Welcome to Jester's Trek.
I'm your host, Jester. I've been an EVE Online player for about six years. One of my four mains is Ripard Teg, pictured at left. Sadly, I've succumbed to "bittervet" disease, but I'm wandering the New Eden landscape (and from time to time, the MMO landscape) in search of a cure.
You can follow along, if you want...

Tuesday, March 26, 2013

Luminaire scary math

I thought it would be fun to play around with the :scary math: associated with the fall of Shiigeru into Caldari Prime.  Don't worry, I'm not gonna go all "Reel Physics" on you and spout a lot of formulas, just conclusions.

First, let's look at the constants involved.  Caldari Prime itself is a fun little impossibility.  The in-game information on the planet reports its radius as 30217 km and its surface gravity as 10.3 m/s2.  For reference, the two figures for Earth are 6371 km and 9.8 m/s2, respectively.  A terrestrial planet with a much higher radius than Earth would normally have correspondingly higher gravity due to higher mass.  However, planetary density plays a part as well.  Earth is quite dense as befitting a planet with a high concentration of heavy metals and an iron-nickel core, but terrestrial planets without heavy metals are quite possible.(1)  To account for her relatively comfortable gravity, we must assume Caldari Prime is quite poor in heavy metals, and much less dense than Earth with a silicate core of some kind.

In any case, knowing these two figures gives us a mass of Caldari Prime of about 1.4x10^26 kg.(2)

The mass of Shiigeru is 2.43x10^9 kg, and is 18km long, 2.7km wide and 4.2km high.  Doing some back-of-the-envelope calculations results in a density of the ship equivalent to a modern U.S. aircraft carrier or typical ocean liner.  This is not a contradiction: the interior of Shiigeru is mostly air, after all.  The mass figure quoted is for the hull itself; presumably the fittings also have a mass equivalent and the fuel certainly does, so I will be assume the total fueled mass of Shiigeru is around 4.0x10^9 kg.

We know (from Luminaire Local chat) that Shiigeru started the fight in an orbit 325 km above the surface and was attempting to maintain a stationary position over the city of Arcurio.  To maintain this position would have required an enormous expenditure of energy, a powered orbit.  Given the radius of the orbit and the mass of Caldari Prime, we can calculate the normal velocity needed to maintain this 325 km orbit: 17.5 km/s.  This speed would allow Shiigeru to maintain a stable orbit over the planet, but Shiigeru isn't trying to do that; she's trying to maintain a fixed position over Arcurio.

That requires a reduction in speed.  We don't know how long the day is on Caldari Prime -- it's not included in the in-game information for the planet that I could find -- but let's say it's 24 hours.  That would mean Arcurio moves at around 2.2 km/s around the circumference of the planetary sphere so that's about the speed Shiigeru needs to match in her own orbit.  That accounts for Caldari Prime's day as the surface rotates.  To stay over this fixed point on the surface, Shiigeru has to reduce her speed to that and then maintain it.  The only thing a longer day does would be to further reduce that speed.

And that reduction in speed is what causes Shiigeru to fall to the surface after losing power so CCP got that part exactly right.  Since she didn't and couldn't maintain the required higher orbital speed to maintain orbit, down she goes.

From the excellent chronicle by CCP Abraxas "After the Fall", an eye witness indicates that Shiigeru breaks in half before falling.  For fun, let's assume that it's the front half he sees; that seems to be consistent with the visual DUST 514 map.  For more fun, let's assume that the rear half including the engines and most of the power systems is destroyed and falls to the surface as debris.  That is both consistent with our eye witness account and consistent with multiple impact craters visible on the surface.  Now fortunately, Shiigeru isn't made of solid rock like a meteorite.  As noted above, most of her is, in fact, air with a very low density.

Still, four billion kilograms falling on your planet is nothing to sneeze at.  The destruction of Shiigeru disintegrates only a very small portion of her total mass.  The rest falls on Caldari Prime.  We know from follow-up in-game news items that the debris fell about 700 km away from Arcurio.  This is also fairly consistent with Shiigeru's velocity at the time of her destruction and her debris would have maintained this velocity before being accelerated straight down toward the center of the planet.

