dies not include a substantial iron core, any determination of the whole Earth, or whole Earth-Moon system composition must include the Earth. 

Our proposal is to use Whole Earth Laser Ablation (WELA) ICP-MS to determine the chemical and isotopic composition of the entire planet. Building the mass spectrometer for this will be an easy task, as the Earth is already located in an extremely good vacuum. We are merely asking for enough funding to purchase a laser powerful enough to ablate the planet, so that the resulting plasma can be sampled by our mass spectrometer. We believe that based on its excellent performance in the Alderaan System, the purchase of a Death Star would allow us to use its primary weapon as our Earth-ablating instrument. We ask that you fund the acquisition of this tool, as we believe it will fundamentally alter the way we view our planet.

The Witch King’s Forest Reserve

Yvon Chouinard, the billionaire CEO of the Patagonia company, must be feeling his mortality. A few months back, he announced that he was transferring ownership of his three billion dollar company to a trust, so that the capital and profits can be used to preserve wild spaces and fight climate change. He is not the first person to do this. About a decade ago, Gilded Age heiress Cordelia Scaife May gave her estate to a trust, which attracted notoriety when New York Times reporters revealed that for every dollar the trust gave to bird sanctuaries, more than twice as much was given to white supremacist groups.

Mr Choulnard’s politics and beliefs appear to be very different to Ms May’s, and what criticism I’ve read of his decision seems to be fairly mild, so I’m going to look at this from more of a structural angle. But because finance bores the teeth out of me, I will use metaphor. And since Stranger Things has made D&D cool again*, I will use that terminology.

In D&D, there are all kinds of monsters. But one of the most feared types are ancient witch kings and sorcerers whose magic is so powerful that it has allowed them to continue to roam the earth long after their bodies have died. These liches (or demi-liches, if they are so ancient their bodies have crumbled into a cloud of bone dust and a skull preserved by hate and enchantments) continue to exist and trouble the world long after their time has past, haunting the people and society of the game with their malice and cunning. And that, essentially, is what a trust is.

With a trust, the money is invested, usually in some sort of growth fund, and part of the returns are spent by a board of directors, who basically channel the spirit of the deceased to augur their long dead wishes. It basically gives the dead the power to reach out of the past and use their money to impact the living. And while it is no surprise that monsters like Scaife May would transform themselves in this way, the idea of a “good lich,” of Yvon the friendly neighbourhood witch king, seems a little bit odd.

Ideally, the future should belong to future generations, and the dead should not be able to rise from their crypts with seed money and bribes. At the same time, there is a role for conservation. After all, if the future generations wish to inherit anything other than a wasteland, then some sort of rules will be needed to preserve some of the Earth’s natural wonder for them. But at the same time, with wealth inequality only growing, and with these trusts and institutes compounding investment returns faster than they can give the money away, it makes me wonder. Does their existence doom the future generations to be serfs in a necrocracy, paying rent to long dead landlords who preserve their planet not for their sake, but according to the whims of a long dead plutocrat?

·      *   For the first time since the Cryogenean ice melted.

Total eclipse of the Death Star

Happy Eclipse day!

Congratulations to everybody who is lucky enough to live in the eclipse path, or who made the effort to get under the shadow of the moon! I hope it was grand; I was on the wrong side of the planet this time, so I have had to enjoy it via the internet.

Of course, the Internet likes to have fun, so along with the various actual eclipse photos (which range from cool to spectacular), there have been some pictures replacing the black disk of the moon with the DeathStar.  Long time readers of this blog will know that this Lounge has a great view of imaginary spacecraft in orbit; the Death Star fits into that category nicely. So with a bit of basic math and physics, we can calculate the conditions under which the Death Star can eclipse the sun, as viewed from here on Earth.

But first, we need to define our Death Star. I won’t dig too far down into the seedy underbelly of Srat Wars fandom, but a oft repeated figure for the size of the Death Star is a diameter of 100 miles, which yields an 80km radius. As for the density (which we’ll need later for reasons I don’t want to spoil), we will go with 800kg/m3. This is the density of something that is 10% steel and 90% air, which would give it the same general construction as modern naval vessels. This makes the Death Star slightly more dence than pure ethanol, but substantially lighter than the beer which fuels this blog.

