What-If 0141: "Sunbeam"

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Re: What-If 0141: "Sunbeam"

Postby Neil_Boekend » Fri Jan 15, 2016 9:52 am UTC

The air is blue at noon because it is rushing towards you at a significant fraction of light speed. The air is red at sunset because the air is rushing back towards the part of the world where it is noon.*

*may not be entirely true
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Re: What-If 0141: "Sunbeam"

Postby rmsgrey » Fri Jan 15, 2016 2:41 pm UTC

GulliNL wrote:One final question (really, I don't have plans of building a Dyson Laser. Trust me. That Powerball money will be invested in bonds and better health care for puppies), how would the star itself react to being trapped in a Sphere? It is now bombarding itself with insane amounts of heat, light, x-ray, matter and probably building up pressure inside the Sphere. Will the star collapse under this stress? Will it become stronger? Will the entire Sphere start acting as a new star?

Really, how does one build a Dyson Sphere?

**edit** I realise that a "normal" Dyson Sphere wouldn't completely enclose a star but in this 'What-If' it would, for the sake of harnessing all the power of the sun, so my questions regard this kind of Sphere.


A first approximation is to assume that the star continues to convert mass into other forms of energy at the same rate. Once things stabilise, the outer surface of the sphere must emit radiation at the same rate, but spread over the entire surface of the sphere, not just the surface of the star, so the sphere's black-body spectrum would be for a lower temperature (a sphere with the same radius as the Earth's orbit would have a similar temperature to the Earth's average).

The other possibility (given that the sphere doesn't break) is that some of the energy contained within the sphere starts condensing back into matter. At those sorts of energies, you will be affecting the star's internal physics, so the assumption above doesn't hold.

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Re: What-If 0141: "Sunbeam"

Postby speising » Fri Jan 15, 2016 2:54 pm UTC

The sphere is supposed to funnel all energy to the lazor, though. So there would'nt be any difference for the star.

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Re: What-If 0141: "Sunbeam"

Postby Extragorey » Fri Jan 15, 2016 3:40 pm UTC

Surely I'm not the only one here who noticed the connection with Star Wars,
Spoiler:
seeing as this scenario is almost exactly what the First Order does in the movie, draining a sun of its energy and using it to blow up planets?

I find it hard to believe Randall wouldn't have explicitly referenced Star Wars somewhere in the article if he'd made the connection himself. Does that mean he hasn't seen it yet? *gasp*
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Re: What-If 0141: "Sunbeam"

Postby brenok » Fri Jan 15, 2016 4:37 pm UTC

Extragorey wrote:Surely I'm not the only one here who noticed the connection with Star Wars,

It's not like it was mentioned on the very first post of the thread.

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Re: What-If 0141: "Sunbeam"

Postby niauropsaka » Fri Jan 15, 2016 8:45 pm UTC

sevenperforce wrote:I particularly loved this:
Randall wrote: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.

Exactly, exactly, exactly! And then when people pause, puzzled, and ask "Well why doesn't air look blue?" you just answer "Because it's usually not thick enough for you to notice." Which is basically true.

Landscape painters (and other visual artists) use this fact a lot. Distant parts of the landscape tend to have not only more air, strictly speaking, between them and the viewer's eye, but water vapor, dust, and/or other kinds of haze suspended in that air. So those features are shown tinted, and even slightly obscured, by a bit of a haze. This is usually bluish to represent the colour of air and water vapor, but sometimes other colours to represent dust or other particles. And it gets "thicker," often bluer, and more obscuring the more distant the painted object is meant to be.

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Re: What-If 0141: "Sunbeam"

Postby sevenperforce » Fri Jan 15, 2016 8:55 pm UTC

"I've got a pocket/Got a pocket full of sunshine"

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Re: What-If 0141: "Sunbeam"

Postby niauropsaka » Fri Jan 15, 2016 9:21 pm UTC

netsplit wrote:
Pfhorrest wrote:
netsplit wrote:The answer I find most satisfying is that the air is iridescent like a hummingbird feather and translucent, color depends on the angle relative to the light source.