Based on her velocity at the time of her destruction, the surface gravity of Caldari Prime, and some assumptions about the density of Caldari Prime's atmosphere and how the front half of a Leviathan would tumble in atmosphere (very little), I calculate that it would have taken Shiigeru and her debris very little time to strike the surface after her engines were shut down at her destruction: something between four and five minutes if my math is accurate.  CCP also gets this part right: the impact and debris field is relatively compact, all things considered.  Shiigeru came down very much like a spear.

And in the process, she and her debris would have released one petajoule of energy per second into the planet's atmosphere and surface, likely punching a hole right through the planet's crust on impact.  That's a one and fifteen zeroes.  CCP gets this one right again in today's in-game news item which says the crust in the area is destabilized.  Too right!  Put another way, Shiigeru bathes the impact zone with one trillion kilowatts of energy as she hits.  Yikes!

The debris field is described as encompassing some two million square kilometers.  This is consistent with a circle with a radius of some 800 kilometers, putting Arcurio within the blast zone.  Energy of this type dissipates in an inverse square relationship from the center of the impact point but there's an enormous amount of energy involved.  Those within 200 kilometers of the impact point would have been subjected to approximately 10 kilowatts per square meter of radiated energy.  Those in Arcurio itself would have been subjected to about 750 watts per square meter.

Full noon-time Sahara sunshine on Earth is rated at about 1000 watts per square meter.  But this is nothing like a little extra warm sunshine, oh no.

If you were within 200 kilometers of Shiigeru's impact point, you were subjected to some 200 degrees Centigrade of heat.  If you're not a DUST 514 soldier in a space-rated drop-suit, you're dead, regardless of any shelter you managed to find.  Even DUSTies would have required shelter from the blast wave.  Those standing outside in Arcurio when Shiigeru came down who were not wearing sunblock of at least SPF 300 are extremely unhappy and had their lungs fried as the temperature increased some 50 to 60 degrees Centigrade for a period of several minutes.  The temperature differential and blast wave almost certainly would have created a sizable pressure wave manifested as gale- or possibly hurricane-force winds across the city for several minutes as well.  In short: those who stood outside in Arcurio to gawk were killed.  That said, people in shelter away from windows or doors, or underground, would survive the effects as long as a collapsing skyscraper didn't fall on them or the building they were in didn't collapse.

Coincidentally, the asteroid that landed on the Yucatan peninsula on Earth 65 million years ago is also believed to have been nine kilometers long.  However, Shiigeru's front half is mostly air, not rock; she has a much lower mass than a nine kilometer long asteroid.  Much of the damage done to Earth 65 million years ago is believed to have been done through pulverized rock and debris exploding back into space and then falling across half the planet.  Shiigeru's lower mass and the greater radius of Caldari Prime protect her from this fate.  Depending on the radioactivity of her power systems and engines, this was not an extinction level event.  In addition, the latest news item mentions "intense atmospheric decontamination" happening on a planetary scale to prevent this sort of ecological catastrophe, so CCP doesn't have to change Caldari Prime to a Barren type planet just yet.  ;-)

One last fun bit of scary math.  The initial chronicle "After the Fall" describes Shiigeru as a "scar" across the sky.  That set me wondering how big a Titan would appear from the surface of a planet.  That's another easy calculation.  At 325 km away, an 18 km long object would have crossed 3.2 degrees of the sky, or a little over six times the size of a full moon when viewed from Earth, or about the size of your fist when held and viewed at arm's length.  That's big enough to be described as a "scar", I guess.  ;-) I know (from a player that was there) that Shiigeru's 325 km orbit was significantly planet-ward of her normal static position, by some several thousand kilometers.  At 2000 km away, Shiigeru's size shrinks to 0.5 degree, or about the size of your thumbnail held at arm's length.  At 10000 km away, Shiigeru is just a moving dot.

But it's probably safe to say that Shiigeru occasionally dropped to that low orbit to make a visceral point to the Gallente citizens on the planet, so that's probably what our unnamed story-teller meant when he used the word scar.

Anyway, hope you've enjoyed this bit of :scary math:.  Hopefully, most or all of my calculations are correct but if you want to challenge some of my math in the comments, go for it!


(1) The in-game reported density of Caldari Prime is the grossest possible fiction and must be ignored.  The game reports 2907.7 g/cm3, when 2.907 is probably much closer to accurate.
(2) The in-game reported mass of Caldari Prime is also wrong, but not by quite as much.