In order to eclipse the sun, the Death Star needs to subtend a larger angle of sky than the Sun. For the sake of simplicity, we will call the sun angle 0.5 degrees, or 30 minutes of arc (it actually varies slightly, as the Earth’s orbit is elliptical, and the eccentricity of this orbit changes between 0 and 6 percent depending on where in the Milanković cycle we are). So, given a 80 km radius, the Death Star can eclipse the sun if it is closer than 80/sin(0.25deg)= ~18,300 km.

This is much farther than near Earth orbit, but much closer than geosynchronous orbit (about 36,000 km altitude). It is also, of course, about 21 times closer than the Moon, which is about 21 times larger than the Death Star.  However, it means that if the Death Star was in Geosynchronous orbit (to ‘hover’ over a target, for example), it would not eclipse the sun; it would block out at most a quarter of the light, which would be barely noticeable by people down below.

On the other had, if the Death Star was in low Earth orbit, like the International Space Station, it could easily eclipse the Sun. An 80km radius space station only 360 km up would be huge from the point of view of an observer directly underneath, blotting out more than 25 degrees of arc in the sky as it zoomed past at 8 km/sec (or one diameter every 20 seconds). However, it isn’t clear if the Death Star could fly this close to our planet.

The orbital velocity of a satellite around the Earth, in meters per second, is sqrt(GM/R), where G is the Gravitational Constant (6.67E-11 m³kg^-1s^-2), M is the mass of the Earth (6E24 kg), and R is the radius of the orbit IN METERS (not km). So with an orbital radius of 6700 km (329km above the mean surface), the orbital velocity is 7728 m/s. The problem for the Empire is that the Death Star has a radius of 80km, so the guys sitting in the gun turrets facing the Earth only have an orbital radius of 6620 km. Thus they will be orbiting at 7775 km/s, 47 m/s faster than the space station. For people who live in the real world, that’s a 105 miles per hour, or 165 km/hour difference. Smashing your troops against the walls at a hundered miles per hour is going to impede their ability to fire their super laser, and it is possible that even the structural integrity of the Death Star would be under threat this close to the Earth.

Back here in Science Land, we call the closest that a satellite can get to a planet without being torn apart by this sort of differential orbital speed the Roche Limit. The Roche Limit determines the closest approach a satellite can orbit a planet without being torn apart. Technically, the Roche limit only applies to objects held together by gravity- e.g. with no tensile strength. Steel, the purported structural material of the Death Star, has substantial tensile strength- this is why it’s used for everything from bicycle spokes to suspension bridge cables. But even if the space station is held together by the tensile strength of the steel, that will be little comfort to everything and everyone that isn’t tied down; even if the Death Star could survive inside the Roche limit, the occupants wouldn’t. So in order to know if a fully operational Death Star can eclipse the sun, we need to calculate the Roche Limit, and determine whether it is closer or farther than the maximum eclipse distance of ~18,300 km calculated at the top of this blog post.

The Roche limit equation is d = R (2 rho_M/rho_m)^1/3, where

R is the radius of the Primary, rho_M is the density of the primary, and rho_m is the density of the moon. And the assumption we are using is that the density of the death star is 0.8 g/cc or 800 kg/m³ (a bit less than my second beer).

 

As for the other numbers, the Earth’s radius is 6371km, and the earth’s density is 5500kg/m³. So the Roche limit for the Death Star is 15,263 km.

This is closer than the maximum eclipse distance of 18,300 km (which is a distance, not a radius, so you can add up to 6371 more km for an equatorial eclipse viewer), so there is a range, albeit a fairly well restricted range, in the orbital radius of roughly 16,000 to 24,000 km where the Death Star is far enough from Earth to not be tidally disrupted, but still close enough to blot out the sun. But it wouldn’t be blotted out for very long. A 16000 radius orbit has an orbital velocity of 5 km/s. So even with an equatorial observer only 10,000 km away, where the shadow is largest, at 72 km wide, totality would last less than 15 seconds. This is almost the exact elapsed time from Tarkin’s “Fire when ready” to weapon discharge. And Bonnie Tyler wouldn’t even have time to get a little bit tired of listening to the sound of her tears.

Star Wars teaser far too tame

 The second biggest thing to hit the internet yesterday was the new Star Wars teaser. Like many, I clicked the link with interest.  But as a planetary scientist, I was disappointed from the first scene (via io9).

This is a wrecked star destroyer, half buried in desert sand.  The obvious implication is that the spacecraft has left space and crashed.  Is this realistic?  luckily, physics, and the internet, can answer this question.

