Science Porn

[pocaracas]

the phase shift is dependent on the time the wave travels in the plasma until it gets to the reflecting layer... along the way, it meets layers which have a non-zero index of refraction which must be accounted for... and these are not always in the same position... or else, why have such a diagnostic at all?

That sounds difficult... is that is why you integrate over those frequencies in your formula? To account for all the stuff happening in between? Or is that thinking too naively...

That's exactly what's happening: each point requires an integration up to that point.

[Alex K]

I find this kind of stuff very fascinating. Being a theorist by training, I sometimes envy those who get to play with cool toys rather than pen and paper.

[pocaracas]

I find this kind of stuff very fascinating. Being a theorist by training, I sometimes envy those who get to play with cool toys rather than pen and paper.

I shall not make you anymore envious, then!

But I've once seen a guy do tomography of tokamak plasma, by using a single spectroscopy 2D camera (that's a standard fast camera with a filter in front so it only "sees" a particular spectral line (interval) for a particular element).... that as awesome!

[SteelCurtain]

I'm so not jealous. I really am not.

[SteelCurtain]

What if all of the sun's output of visible light were bundled up into a laser-like beam that had a diameter of around 1m once it reaches Earth?
—Max Schäfer

Here's the situation Max is describing:



If you were standing in the path of the beam, you would obviously die pretty quickly. You wouldn't really die of anything, in the traditional sense. You would just stop being biology and start being physics.

When the beam of light hit the atmosphere, it would heat a pocket of air to millions of degrees (Fahrenheit, Celsius, Rankine, or Kelvin—it doesn't really matter.) in a fraction of a second. That air would turn to plasma and start dumping its heat as a flood of x-rays in all directions. Those x-rays would heat up the air around them, which would turn to plasma itself and start emitting infrared light. It would be like a hydrogen bomb going off, only much more violent.



This radiation would vaporize everything in sight, turn the surrounding atmosphere to plasma, and start stripping away the Earth's surface.
But let's imagine you were standing on the far side of the Earth. You're still definitely not going to make it—things don't turn out well for the Earth in this scenario—but what, exactly, would you die from?

The Earth is big enough to protect people on the other side—at least for a little bit—from Max's sunbeam, and the seismic waves from the destruction would take a while to propogate through the planet. But the Earth isn't a perfect shield. Those wouldn't be what killed you.

Instead, you would die from twilight.



The sky is dark at night[citation needed] because the Sun is on the other side of the Earth.[citation needed] But the night sky isn't always completely dark. There's a glow in the sky before sunrise and after sunset because, even with the Sun hidden, some of the light is bent around the surface by the atmosphere.

If the sunbeam hit the Earth, x-rays, thermal radiation, and everything in between would flood into the atmosphere, so we need to learn a little about how different kinds of light interact with air.

Normal light interacts with the atmosphere through Rayleigh scattering. You may have heard of Rayleigh scattering as the answer to "why is the sky blue." This is sort of true, but honestly, a better answer to this question might be "because air is blue." Sure, it appears blue for a bunch of physics reasons, but everything appears the color it is for a bunch of physics reasons.(When you ask, "Why is the statue of liberty green?" the answer is something like, "The outside of the statue is copper, so it used to be copper-colored. Over time, a layer of copper carbonate formed (through oxidation), and copper carbonate is green." You don't say "The statue is green because of frequency-specific absorption and scattering by surface molecules.")

When air heats up, the electrons are stripped away from their atoms, turning it to plasma. The ongoing flood of radiation from the beam has to pass through this plasma, so we need to know how transparent plasma is to different kinds of light. At this point, I'd like to mention the 1964 paper Opacity Calculations: Past and Future, by Harris L. Mayer, which contains the single best opening paragraph to a physics paper I've ever seen:

Initial steps for this symposium began a few billion years ago. As soon as the stars were formed, opacities became one of the basic subjects determining the structure of the physical world in which we live. And more recently with the development of nuclear weapons operating at temperatures of stellar interiors, opacities become as well one of the basic subjects determining the processes by which we may all die.

Compared to air, the plasma is relatively transparent to x-rays. The x-rays would pass through the plasma, heating it through effects called Compton scattering and pair production, but would be stopped quickly when they reached the non-plasma air outside the bubble. However, the steady flow of x-rays from the growing pocket of superhot air closer to the beam would turn a steadily-growing bubble of air to plasma. The fresh plasma at the edge of the bubble would give off infrared radiation, which would head out toward the horizon (along with the infrared already on the way), heating whatever it finds there.