That's not really accurate though, because it's not as though the sky near the sun is red and the sky far from the sun is blue. Two people on different parts of the Earth looking at (very nearly on a solar scale) the same angle toward the sun, but through different amounts of air, will see different colors, e.g. if it's noon where you are and you look at where Venus should be (not that you can see it in broad daylight), and it's dusk or dawn somewhere else and someone there is also looking at where Venus should be, you'll see blue at that spot while they see red-orange.


That's a good point about thickness of air affecting the color, so maybe iridescent isn't the right word. I can't think of a good single word or simple name that describes the coloring of the atmosphere. At short distances it scatters blue, at longer distances only red remains to be scattered. Its really the only thing we deal with of it's size in every day life, and particular color schemes happen at specific times so that's what langauge, at least English, went with.

That seems to be the definition of opalescent, as mentioned above.

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Re: What-If 0141: "Sunbeam"

Postby moti43 » Wed Jan 20, 2016 8:11 am UTC

I believe that randell forget the vacuum non-linearity that might save the earth.
When considering such high powers (10^23 KW) the vacuum itself has non-linearity parameter which will collapse the laser beam into a filament which will radiate in all directions and by the time the beam reaches the earth it will be harmless.

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Re: What-If 0141: "Sunbeam"

Postby cellocgw » Wed Jan 20, 2016 12:44 pm UTC

BFGaloot wrote:Someone asked if we could physically do this with mirrors. The answer is "no", since etendue (or radiance or luminance or in non-qualitative terms as used by laser jocks, brightness) is a conserved quantity. These quantities have units of power per steradian, and since the sun emits over 4 pi steradians, you can't just stuff it all into a collimated beam.

This is often missed by even experienced engineers, they often think that you can just put in a lens or something to increase the luminance of a source. As an example, if you tried to focus the sun's energy on a 1-meter diameter optical fiber, the vast majority of the light would not continue down the fiber but would leak out the sides since it is not confined within the numerical aperture of the fiber.


Well, yes, but then again what-if (sorry) you simply took a bunch of separate concave mirrors and focussed them all at the same point. Each mirror's output can't exceed the surface brightness of the sun, but even without an adaptive optic system to phase the mirrors you can add the intensities to get a pretty decent power density. Skipping around the "collimation" part makes the difference here.
For extra credit, calculate the force required to keep the mirrors in place, counteracting the total incident photon momentum.

ETA : already this what-if is in position number 3 on a Google search for that article on opacity
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Re: What-If 0141: "Sunbeam"

Postby GreenTom » Wed Jan 20, 2016 9:41 pm UTC

moti43 wrote:I believe that randell forget the vacuum non-linearity that might save the earth.
When considering such high powers (10^23 KW) the vacuum itself has non-linearity parameter which will collapse the laser beam into a filament which will radiate in all directions and by the time the beam reaches the earth it will be harmless.


Thanks, I was wondering about this...this is so much energy that something strange has to happen. I wasn't sure if pair production happens from very intense light of reasonable wavelengths. The energy here is ridiculous, the beam's density is 15kg/m^3, and just by mass-energy equivalance it's moving more mass than the amazon.

Assuming this beam does somehow arrive at the surface of the earth, the lights mechanical properties dominate. (Someone who actually knows physics feel free to tell me how I got this wrong).

Radiation pressure = E/c = 1.2x10^17 N. This is on 1 m^2, so the pressure is also 1.2x10^17Pa, which wikipedia tells me is around the order of magnitude of pressure in a atomic nucleus and about a million times the pressure at the center of the Earth. So, I think the "expanding cloud of plasma absorbing the beam" scenario doesn't play out. The beam easily shoves all the plasma out of the way, even when it gets to the center of the earth it can force the plasma into the core far easier than a bullet in a gun pushes the air out of the barrel.

A one square meter section right through the earth masses about 6x10^10kg. So, this beam can, by momentum alone, accelerate that by 5 million m/s^2. If the beam tracks a spot on the Earth, my vote is that 2-3 seconds after it starts, it forces a plug of iron plasma out the far side. Does radiation pressure in a beam push forward like my intuition says, or is it omnidirectional like a gas? If the former, it becomes a fountain of iron nuclei at way beyond escape velocity, if the latter, can it actually just hold a tunnel through the earth open and shine through?

Not sure what happens if it doesn't track, but I suspect it's still able to push 100s of km into the earth even if it's scanning across the surface at 30 km/sec.

