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.