According to this fan site a star destroyer weighs something on the order of 30-50 million metric tons. This makes it about 3000-5000 times larger that the meteorite which blew up over Chelyabinsk. If we assume the slowest possible re-entry, that from low orbit (about 8 km/s on Earth), then we can calculate what sort of impact this would have.  Better yet, we can use the internet to let the experts calculate it for us.

The Earth Impact Effects Program, by Marcus, Melosh, and Collins, simulates the effect of impactors of various sizes on Earth (our trusty stand-in for human-inhabitable worlds around the universe). Simplifying a star destroyer to a 1 km sphere with a density of 100 kg/m3 gives us the correct mass and a sensible size.  Falling from low Earth orbit, this object would need to dissipate 1.68 x 10¹⁸ Joules into the atmosphere or ground.  That’s about 400 megatons, or about 8 times more energy than the Tsar Bomba, the biggest nuclear weapon ever detonated.  Given a shallow impact angle, this object explodes in the atmosphere, raining small debris down onto the ground.

This, of course, is exactly what happened when real spacecraft suffered uncontrolled or malfunctioning re-entry: Skylab and the space shuttle Columbia (at ~70 tons, almost a million times smaller than a Star Destroyer) both broke up high in the atmosphere, raining debris down over very wide areas.

Of course, the die-hard fan might claim that the Star Destroyer is much tougher than a 20th century spacecraft, and would reach the ground intact.  In this case, the kinetic energy would be adsorbed by the ground, not the atmosphere.  We can simulate that as well, by using a solid iron meteorite of the same mass (only 232 meters across, due to the higher density), with a vertical descent.  It still imparts 400 megatons of kinetic energy on the planetary surface. But instead of an airblast, we end up with a crater 4.5 km in diameter, and half a km deep.  Nothing of this scale is evident in the Star Wars teaser.

As shown in the Chelyabinsk post a few years ago, the speeds- and energy- associated with space travel are so huge that even the most creative minds of Hollywood are unable to grasp their enormity and power. This was forgivable 30 years ago, before the internet, but in this day and age, fantastical videos that are tamer than reality are disappointing.

Edit:
Related post: Viewing Imaginary Spacecraft from the Ground"

Putting the Russian meteorite in perspective

Friday morning, a large meteor entered the atmosphere over the southern Ural area of Russia, detonating with enough force to shatter windows in nearby towns and injure over 1000 people.  Preliminary estimates suggest an impactor traveling at 15 to 20 km/s, and weighing 8000 to 10,000 tons, exploding at an altitude of 20-30 km with the force of a nuclear weapon.

These are hard numbers to wrap one’s head around.

Let’s start with the size. There are numerous reports around on the bolide being “bus sized.”  But buses are not made of solid rock, so this is deceptive. In this situation, mass is more important than dimensions. A bus weighs about 15-20 tons. That’s a lot less than 8000-10,000.  For example, 8000-10,000 tons is the approximate size of the naval destroyer USS Cole, which was famously attacked by Al Qaeda in Yemen in 2000. It’s a lot bigger than a bus. Of course, that ship doesn't fly in space.  Rather, it sails in the ocean at about 50 km/ hour, thousands of times slower than 20 km/ second. The International Space Station is about 450 tons.

Orbital velocity for a low earth orbit is about 8 km/second, and reentry speeds returning from low earth orbit are similar.  So this meteor was traveling at about twice orbital speed when it hit the atmosphere.  This is substantially faster than the 11 km/s reentry of the Apollo missions returning from the moon, and about twice as fast as the space shuttles (and other low earth orbit spacecraft) re-enter.  It is about 50 times faster than a handgun bullet.

The total energy released, between a quarter and a half a megaton, was similar to a modern H-bomb.  However, it was more dispersed, and released high in the atmosphere. Because the impactor was traveling at twice orbital speed, the energy would be equivalent to an orbital object of four times the mass re-entering.  32,000 to 40,000 tons is about the size of the Titanic, or a WWII battleship. 

Something similar to this has been imagined.  Below is a model of CV-6, the famous 20,000 ton WWII aircraft carrier Enterprise.

Compare that to the fictional NCC 1701 spaceship enterprise, at the same scale.

The internet gives a spaceship mass of 10 times the aircraft carrier, which seems way to heavy to be sensible. 