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Re: What-If 0141: "Sunbeam"

Postby david.windsor » Wed Jan 20, 2016 10:08 pm UTC

With the energies involved, after any trivial bit of mater in the path of this beam 'becomes physics', how long before the Sun starts to leave the local group and how long till it hits lightspeed?
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Re: What-If 0141: "Sunbeam"

Postby Pfhorrest » Wed Jan 20, 2016 10:39 pm UTC

david.windsor wrote:how long till it hits lightspeed?

∞s.
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Re: What-If 0141: "Sunbeam"

Postby david.windsor » Wed Jan 20, 2016 10:50 pm UTC

Pfhorrest wrote:
david.windsor wrote:how long till it hits lightspeed?

∞s.

ok ok, 99% then. :lol:
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Re: What-If 0141: "Sunbeam"

Postby ps.02 » Thu Jan 21, 2016 5:49 am UTC

david.windsor wrote:
Pfhorrest wrote:
david.windsor wrote:how long till it hits lightspeed?

∞s.

ok ok, 99% then. :lol:

In what reference frame? I mean, it's already going 0.99c in some reference frame.

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Re: What-If 0141: "Sunbeam"

Postby Pfhorrest » Thu Jan 21, 2016 6:17 am UTC

In its own initial reference frame, I would assume.
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Re: What-If 0141: "Sunbeam"

Postby ijuin » Thu Jan 21, 2016 6:59 am UTC

GreenTom wrote:A one square meter section right through the earth masses about 6x10^10kg. So, this beam can, by momentum alone, accelerate that by 5 million m/s^2. If the beam tracks a spot on the Earth, my vote is that 2-3 seconds after it starts, it forces a plug of iron plasma out the far side. Does radiation pressure in a beam push forward like my intuition says, or is it omnidirectional like a gas? If the former, it becomes a fountain of iron nuclei at way beyond escape velocity, if the latter, can it actually just hold a tunnel through the earth open and shine through?

Not sure what happens if it doesn't track, but I suspect it's still able to push 100s of km into the earth even if it's scanning across the surface at 30 km/sec.


Roughly, then, the beam becomes an enormous laser cutter-like effect that effectively slices the Earth in half as the planet moves past, with only the Earth's gravity preventing the two halves from separating.

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Re: What-If 0141: "Sunbeam"

Postby eviloatmeal » Thu Jan 21, 2016 9:16 am UTC

ijuin wrote:Roughly, then, the beam becomes an enormous laser cutter-like effect that effectively slices the Earth in half as the planet moves past, with only the Earth's gravity preventing the two halves from separating.

Do the two halves make a coconut clop sound when they snap together?
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Re: What-If 0141: "Sunbeam"

Postby Neil_Boekend » Thu Jan 21, 2016 9:21 am UTC

eviloatmeal wrote:
ijuin wrote:Roughly, then, the beam becomes an enormous laser cutter-like effect that effectively slices the Earth in half as the planet moves past, with only the Earth's gravity preventing the two halves from separating.

Do the two halves make a coconut clop sound when they snap together?

Depends. Would the plasma from the vaporized part be dense enough to conduct sound?
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Re: What-If 0141: "Sunbeam"

Postby eviloatmeal » Thu Jan 21, 2016 10:36 am UTC

Assume you're standing very close to the coconutEarth. I'm not concerned about the sound traveling any considerable distance, just what it would sound like.

I'm thinking "dull thud", but maybe some of the molten stuff would make a squelch, if it's still in any sort of molten state after the cut?
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Re: What-If 0141: "Sunbeam"

Postby SDK » Thu Jan 21, 2016 2:34 pm UTC

Whatever the sound, there would be nothing "dull" about it. That is going to be a crash so loud that the pressure wave is likely going to be loud enough to kill anyone in close proximity (assuming they somehow haven't already died).
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Re: What-If 0141: "Sunbeam"

Postby ijuin » Thu Jan 21, 2016 4:28 pm UTC

eviloatmeal wrote:Assume you're standing very close to the coconutEarth. I'm not concerned about the sound traveling any considerable distance, just what it would sound like.

I'm thinking "dull thud", but maybe some of the molten stuff would make a squelch, if it's still in any sort of molten state after the cut?


I would think that it would be something like http://what-if.xkcd.com/57/ but on a much larger scale.