33 comments:

  1. Actually, with such I large radius I would venture to a guess that a metallic core would still be an option. So long as it was surrounded by a thick outer layer of lighter elements.

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    1. Maybe. With that radius and surface gravity I calculate a density of ~1.2 g cm^-3, which is significantly less dense than silicon. It is, in fact, about the same density as glycerol or PVC.

      Similarly dense objects in our system are primarily composed of water, which Caldari Prime emphatically is not. In fact, its surface is 80~90% land, looking at the planet view. What the fuck it is actually supposed to be made of is a mystery, especially given that the surface will have to be much less dense than the core. I'd have to suggest some sort of light organic material, like wood. Fuck, maybe it actually is plastic.

      If there's any metal in it, it's definitely nowhere near the surface.

      I think it would cause less headaches all round if we just assumed that 2.907 g cm^-3 is the density and the stated radius is gibberish. That's a pretty sensible density for a terrestrial planet, if a little on the low side.

      Radius with that would be ~12,700km.

      I have to say that I'm disappointed that CCP's planet stats are such gibberish. The maths involved in generating these things is relatively trivial; it's by far the easiest sort of procedural generation. :(

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    2. Agreed. A planet with a radius of 30,000km would be half the size of Jupiter and bigger than both Neptune and Uranus. My material science is not up to the task but frankly I think the stated radius and gravity is physically impossible if Caldari prime is to have a solid surface.

      For reference the densities of the four rocky planets in the solar system range from 3.96g/cm3 (Mars) to 5.51g/cm3 (Earth).

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    3. While complaining about unrealistic mass/radius, take a look at stargates. Black holes, every one of them

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  2. On a completely different note ... has anyone attempted to calculate the loss of human lives during this event? According to official numbers a (promethean?) titan has a maximum capacity of about 70,000 - 145,000 people, with Caldari vessels generally being located at the mid to upper range. However, given the fact that the Shiigeru was on permanent deployment far into enemy territory, Most of the crew's families were probably stationed on board, so a total complement of 100,000 or more people aboard is likely. However, given the relative small size of the Gallente assault force, the Shiigeru should have held out pretty long before finally going down. Sadly, we do not know the exact fitting of the Shiigeru, but we may make some educated guesses. Given from the loot dropped, we can assume that the Leviathan had a full rack of CN active shield hardeners fitted, with at least one CN Invul. In the lowslots I would assume a DC II and two faction PDS, with the rigs being a full rack of T2 CDFE. For the damage spread I will assume 75% therm, 15% kin, 5% each EM and explosive. This would result in about 17 million eHP. World news stated the Gallente attack force to consist of 4 Nyx, 25 Moros and 11 Thanatos. With each Nyx doing 10k DPS, each Moros 11k DPS and each Thanatos 1k DPS, the Gallente had an combined DPS of about 326k DPS. For the combined capsuleer force, I will assume a combined DPS of 100k. Sadly, no killmail of one of the Caldari carriers appeared, so I cannot extimate the tank they could have generated on the Levi. However, if the Gallente would be smart, they would have nuked the carriers first with their DPS. Given this figures, the Shiigeru would have gone down within mere 40 seconds. (Seriously, the Leviathan sucks) However, since 40 seconds are hardly dramatic, lets just assume that the Titan held out for 5 minutes of concentrated fire. I seriously doubt if it is possible to evacuate such a massive ship in such a short time. We don't even know if the admiral in charge of the Shiigeru gave command to abandon ship (this 'genius' thought it would be smart to kill a CONCORD ship after all). In any case, only a very small fraction of the people on board would have been evacuated. However, we sadly know nothing about the technology of escape pods in EVE. If they are like our capsules, those who manged to get out of the Shiigeru should be rather fine, save for becoming POW and stuff. But if they are these stupid low-tech escape pods seen in most of science fiction, I doubt they could generate nearly enough thrust to signifcantly alter their descend vectors ... meaning they just got crusher/vaporized when the wreckage of the Shiigeru impacted. So we look at 100,000+ losses on the Shiigeru alone, with the total amount probably numbering in the low millions, and that is without the planetary casualties.

