Nkllon Shield-Ship Analysis
The Nkllon shield-ships were specialized vessels built by Lando Calrissian for protecting starships en-route to the planet of Nkllon which very closely orbited its sun, Athega. Curiously enough, the Nkllon mining installation has often been used by Star Trek fans as "evidence" against Star Wars technology, but in reality we will see that it is evidence for Star Wars technology, particularly Star Wars mining technology.
The Nkllon shield-ships are extremely useful for the purposes of analysis, because they used a combination of radiative and convective heat transfer processes to cool their 800m diameter shield cones. They did not use energy-shielding of any kind, so we can use them to obtain fairly accurate estimates of the power intensity present in orbit around Nkllon (ref. Star Wars Essential Guide to Vehicles and Vessels).
Some have attempted to analyze the Judicator, an ISD which remained in orbit around Nkllon without the protection of a shield-ship long enough for ground assault team to execute its mission and which suffered serious damage, but there are too many unknown variables in the case of the Judicator: its orientation, its shield status, the extent to which the endothermic phase-change associated with armor vaporization cooled the vessel, the length of time it spent in orbit, why it didn't simply approach the planet while staying in its shadow, whether there was similar incompetence when they approached, in terms of their approach vector, etc.
The shield-ships are much easier to analyze than the Judicator because they have no energy shields and their orientation is known to be pointing directly toward Athega. They were absorbing solar radiative energy over their entire front face, and they were emitting radiative energy over an area at least twice as large, since the extensive heat-conduction system suggests near-isothermal operation over the entire dish (both sides) as well as a portion of the 400m long pylon.
An extensive network of heat-radiating pipes and fins is also described, as well as a "venting system" which must slowly bleed coolant material into space as a method of removing excess heat. Obviously it can only carry a finite amount of this coolant material (perhaps liquid hydrogen, stored at high density, slowly heated to high temperatures and released through the vents during high-load periods), so it must be used only for the short period that the ship must be exposed to Athega's rays. The fact that these extra measures are necessary is proof that the simple radiative output of the dish and the radiating portion of the pylon is actually a lower limit for the radiative power being absorbed by the vessel as it approaches Nkllon, otherwise these extra measures would not be necessary.
By basing our calculations on the radiative effect of the dish and the pylon alone, we can therefore come to a lower limit of the power being absorbed by the shield-ship (remembering that under steady-state conditions the power absorption must be equal to the power dissipation), and we can therefore determine the power intensity at Nkllon's location, from which we can determine how close Nkllon would have to be to Sol in order to absorb the same power.
P = esT4
P = Power radiated per square metre
e = Emissivity
s = Stefan-Boltzmann constant
T = Surface temperature
Emissivity: the designers would obviously choose a high-emissivity surface. Although it is often assumed that highly polished metals are good emitters, they are actually very poor emitters. They make good reflection surfaces because they reflect incident light in a predictable direction rather than emitting large amounts of radiative energy, and in fact very rough surfaces are much better emitters than smooth surfaces for any given material because a rough surface will have many times more surface area (at the microscopic level) than a highly polished smooth surface. An example of a high-emissivity modern material is AISI 347, which has an emissivity e = 0.90 at 1200K when highly oxidized (ref. page A27, Fundamentals of Heat and Mass Transfer 3rd Edition, by Incropera and Dewitt).
Surface temperature: it is reasonable to assume that an advanced society like the Star Wars civilization would be able to create materials with maximum service temperatures at least as high as typical 20th century engineering materials, and that they would use those materials for this specialized application. We can also assume that the shield-ship's dish was running at its maximum service temperature because of the extraordinary measures taken to dissipate heat (some of which we do not even account for at all). The melting temperature of thorium dioxide is 3600K (ref. page A13, Ibid), so T=2500K is a reasonable estimate.
s = 5.67E-8 W/m²·K4 (ref. page 837, Fundamentals of Physics 2nd Edition, by Halliday and Resnick).
POUT = esT4
\POUT = 0.9 · 5.67E-8 · 25004
\POUT = 2 MW/m²
Surface area A = 2(dish area) + (pylon cooling section area)
\A = 2pr1² + Lpr2²
\A = 2p(400²) + 60·p·45²
\A = 1.39E6 m²
Therefore, the total power being dissipated by the Nkllon shield-ships in orbit around Nkllon was most likely in the area of 3 TW. If we divide this total power output by the frontal area of the dish, we can determine the intensity of the power input:
PIN = APOUT / pr1²
\PIN = 6 MW/m²
Location of Nkllon
Some Federation cultists have taken to claiming that Nkllon's surface conditions were similar to Mercury, the first planet in the Solar system. However, the surface temperature of Mercury is less than 700K even at its hottest extreme, and this is totally insufficient to melt most primitive 20th century engineering materials. Since starship hulls and the Nkllon mining facility were easily melted by Athega at Nkllon's orbital distance, Nkllon was obviously undergoing radiative bombardment greatly in excess of that withstood by Mercury. As usual, these Federation cultist claims come with no quantitative analysis whatsoever, and they have no answer for analyses such as this one other than simply repeating their original claims.
Since the power intensity absorbed by the shield-ships was at least in the 6MW/m² range, we can deduce that Nkllon, if it were located in the Solar system, would be roughly 2.25 million km from the centre of Sol, or 1.55 million km from the surface of Sol (by way of comparison, Mercury is 58 million km from Sol). This places Nkllon in the outer regions of Sol's corona, and this is a lower limit, which completely ignores the shield-ship cooling tubes and fins, as well as the mass-venting system! Clearly, either Athega was an exceptionally luminous star or Nkllon was extremely close to it. The fact that they could maintain civilian mining facilities in such conditions reinforces the fact that they are known to mine tibanna gas from the corona of stars (ref. Rebel Dawn) and the fact that they can mine Bespin's lower atmosphere even though its temperature is close to the temperature of a star's photosphere (ref. Star Wars Illustrated Universe).
We must also remember that the Star Destroyer was in no danger is actually being destroyed; it suffered damage to some of its more delicate externals, such as antennae and light gun barrels. Its shields were never mentioned; it is possible that they were already drained from some other incident, or they suffered some damage from attempting to jump into the system so close to the planet (since realspace energy releases affect ships in hyperspace, as described by Han Solo in ANH, it is probable that there are deleterious effects associated with using hyperspace so close to a star). The fact that a civilian-built shield-ship could survive in that environment is proof that an Imperial military ship could have survived had it been properly prepared.