Hmm, that's a possibility for a new what-if: What if the Earth were sliced in half with a giant laser beam X meters wide?

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Re: What-If 0141: "Sunbeam"

Postby eviloatmeal » Fri Jan 22, 2016 10:20 am UTC

ijuin wrote:I would think that it would be something like http://what-if.xkcd.com/57/ but on a much larger scale.

Yes, more of a snap than a clop. That sounds reasonable.

ijuin wrote:Hmm, that's a possibility for a new what-if: What if the Earth were sliced in half with a giant laser beam X meters wide?

I'm thinking more along the lines of "What if a slice of the Earth X meters thick suddenly disappeared?"

Because this one already mostly covered the "immense laser beam" scenario; lots of plasma, lots of kids becoming human microwave-dinners, etc..

Or, "What if a slice of the Earth disappeared, and something (like really big PCB spacers) kept the two halves apart?" Would water from the sea start dripping rushing into the gap? Would it cool off the molten core, like the ventilation shaft on a Death Star? Could you fly an X-Wing along the trench?
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Re: What-If 0141: "Sunbeam"

Postby Mikeski » Sat Jan 23, 2016 4:54 am UTC

eviloatmeal wrote:"What if a slice of the Earth disappeared, and something (like really big PCB spacers) kept the two halves apart?"

There's no (known) material strong enough to do that. And if there was, the earth would just "melt" back together around them, because the earth is not strong enough to do that.

You're trying to make something like the bowling-ball earth, and it'll collapse for exactly the same reason. Anything that massive pulls itself into spherical shape with its own gravity. Also seen here.

This is also the reason that the "planet" with the ginormous notch cut in it, as seen in a recent sci-fi movie, is a bunch of hogwash.

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Re: What-If 0141: "Sunbeam"

Postby ijuin » Sat Jan 23, 2016 2:33 pm UTC

Said planet could indeed only maintain such constructs due to extensive use of anti-gravity technology ("repulsor lifts").

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Re: What-If 0141: "Sunbeam"

Postby keithl » Sat Jan 23, 2016 7:51 pm UTC

GulliNL wrote:And another question, when building a Dyson Sphere/Swarm with mirrors, aren't we already focussing the light from the star in the building progress? Every unit (mirror) that gets put in it's position blocks the light from going straight outwards to back to the star or another direction. ... Really, how does one build a Dyson Sphere?

I spent September through November studying how to do that - writing about that now, with some notes at http://server-sky.com/StaDyShell and related pages.

The purpose of this distraction is to estimate the eventual endstate, millions of years from now, of a nearterm technology I am developing. BTW, it is easier to just build and ship and ignore the long term consequences, like the first automobile manufacturers, or the current generation of data smog makers AKA software entrepreneurs.

A bit of pedantry first, Dr. Dyson credits the idea to Olaf Stapledon's space fantasy "Starmaker", it was an ignorant reporter who turned Stapledon's "shell" into Dyson's sphere. I label the variety I work on "StaDy" shells, both for "STAtite DYnamic" and "STApledon DYson", after the process and the pair of visionaries who taught us about these.

Statite shells are supported by P/c light pressure, and depending on reflectivity (one minus absorption) on the inner and outer surfaces, will balance different mass densities. By changing the type of reflection from specular to scattering, the light pressure can be modulated and and the light pressure thrust as well. This is how a statite shell can be gravitationally stable, although real shells will absorb some light and re-radiate it as heat, on both sides. Lots of complications, of course.

I studied a shell mostly made of ice at 50AU, at a temperature of 60K, with a mass density around 0.4 gram per square meter. There's more than enough ice and other materials in the Kuiper belt to build a complete shell, including the reaction mass you must eject from the solar system to shed the momentum of the orbiting objects you are stopping to build the shell from. BTW, we will keep Pluto and Charon, because they make excellent platforms to string a web of kevlar space elevator cables between - they are exactly co-rotating and isosyncronous. They will be used to slowly clear the rest of the Kuiper belt of objects, and thus become the first artificial planet (that is, be promoted to planetary status by artificial technological means).