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    1. [ 2013.03.22 17:55:51 ] Visera Yanala > THIS IS [CN] SHIIGERU, PRIMARY REACTOR CONTAINMENT FAILURE - SECONDARY REACTOR ONLINE. PRIMARY MAGPULSE PROPULSION SYSTEM FAILURE - WE ARE ADRIFT
      <...>
      [ 2013.03.22 17:59:27 ] Visera Yanala > THIS IS [CN] SHIIGERU, ALL HANDS ABANDON SHIP. REPEAT, ALL ABLE PERSONNEL ABANDON SHIP.
      <...>
      [ 2013.03.22 17:59:58 ] Visera Yanala > THIS IS [CN] SHIIGERU, ALL HANDS ABANDON SHIP. REPEAT, ALL ABLE PERSONNEL ABANDON SHIP. - FULL REACTOR CONTAINMENT FAILURE IMMINENT

      At 18:00:11 my Hobgoblins hit the last time. But I assume even after the Titan was destroyed in gameplay terms there was still a chance to get to the pods.

      So I would assume 1-2 Minutes time for the "able personnel" to get to an escape pod. I also assume civilians and non-able personnel got out before that.

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  3. Does anyone have video or screen caps of the Shiigeru crashing into the planet? Or is it just lore text?

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    1. It's just lore. In "reality", the titan wreck appeared, the expensive stuff was looted by an Enyo, the less expensive stuff was looted by a hauler, and then someone salvaged the wreck causing it to slowly vanish from the field.

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  4. I sat staring at my keyboard trying to think of a way to frame a tongue-in-cheek CSM election question from this post, but I didn't get anywhere. ;)

    In lieu of that, good post, +1

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  5. WARNING: Seriously scary math:
    The minimum speed required for a certain orbit distance is always given by the formula a=v^2/r, where a =Gm/r^2.

    The minimum velocity needed for the Shiigeru to maintain its orbit at 325km above the planets surface is 17 km/s. Any slower and it would plunge into the atmosphere. Solving the previous equation for r, and setting v = 2.2km/s, the orbit distance for the geosynchronous orbit above the city is

    r = G*m/v^2 = 6.67E-11 m^3/(kg*s^2)*1.4E26kg/(2200m/s^2) = 1,929,338 km, or 1,899,121 km above the planet's surface.

    I think my math is correct here, If anyone spots an error, feel free to point it out.

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    1. Your math looks fine, but we're 100% sure of the 325km low orbit because that's what was stated in local by the Shiigeru's pilot. Therefore, Shiigeru would have had to maintain a thrust vector away from the planet's center of mass that also maintained the difference between the 17.5 km/s speed needed for a stable orbit and the 2.2 km/s speed needed to hold position over Arcurio.

      The thrust needed to maintain that vector against the force of the planet's gravity would have been extremely substantial and when that force was removed, Shiigeru indeed fell into the planet's gravity well.

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    2. Ah, that makes sense. In all of my physics classes we never dealt with using thrust like that, but it's a pretty obvious thing. That's some serious thrust though.

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  6. For comparison the recent Chelyabinsk meteor released about 1.8PJ total [wikipedia]. Which was mostly kinetic energy since the meteor was relatively light compared to Shiigeru but travelling much faster. I think your statement of 1PJ per second energy release is misleading since none of the gravitational energy is going to get released until Shiigeru hits the atmosphere ~100km up, say around halfway through the descent. Therefore the energy release will start later and will be more intense.

    Mike


    Nitpick : holding a position 325km over a fixed point on the ground isn't really any sort of 'orbit'. At least not for Earth or Caldari Prime.

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    1. Yes, and yes. I simplified the orbital mechanics quite a lot. And it's going to release a lot of energy as it passes through the atmosphere. The total energy release will be partially into the atmosphere (causing the heating), partially into the ground (causing more heating), partially due to the explosion throwing more debris well clear of the thickest part of the atmosphere where it will fall through a second time (causing yet more heating).

      I just calculated the total energy released based on mass and gravitational forces.

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    2. Counter-nitpick: 100km is the conventionally accepted edge of "space" for Earth, so as long as the Leviathan is in "space" it can be considered to be in geosynchronous orbit.

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  7. Assuming that your 1 Trillion kW estimate is correct and the unit converter isn't lying to me, the impact would be equivalent to an 860 Mt TNT explosion, or 3.8 times the energy released in the explosion of Krakatoa. For comparison: The largest nuclear bomb ever tested on Earth had 'only' a 57 Mt yield. (http://en.wikipedia.org/wiki/Tsar_Bomba).