This bubble of heat and light would wrap around the Earth, heating the air and land as it went. As the air heated up, the scattering and emission from the plasma would cause the effects to propogate farther and farther around the horizon. Furthermore, the atmosphere around the beam's contact point would be blasted into space, where it would reflect the light back down around the horizon.

Exactly how quickly the radiation makes it around the Earth depends on many details of atmospheric scattering, but if the Moon happened to be half-full at the time, it might not even matter.

When Max's device kicked in, the Moon would go out, since the sunlight illuminating it would be captured and funneled into a beam. Slightly after the beam made contact with the atmosphere, the quarter moon would blink out.



When the beam from Max's device hit the Earth's atmosphere, the light from the contact point would illuminate the Moon. Depending on the Moon's position and where you were on the Earth, this reflected moonlight alone could be enough to burn you to death ...



... just as the twilight wrapped around the planet, bringing on one final sunrise.[3]



There's one thing that might prevent the Earth's total destruction. Can Max's mechanism actually track a target? If not, the Earth could be saved by its own orbital motion. If the beam was restricted to aiming at a fixed point in the sky, it would only take the Earth about three minutes to move out of the way. Everyone on the surface would still be cooked, and much of the atmosphere and surface would be lost, but the bulk of the Earth's mass would probably remain as a charred husk.

The Sun's death ray would continue out into space. Years later, if it reached another planetary system, it would be too spread out to vaporize anything outright, but it would likely be bright enough to heat up the surfaces of the planets.



Max's scenario may have doomed Earth, but if it's any consolation, we wouldn't necessarily die alone.

http://what-if.xkcd.com/141/

[vorlon13]

I might do some actual maths later, but 3 minutes exposure to the total luminosity of the sun is going to be a little rough on the planet.

Just noodling this out mentally, doing E=MC\2 on

ONE BILLION TONS OF MASS

is going to make quite a bang.  I'm thinking the earth gets pulverized/powderized/vaporized from the shock wave.

[Anomalocaris]

I might do some actual maths later, but 3 minutes exposure to the total luminosity of the sun is going to be a little rough on the planet.

Just noodling this out mentally, doing E=MC\2 on

ONE BILLION TONS OF MASS

is going to make quite a bang.  I'm thinking the earth gets pulverized/powderized/vaporized from the shock wave.

Assuming the sun does put out equivalent of a billion tons mass worth of energy every 3 minutes, it Seems to me an order of magnitude calculation says a billion tons of mass converted to energy would be around 10e26 Jules.  Gravitational binding energy of the earth would be 6 orders of magnitude more than that.  

Earth won't pulverize into an expanding, gravitationally unbound, ball of dust from just 3 minutes of total solar output, not even 3 years.

Sorry.

The Death Star super laser that blows Aldaaran into a gravitationally unbound cloud of debris with a single almost instantaneous shot would have to have a power output about a billion times greater than the sun, and somehow ensure the beam won't just bore a hole through the planet and go out the other side before the planet can collapse into upon the hole.  

If such a laser is built, it would be focusing the power output not of a star, but of a supernova into a laser like beam.  Such a beam would literally be visible to the naked eye from across the entire universe.

Wonder if anyone working on Star Wars script ever had any inkling of the implied power of Death Star.

[vorlon13]

Ouch.

The largest nuke the US ever set off was around 15 megatons.

Noodling out around 500,00 kilotons per ounce into 1 billion tons and the surface are of the earth, we get about one 15 MT nuke over every square yard of the earth's surface (m/l).

Looks like we will still have a planet of sorts, and clearly the energy isn't evenly distributed, but it's going to be an EXTREMELY rough 3 minutes. Everywhere.

I note the 15 MT test was detectable via seismograph from Eniwetok atoll to California, the shock waves transmitted through the earth's structure from the 'sun zap device' are going to trigger a phase of extreme vulcanism, globally.

And burn off all the atmosphere.

And the ocean.


Curiously, the mass of the collector and the focusing device will essentially be 'felt' as focused in the direction of the sun from earth.

It looks pretty thick and meaty. It's additional gravitational pull will DRASTICALLY alter the earth's orbit. I'm thinking we impact the thing pretty quick.

That won't be pretty either.

[pocaracas]

wuuut?!

https://www.youtube.com/watch?v=VylZJrep1MM

[SteelCurtain]

Can you use a magnifying glass and moonlight to light a fire?
—Rogier Spoor

At first, this sounds like a pretty easy question.
A magnifying glass concentrates light on a small spot. As many mischevious kids can tell you, a magnifying glass as small as a square inch in size can collect enough light to start a fire. A little Googling will tell you that the Sun is 400,000 times brighter than the Moon, so all we need is a 400,000-square-inch magnifying glass. Right?