The shell described in the whatif is perfectly reflective, and would rapidly fill with light bouncing around. Inside, it would soon look like the surface of the Sun in all directions. The Sun will keep emitting energy, so the surface of the sun will slowly get hotter and more emissive. The key here is "slowly" - if the shell was 0.1 AU out, 50 light seconds, it will take some time to fill the shell with light, and even more time for the surface of the Sun to warm significantly from it's current 5800K. The light coming out of the meter-squared hole would be at this temperature for quite a while. If it comes out of a long reflective tunnel as shown, it will still scatter in all directions when it leaves (en.wikipedia.org/wiki/Etendue), so the amount of light reaching the earth would be very very dim, appearing like a very distant and very hot star.

Over a vast stretch of time, the surface of the sun will get signficantly hotter and more blue, and the temperature of the light spectrum coming out the hole will increase also. Doubling the surface temperature increases black body thermal emissions 16x. In the very VERY long term, the surface of the sun might heat to millions of Kelvins, and the core somewhat more, which will reduce the nuclear reaction rate and total sun emissivity. I imagine the sun would grow to fill the sphere, perhaps adding gas pressure to the light pressure, and if it was a statite shell you would need to pile on a LOT of mass for the weight to balance both pressures. I'm no stellar physicist, but my guess is that overall, the sun would be much larger but emit much lower total power. Much of that power would be emitted as the kinetic energy of high speed incandescent plasma spewing out the hole, more collimated than the light, but still pretty wide when it reached the earth at 1 AU. Indeed, the plasma would probably be the source of most of the light.

Assuming this magic source of new mass (and the Earth orbit moving inwards to balance angular momentum and gravitational energy), the light coming out the top of the hole or reflective pipe would be incredibly intense and mostly UV and soft X rays, but emitted in all directions from a very small spot and not providing much total illumination.

Conclusion: A perfectly reflective shell built around the shell would produce dim light scattered in all directions, and a powerful jet of plasma. It would not behave like the what-if sunbeam. The W.I.S. requires all the light to be absorbed with 100.0% efficiency, conveyed with 100.0% efficiency to the Big Effing Laser, and converted to a perfectly collimated (zero etendue) beam with 100.0% efficiency. If you buy that, I can sell you this bridge in Brooklyn ...

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Re: What-If 0141: "Sunbeam"

Postby Znirk » Mon Jan 25, 2016 9:53 am UTC

keithl wrote:The [What If Sunbeam] requires all the light to be absorbed with 100.0% efficiency, conveyed with 100.0% efficiency to the Big Effing Laser, and converted to a perfectly collimated (zero etendue) beam with 100.0% efficiency. If you buy that, I can sell you this bridge in Brooklyn ...

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Re: What-If 0141: "Sunbeam"

Postby Priceguy » Tue Feb 02, 2016 12:19 pm UTC

This is the part that caught my interest:

"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."

Let's say that after ten years the ray encounters an Earthlike planet. In fact, skip "Earthlike"; by extraordinary coincidence there is a perfect copy of Earth, population at all, ten light-years away and in the path of the ray. Not only that, but the planet is magically stationary relative to the ray. What happens now, exactly? Presumably they can't see the ray coming as it's light; by the time you see it, it's already there. How do the copy-humans experience the coming of the ray? What's it like when the surface is heated up? What does it look like?

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Re: What-If 0141: "Sunbeam"

Postby Neil_Boekend » Tue Feb 02, 2016 3:22 pm UTC

A perfect laser of 1 meter diameter has a beam angle of about 0.116 arcsecond (using the Dawes' limit for telescopes, since the data for telescopes is far more available)
Some simple trigoneometry:
10 lightyears is 9.4605284e16 meters
tan (0.116 arcseconds) = tan(3,2222222e-5°)=5,6238386e-7 =diameter/9.4605284e16 meters
diameter = 9.46e16*5,62e-7=53e9 meters = 0,36 AU, or about the radius of Mercury's orbit.

Ergo the beam would be several times as luminous as the sun on Mercury, only far smaller. They'd see a small pinprick with massive, massive blinding brightness. The sky would be far brighter than a normal day. The planet would heat up quickly, to a thermal equilibrium at somewhere over 1000°C (if you include the sun they probably already had). The beings on that planet would all die.
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Re: What-If 0141: "Sunbeam"

Postby Beavertails » Tue Feb 02, 2016 8:37 pm UTC

Neil_Boekend wrote:The beings on that planet would all die.