If we say the spaceship is twice the mass of the aircraft carrier (it is bigger, after all, even if it is also probably made from a lighter & stronger material than steel), then it would have about the same energy on re-entry as the Chelyabinsk bolide.

We can compare the videos:

Star Trek III

Chelyabinsk Friday morning:

Reality is still far more gripping than imagination. 

Finally, here is what the Earth looked like from the asteroid’s point of view an hour before impact.  A few things to note:

First, the Earth is almost full.  As a result, the side of Earth facing the asteroid was in day, so it would have been hard to spot, as the sun was behind it.  However, the US space junk tracking radars in Hawaii should have been able to pick it up.  I wonder if they did, if they passed any sort of a warning on, or even are they allowed to?  It would be a shame if the 1200 injuries that occurred were preventable, but for American government red tape.

Viewing imaginary spacecraft from the ground

I read and watched a lot of science fiction when I was young. I don’t much any more, mostly because I’m too busy, but every now and then I have a relapse. Also, for the most part, real science is more fun these days. But they aren’t necessarily mutually exclusive.

For example, this evening, I was thinking about the International Space Station. Under optimal viewing conditions, the ISS is the brightest thing in the sky, aside from the sun and moon. But while the station is surprisingly large (about the size of a football field), it is generally smaller than most science fiction spacecraft which are capable of interstellar travel.

Science fiction generally depicts people walking around on the ground, or starships floating close above a planet, but with little connection between the two; The only time I can recall people on the ground seeing spacecraft above are when the Death Star explodes in Return of the Jedi, and when the remains of the Enterprise re-enter the atmosphere in Star Trek 3. But if you can see the ISS from here on Earth, then surely a larger science fiction (or alien) spacecraft would be brighter still.

Figure 1. Since you can see the ISS from your backyard, you don’t need the force to detect something much bigger in the same orbit. Click for larger image.

Thanks to Jeff Russell’s Starship dimensions, scaled profiles of most major starships can be easily compared to the ISS. That’s all well and good, and we can estimate areas and visual magnitudes in the -7 to -10 range for various popular starships. But since there isn’t anything of that brightness in our skies, it doesn’t mean much, except to tell us that they would be easily visible from the back yard of anyone looking for them (assuming they aren’t in Earth’s shadow). But there is a useful celestial yardstick.

Figure 2. relative apparent sizes of various spacecraft (and the ISS) when directly overhead in a 350 km low Earth orbit, when compared to the apparent size of moon. The moon is of course 1000 times larger and 1000 times farther away. Click for larger image.

The Moon, which has a radius of about 1740 km, is about 1000 times farther away than low earth orbit. So a spacecraft 1000 times smaller- say, a flying saucer with a 1.7 km radius- would have the same apparent size when directly overhead. Thirty degrees above the horizon, it would appear half a big. In other words, the shape of kilometer-scale spacecraft, such as a Star Destroyer, or a Babylon 5 capital ship, would easily be discernable to people below. The 24 km-wide flying saucers from Independence Day would appear to be seven times larger than the moon, and would blot out the sun for up to 4 seconds as they passed in front of the sun.

So forget all the garbage you hear about radar jamming and government cover-ups. When the alien invasion fleet comes for us, we’ll be able to watch it from the back yard.

Figure 1 is from STS 118 and Return of the Jedi.

Pie crust phase equilibria: update

Four years ago, I posted the basics on the phase equilibria of pie crust in this blog. A summation of that post, as well as an update, appears below:

With American Thanksgiving and Christmas rapidly approaching, the pie baking season is rapidly approaching. One of the most important, but least quantified, aspects of pie creation is the crustal composition. A simple ternary phase diagram for three-phase pie crust is presented below.

While the “traditional composition” point is plotted to scale, the positions and shapes of the curve are poorly constrained approximations. Lack of accurate thermodynamic data for the system precludes accurate prediction of these fields. It is the shapes and positions of the top two curves that is of paramount importance; anyone who reaches the butter-water two phase field should be banished from the kitchen.

As anyone with baking experience knows, the stability region for pie crust is a relatively small area on the wet side of the two phase flour + dough field. This field is generally approached by adding water to a flour/butter mixture, as is shown below.

Four years ago, I suggested the following approach:

However, if the approximated slopes shown above are correct, then a radical new approach to crustal formation might be advisable. By generating a flour-water mixture, and then adding butter, a wider range of valid crustal compositions should be achievable before exiting the edible portion of this phase diagram. This approach is shown below.