Wrong. Here's the real answer: You can't start a fire with moonlight[Pretty sure this is a Bon Jovi song.] no matter how big your magnifying glass is. The reason is kind of subtle. It involves a lot of arguments that sound wrong but aren't, and generally takes you down a rabbit hole of optics.

First, here's a general rule of thumb: You can't use lenses and mirrors to make something hotter than the surface of the light source itself. In other words, you can't use sunlight to make something hotter than the surface of the Sun.

There are lots of ways to show why this is true using optics, but a simpler—if perhaps less satisfying—argument comes from thermodynamics:

Lenses and mirrors work for free; they don't take any energy to operate. If you could use lenses and mirrors to make heat flow from the Sun to a spot on the ground that's hotter than the Sun, you'd be making heat flow from a colder place to a hotter place without expending energy. The second law of thermodynamics says you can't do that. If you could, you could make a perpetual motion machine.

The Sun is about 5,000°C, so our rule says you can't focus sunlight with lenses and mirrors to get something any hotter than 5,000°C. The Moon's sunlit surface is a little over 100°C, so you can't focus moonlight to make something hotter than about 100°C. That's too cold to set most things on fire.

"But wait," you might say. "The Moon's light isn't like the Sun's! The Sun is a blackbody—its light output is related to its high temperature. The Moon shines with reflected sunlight, which has a "temperature" of thousands of degrees—that argument doesn't work!"

It turns out it does work, for reasons we'll get to later. But first, hang on—is that rule even correct for the Sun? Sure, the thermodynamics argument seems hard to argue with,[Because it's correct.] but to someone with a physics background who's used to thinking of energy flow, it may seem hard to swallow. Why can't you concentrate lots of sunlight onto a point to make it hot? Lenses can concentrate light down to a tiny point, right? Why can't you just concentrate more and more of the Sun's energy down onto the same point? With over 1026 watts available, you should be able to get a point as hot as you want, right?

Except lenses don't concentrate light down onto a point—not unless the light source is also a point. They concentrate light down onto an area—a tiny image of the Sun.[Or a big one!] This difference turns out to be important. To see why, let's look at an example:

This lens directs all the light from point A to point C. If the lens were to concentrate light from the Sun down to a point, it would need to direct all the light from point B to point C, too:

But now we have a problem. What happens if light goes back from point C toward the lens? Optical systems are reversible, so the light should be able to go back to where it came from—but how does the lens know whether the light came from B or to A?

In general, there's no way to "overlay" light beams on each other, because the whole system has to be reversible. This keeps you from squeezing more light in from a given direction, which puts a limit on how much light you can direct from a source to a target.

Maybe you can't overlay light rays, but can't you, you know, sort of smoosh them closer together, so you can fit more of them side-by-side? Then you could gather lots of smooshed beams and aim them at a target from slightly different angles.

Nope, you can't do this.[We already know this, of course, since earlier we said that it would let you violate the second law of thermodynamics.]

It turns out that any optical system follows a law called conservation of étendue. This law says that if you have light coming into a system from a bunch of different angles and over a large "input" area, then the input area times the input angle[Note to nitpickers: In 3D systems, this is technically the solid angle, the 2D equivalent of the regular angle, but whatever.] equals the output area times the output angle. If your light is concentrated to a smaller output area, then it must be "spread out" over a larger output angle.

In other words, you can't smoosh light beams together without also making them less parallel, which means you can't aim them at a faraway spot.

There's another way to think about this property of lenses: They only make light sources take up more of the sky; they can't make the light from any single spot brighter,[A popular demonstration of this: Try holding up a magnifying glass to a wall. The magnifying glass collects light from many parts of the wall and sends them to your eye, but it doesn't make the wall look brighter.] because it can be shown[This is left as an exercise for the reader.] that making the light from a given direction brighter would violate the rules of étendue.[My résumé says étendue is my forté.] In other words, all a lens system can do is make every line of sight end on the surface of a light source, which is equivalent to making the light source surround the target.

If you're "surrounded" by the Sun's surface material, then you're effectively floating within the Sun, and will quickly reach the temperature of your surroundings.[(Very hot)]

If you're surrounded by the bright surface of the Moon, what temperature will you reach? Well, rocks on the Moon's surface are nearly surrounded by the surface of the Moon, and they reach the temperature of the surface of the Moon (since they are the surface of the Moon.) So a lens system focusing moonlight can't really make something hotter than a well-placed rock sitting on the Moon's surface.

Which gives us one last way to prove that you can't start a fire with moonlight: Buzz Aldrin is still alive.

http://what-if.xkcd.com/145/