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    1. Seems legit. This impact would be every bit as damaging as a good size volcano explosion. See Mike's comment above.

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    2. And something I just thought of: seismic shockwaves. I wonder how far they would have been felt without instruments (taking the lower density of the planets material into account).

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    3. And this is still supposed to be orders of magnitude smaller than the devastation that the DD would have unleashed on the planet.

      ...given that a DD is supposed to be a mass-extinction event, do you think we could use this to work out an HP value for planets?

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    4. Does it not bother anyone else that the mostly air-filled, shieldless and severely battered and hence structurally compromised (from previous bombardment by the Gallente fleet) hull survived the impact relatively intact, impaling itself into the planet and towering over its surface like some sort of apocalyptic monument? Considering the energies quoted by the parent, everything in the impact zone but first and foremost the impactor itself would disintegrate on a microscopic scale stern to bow many times over. I know deformation physics isn't at home in EVE much but the assumption of Shiigeru impacting as a rigid body totally blows out of the water the whole scenario, wasting in the process all the effort invested previously in getting right other tidbits such as orbital speeds and impact zone radius.

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  8. http://impact.ese.ic.ac.uk/ImpactEffects/
    useful calculator for impact effects

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  9. awed. thanks for detail. you just made a well planned event more real.

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  10. nerds

    Don't get me wrong, I'm a numbers guy in RL, but trying to impart RL physics to a game where the physics are iffy, at best, is a futile exercise. Nothing really orbits anything else in Eve. The planets don't orbit around their stars, ships "in orbit" just hang in space with zero indicated velocity, the physical numbers for planetary mass are bogus to begin with.

    "That's so awesome!" Right. And about as far removed from reality as we're likely to ever get. Spare me the calculated release of energy in Joules. Please.

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    1. You must be a hoot at parties.

      But if you want a practical reason: part of the fun of what-if exercises like this one is to identify all the assumptions you have to make in order to create a coherent picture, and then see how coherent the picture is. Kind of like an episode of Mythbusters where they first bust the myth itself, but then keep working on it to figure out what it would take to make the myth real (usually this involves explosives).

      It trains out-of-the-box thinking, and an awareness of how many assumptions we make daily without even thinking about them.

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    2. "Some people can read War and Peace and come away thinking it's a simple adventure story. Others can read the ingredients on a chewing gum wrapper and unlock the secrets of the universe."
      Lex Luthor
      Ripard Teg = Lex Luthor?

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  11. I'm struggling to fit a frig for faction warfare and Ripard can spend his time thinking about these things - I'll never catch up:-( Interesting read - I enjoyed it. Does anyone have any asprin?

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  12. There's also the possibility that the energy released was lower. After all, in a system that big, you distribute things. So some of the reactionless engines may have still been online. Not enough to keep it from crashing, but reducing it from being /quite/ so devastating.

    maybe. ;)

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  13. Something that may be worthy of comment is what affects this will have had on global weather patterns. The displacement of air and the heat added into the atmosphere will have surely caused a whole plethora of extremely severe weather patterns across the entire world, which should be still causing masses of damage and loss of life.

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    1. As the latest news mentions "intense atmospheric decontamination", I think this is unlikely to be a problem. Future tech, and all that.

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    2. Perhaps I took the "intense atmospheric decontamination." to be removal or radiological, and other harmful particles and possibly dust from the atmosphere, but not weather manipulation.
      Still I guess its possible that at the same time they are able to correct pressure changes and disperse cloud formations without intense rainfall or reduce tidal waves/tsunami's.

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  14. Has anyone commented on the fact that the planet is now exposed over its entire surface to a dust who knows how thick containing toxic heavy metals and whoknowswhat radioactivity?

    I think back to the internet classic analyzing the destruction of the deathstar and the Ewok planet.
    I hope CCP revisits the planet 6 months from now to see how much of the population is dying or dead from radiation poisoning and exposure to toxic reactive metals.

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    1. As the latest news mentions "intense atmospheric decontamination", I think this is unlikely to be a problem. Future tech, and all that.

      And yes, I was all prepared to bring up that Death Star post. ;-) Turns out not to be necessary.

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