In hindsight, this was silly. There are two reasons. Firstly, accurately ganguing the initial water/flour mixture is difficult, as your starting composition is in the 2 phase flour water field. And secondly, this procedure generates a crust with the minimum possible butter, and butter is yummy. So this year, I will endeavor to explore the left hand side of the diagram. I suspect that the dough / slime boundary curves over a bi farther than is illustrated here.

Is Twitter...

the heaven to which bloggers ascend after they die?

The right sky

Jen over at Twisted Physics and Cocktail Party Physics has recently set up SEEx- a translation service which allows speakers of science and media to communicate with each other. In her introductory blog, she mentioned the story of Neil Tyson and the wrong sky. In short, Dr. Tyson complained that despite getting all this historical trivia about the Titanic correct- which nobody would notice, much less care about, they screwed up the starscape that was visible after the ship sank. The thing that ticks me off about this is that it is trivial to do correctly. Fifteen minutes browsing the web (even the 1996 web) would have found them a downloadable program that would inform them that the survivors of the shipwreck would have seen this:

Ill-fitting lab coats

I was gabbing with some of the technical guys at work today, and the subject of lab coats came up. Our lab manager is getting coats for anyone who spends more than a millisecond in the machine room, and he’s even taking the unusual step of making sure that they fit. To me this sounds suspicious.

As a serial lab coat borrower, I am used to them being small, and generally short-sleeved. But evidently there is more to it. I'm told they can be procured in all sorts of shapes and sizes to fit a variety of body types. In fact, I believe that there was only one person in the building who they had trouble fitting with a lab coat. This person is not particularly large, small, or gangly. He just has broad shoulders, a strong upper body, and very good posture.

After an exhaustive search, they finally realized that lab coats simply weren’t made for people built like that. Can’t imagine why not...

Fantasy GIS

When I was a kid, I played a fair bit of Dungeons & Dragons. Rummaging through old files this winter, I recently found a folder full of maps from a campaign I ran as DM from 8th grade through the early part of college. As they were a bit ratty looking, I decided to scan some of them, just for posterity. And that got me thinking.

One of the largest learning curves in my new job is learning GIS software. GIS, or geographical information systems, are computer programs that replace the laborious and repetitive math of map drawing with arcane buttons and incomprehensible menu selections which allow the computer to do the math for you. As I’m old enough to have learned geology in the paper and pencil era, I’m on a bit of a learning curve with plotting everything up. So I figured I’d register the adventure maps just for kicks.

A bit of sober reflection altered my plans, however. For one thing, I didn’t want all that junk on my work machine, and for another, using a format for a (very expensive) program I didn’t own seemed sort of silly. As Brian and Ron have been pointing out over the past few years, Google Earth is basically a poor man’s GIS. So I decided to use that instead.

Just like Google Earth, this ‘Google D&D’ is fully zoomable through the continental scale...

The regional scale...

And the local scale. The continuity between maps is better in some instances than others. The regional to local transition, which was done at high latitude and involved maps drawn several years before I learned trigonometry, is probably the dodgiest. But it is that scale at which the various tags and hypertext attributes start to become useful, as is shown here.

And at the dungeon level, layer control is great. Here I’ve color coded the dungeon layers so that their overlap is clear. The black ruined castle is the surface layer, while the underground layers are red, blue, and green.

And finally, we can turn off the clutter and zoom all the way down to look at the individual rooms in the adventure.

I don’t know if I would go so far as to try DMing paperless- there is a lot to be said for scribbling on maps and ticking things off. But it would be a great tool for generating things like player maps, as you can hide the DM only information just by deselecting the layer it is in. And if someone spills coke on the tactical map you can just print out another one and move the figurines.

And as a geologist, this has got me thinking. I’d love to plug the continental parameters into a coupled ocean-atmosphere GCM to see if I put the forests and deserts in the correct places. And I should probably check the orbital stability of the three moons*, as well.

I don’t know how useful this sort of thing would be for normal, well-adjusted RPG moderators. But I would have loved it 20 years ago. And I suspect it would be useful for anyone else who was socially awkward enough that they couldn’t say how a drunk goblin would react without knowing the orbital parameters, geologic setting, historical background, religious persuasion, and gardening habits of every sentient denizen of the craton.

* Unfortunately, in my ignorant youth I put the farthest moon beyond the planet’s Hill Sphere. I should really be more careful with my satellites.