Pro-Wars debaters like to use the scene of asteroid being fired on by a Star Destroyer in The Empire Strikes Back to claim huge firepower estimates for turbolasers, somewhere in the range of mega-uber-gazillions of mega-uber-google-gazilla-joules. They say the asteroids are totally vaporized, and that the asteroids are very large.
Let's take a look at that, shall we?
The "Bad Science Argument" from 'The Ambivalent DMZ':
One debater has pointed out a serious flaw in one of the most touted calculations for asteroid-destruction firepower. *Even if* we grant the energy levels the pro-Wars debaters generally claim for turbolasers, it is not possible for them to have totally vaporized the asteroid, as is claimed. Observe:
Wong's argument is a case of "bad science" rather than
"pseudoscience" - he applies some physical principles to the
and yet avoids others which could critically effect the results. This isn't comparison shopping, folks - you can't choose
which physical laws you want to apply if you go down this road - it's all or nothing. An analogy would be the calculations to determine a
man falling off a cliff - what speed does he have before impact? - the answer is much higher if we forgot to account for air resistance.
Silicates have very poor thermal conductivity, even given the
(unspecified) iron content. Given the timescale over which the energy
is absorbed (1/12s), we can expect local vaporisation to occur almost immediately. This local expansion is much greater than that required
to blast said asteroid apart.
The "blobs of superheated liquid" can only be from the area
immediately adjacent to the initial impact. The vast bulk of the
asteroid has been shattered and dispersed long before they have absorbed sufficient energy to "visibly glow."
The "lower limit" calcs are nothing of the sort. The figure
obtained is meaningless, based on a false assumptions - namely that the entire mass of the asteroid is vaporised, and that the energy
is absorbed uniformly and instantly throughout the entire mass (this second assumption also flies in the face of all known physics).
Pro-Wars debaters attempt to override the physics lesson mentioned above by claiming that the melting and vaporization would be supersonic, meaning that the expansion stress on the rock wouldn't even have a chance to start breaking it apart before the entire rock was simply gone.
However, this is also contradictory to physics. Impact shockwaves are not always subsonic phenomena, unlike the normal elastic and seismic waves that the pro-Wars debaters seem to be thinking about. (In rock on Earth, the speed of sound (or, to use a more intuitionally valid term, the speed of your average vibration) is going to be around three kilometers per second, or about ten times the speed of sound in air. Solids allow for faster vibration wave velocity, since they are more compact, molecularly.) For example, a meteor impact on the surface of Earth can cause pressures of 100 GigaPascals on the target material, which will vaporize and melt much of the surrounding target rock. What's happening there is that a meteor strikes at a speed far greater than what the rock could transmit elastically at the speed of sound. The kinetic energy of the meteor therefore is moving at supersonic speeds, beyond what the rock could otherwise tolerate. Therefore, the kinetic energy gets translated to heat, which melts or vaporizes the immediate area of impact. Further outward, shock pressures decrease exponentially as the supersonic shockwaves travels through more rock. On a planetary impact site, shockwave pressures of 5-50 Gpa will "only" cause metamorphism, depending on the material. 5 Gpa is the usual lower limit for what is referred to as the Hugoniot Elastic Limit, beyond which irreversible distortions of the target material occur, ranging from fracture to metamorphosis of the rock types.
It is only when the shockwave weakens to 2Gpa that the shockwaves transition from supersonic to sonic and subsonic velocities, and become the seismic waves we all know and love. (in progress, more details to come)
Note: This site has the most succinct quote in reference to something I've read repeatedly lately about asteroids . . . that they are often mere conglomerations of asteroidlets:
"Not long ago, astronomers thought of asteroids as rocks, perhaps rubble covered, but still mainly single bodies. But evidence has accumulated that asteroids are rubble piles all the way through, loosely bound together by what is generously called "gravity" (escape velocity is 11,000 meters per second on Earth but less than 1 meter per second on a typical small asteroid)." . . . "Crater chains on the moons of Jupiter, on Earth's moon, and on Earth itself also point to the gravity-induced disintegration of many asteroids prior to impact. Asteroids which rotate fast enough to fling pieces clear are extremely rare -- only two are known -- which suggests that these are the rare single-rock objects."