Copy cockroaches would likely still survive.
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Re: What-If 0141: "Sunbeam"

Postby Priceguy » Wed Feb 03, 2016 7:15 am UTC

Neil_Boekend wrote:They'd see a small pinprick with massive, massive blinding brightness. The sky would be far brighter than a normal day. The planet would heat up quickly, to a thermal equilibrium at somewhere over 1000°C (if you include the sun they probably already had). The beings on that planet would all die.


Cool. Would this be sudden? As in, the copy-humans are walking around minding their own business when all of a sudden there is a blinding pinprick in the sky, brightening everything? Or would the day (assuming it's daytime on the side facing the ray) get brighter and brighter and as the copy-humans wonder what's going on, the pinprick becomes visible and then more and more blinding?

Come to think of it, what would it be like on the opposite side of the planet from the ray? Would it just become inexplicably warmer and then everything dies?

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Re: What-If 0141: "Sunbeam"

Postby Pfhorrest » Wed Feb 03, 2016 8:13 am UTC

How quickly is "quickly"? Would it be less than an otherearth day, or would everyone on the otherearth get to see the blinding pinprick for a while before the planet burnt to a crisp?
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Re: What-If 0141: "Sunbeam"

Postby Neil_Boekend » Wed Feb 03, 2016 9:42 am UTC

Well, I am just an idiot with a keyboard, some educated guesses and a love for these kind of things, while there are plenty of real world astrophysicists around here, but here is my best guess:

Let's first do some better calculations:
The beam has a diameter of 53x109. That is a surface area of about 2.2x1021m2.
The sun has a total energy output of 3.846×1026 W, This means that, if we assume the beam is simple, the intensity of the beam would be about 1.7x105 W/m2 (for comparison, an object at Earth's orbit currently receives about 1476 W/m2)
Of course the beam is not simple, it'll be strongest in the middle and taper of to the ends. Since I can't find exact numbers on that I just assume the energy density in the middle is twice the average => 3.4x105 W/m2.
The earth has a radius of 6.371.000 m, and thus the surface area receiving energy from the beam is 1.3x102. Ergo it receives 1.3x102 times 3.4x105=4.42x107 W.
Initially we're only going to heat the atmosphere. The earth's atmosphere has a mass of 5.1480×1018 kg and air has a specific heat of about 1 kJ/kg K
A watt is a joule per second. Thus 4.42x107 W = 4.42x104 kJ/s
This means that the atmosphere, on average, is going to heat up with about 8.5x10-15 K/sec, or about 0.0000003 K/ year. Global warming is faster than that. It's even less, because with that slow speed we'll also heat the rock, with a total mass of 6x1024 kg.

Hmm. That is far less than I expected. I'll have to check my calculations, because I may have had an exponent wrong somewhere. Feel free to check yourselves.
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Re: What-If 0141: "Sunbeam"

Postby SDK » Wed Feb 03, 2016 1:47 pm UTC

You definitely messed something up, because like you said, 1.7x105 W/m2 (your sunbeam intensity) is a hundred times more than 1400 W/m2 (what the sun supplies to the Earth). If the sun suddenly upped it's brightness by 100 times, you can be sure we'd all roast.

... q = mcΔT, so the mass is going to be on the bottom... okay, looks like you did that properly. I don't know where you went wrong. Your calculations look okay. If you're going to have sustained warming, you've got to warm the entire system, so using the total mass of air is good for a long term look. Short term the surface is going to warm much faster. Could that be the error? We're still out by several orders of magnitude...

Given that the sun heats the Earth on the order of 1K/hr (source: the night and day cycle), I'd assume we should be getting an answer on the order of 100K/hr here.
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Re: What-If 0141: "Sunbeam"

Postby sevenperforce » Wed Feb 03, 2016 2:20 pm UTC

Neil_Boekend wrote:Well, I am just an idiot with a keyboard, some educated guesses and a love for these kind of things, while there are plenty of real world astrophysicists around here, but here is my best guess:

Of course the beam is not simple, it'll be strongest in the middle and taper of to the ends. Since I can't find exact numbers on that I just assume the energy density in the middle is twice the average => 3.4x105 W/m2.

Because we can arbitrarily posit that the Copy Earth is at the center of the beam, it's fine to just use the peak intensity of 1.7e5 W/m2.

The earth has a radius of 6.371.000 m, and thus the surface area receiving energy from the beam is 1.3x102. Ergo it receives 1.3x102 times 3.4x105=4.42x107 W.

Errrr....

The radius of the Earth is 6.4e6 m, and so the cross-sectional area of the earth is π*(6.4e6 m)2, or 1.23e14 m2. I think that's what you must have gotten wrong. Multiply this cross-sectional area by the peak beam intensity of 1.7e5 W/m2 and you get 2.21e19 W, which a factor of 5e11 greater than your value.

Assuming the rest of your math was correct, we're looking at a rate of heat increase on the order of 15 K per hour.

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Re: What-If 0141: "Sunbeam"

Postby Neil_Boekend » Wed Feb 03, 2016 3:08 pm UTC

sevenperforce wrote:
Neil_Boekend wrote:Well, I am just an idiot with a keyboard, some educated guesses and a love for these kind of things, while there are plenty of real world astrophysicists around here, but here is my best guess:

Of course the beam is not simple, it'll be strongest in the middle and taper of to the ends. Since I can't find exact numbers on that I just assume the energy density in the middle is twice the average => 3.4x105 W/m2.

Because we can arbitrarily posit that the Copy Earth is at the center of the beam, it's fine to just use the peak intensity of 1.7e5 W/m2.
1.7e5 is the average. I don't have data on the spread pattern of lasers in vacuum so I assume the middle has an intensity of a factor 2 of the average. Exactly because we can arbitrarily posit that the Copy Earth is at the center of the beam.

sevenperforce wrote:
The earth has a radius of 6.371.000 m, and thus the surface area receiving energy from the beam is 1.3x102. Ergo it receives 1.3x102 times 3.4x105=4.42x107 W.

Errrr....

The radius of the Earth is 6.4e6 m, and so the cross-sectional area of the earth is π*(6.4e6 m)2, or 1.23e14 m2. I think that's what you must have gotten wrong. Multiply this cross-sectional area by the peak beam intensity of 1.7e5 W/m2 and you get 2.21e19 W, which a factor of 5e11 greater than your value.

Assuming the rest of your math was correct, we're looking at a rate of heat increase on the order of 15 K per hour.

DOH! Of course the cross sectional area is not 130 m2! That would be ridiculous.
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Re: What-If 0141: "Sunbeam"

Postby sevenperforce » Wed Feb 03, 2016 3:54 pm UTC

Yes, that would be ridiculous.

With the additional factor of 2 you mentioned before, that's 30 K per hour. Everyone will need to turn on the air conditioning at full-blast.

Of course that won't be possible, because everyone will already be burnt to a crisp in the firestorm that engulfs the entire surface. The initial impact of the beam with the upper atmosphere will turn it to plasma, which will begin to wrap itself around the Earth rapidly, and which will glow bright enough to set everything on fire at once.

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Re: What-If 0141: "Sunbeam"

Postby Soupspoon » Wed Feb 03, 2016 4:28 pm UTC

Priceguy wrote:Presumably they can't see the ray coming as it's light; by the time you see it, it's already there.
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Re: What-If 0141: "Sunbeam"

Postby ps.02 » Wed Feb 03, 2016 4:55 pm UTC

Priceguy wrote:Presumably they can't see the ray coming as it's light; by the time you see it, it's already there.

Well, if they can detect all those famous FTL neutrinos CERN found, maybe they get a little advance warning.

Oh wait, that wasn't real, was it.

(And come to think of it, the neutrino flux would extremely weak anyway, as they presumably can't be focused in a beam with the photons.)
sevenperforce wrote:With the additional factor of 2 you mentioned before, that's 30 K per hour. Everyone will need to turn on the air conditioning at full-blast.

But on the other hand*, PV arrays would finally make economic sense.

*Or "on the bright side", if you will.

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Re: What-If 0141: "Sunbeam"

Postby Jorpho » Thu Feb 04, 2016 6:03 am UTC

Bloody heck! New What-Ifs started up, and I only just noticed!

The sky is dark at night[citation needed] because the Sun
The citation here links to Flunixin and I'm afraid I'm not getting the joke. Could someone please enlighten me?


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