For example, we know the densities of several asteroids in our own solar system to a very good degree of accuracy. Some, like Eugenia, are only 1200 kg/m3, whereas others such as Ida are in the range of 2600 kg/m3, plus or minus 600kg/m3.
This may explain the picture below, wherein asteroidlets are visible after a collision between two asteroids. These asteroidlets are not propelled in any particular direction, instead simply sitting there. A loose conglomeration of material might demonstrate this, also, since individual asteroidlets would be unlikely to impart significant velocities on their fellows, as compared to fragments of an obliterated solid object. This also suggests additional reason for the fragmentation of the turbolasered asteroid.
Note: the following is unedited, and may thus appear to be something of a "stream-of-consciousness" piece. However, it should be understandable.
I will revise this as soon as possible.
In TESB, we see the Falcon enter an asteroid field while being pursued by four TIE fighters. In the early phase of this, we see, outside the cabin of the Falcon, an asteroid come flying from the right, colliding in the upper center of the screen with a larger asteroid.
This results in a bright flash, followed by a quick, gaseous explosion that dissipates within a scant few frames. The collision causes the total destruction of the two asteroids, leaving only a small dust cloud and a large number of asteroidlets that the Falcon flies through. The asteroidlets cause no apparent damage, though they do cause a little shake.
Were we to compare this to the scene in which an ISD is popping asteroids later on, we find that the effects are remarkably similar. We observe the destruction of an asteroid in a quick explosion that dissipates rapidly. There are virtually no glowing embers drifting off from either destroyed asteroid. The only debris from the explosions is seen by the Falcon, which happens to fly through the apparently cool asteroidlets.
The question is, could similar asteroidlets have resulted from the later scene, where turbolasers are being used? Such asteroidlets would not have been visible in the Star Destroyer scene, much as they were only barely visible in the Falcon scene until the Falcon was going through them. The popping scene explosion seems less detailed, somehow, possibly due to a difference of range or scale.
Granted, there is a difference between a turbolaser hit and a hit from a smaller asteroid, but the energy involved can be determined in both cases.
Unfortunately, it is difficult to get a size estimate of the Falcon's larger asteroid (the one that was hit by the smaller). However, were we to assume a strikee asteroid width of, say, 15 meters, we'd have a striking asteroid of some 5 meters width (approximately).
I can make an estimate of the speed of this 5 meter asteroid. First, I observe that the asteroid is able to move twice it's own width per frame. Assuming 30 frames per second on my borrowed TESB SE tape, and assuming the asteroid is five meters wide, we come to an approximate speed of 300 meters per second, which is a fairly nice clip.
From this, we can use assumptions and some calculations to get an estimate of the kinetic energy. For instance, if we assume (generously) that the asteroids are made of pure iron, the mass of the asteroid would be on the order of 515,090 kilograms.
According to my calculations, this places the kinetic energy of the striking asteroid at 23.2 GJ. The asteroid that was struck, if 15 meters wide, was about 25 meters top to bottom, and I assume about 15 meters thick. Estimating it's volume with the simple length x width x height, we find that it had a volume of about 5625 cubic meters.
This is over fifteen hundred cubic meters larger than common pro-Wars estimates of a 20 meter diameter spherical asteroid from the ISD asteroid scenes.
What have we found out thus far? That it took 23.2 GJ to destroy an asteroid of 5625 cubic meters. Whoopty-doo, right? Ah, but wait . . . the destruction of the Falcon's asteroid and the destruction of the ISD's asteroids are remarkably similar effects. They both have the impact, the glowing eruptions opposite the impact point, the fiery burst, and then nothing, and all this occurs in mere fractions of a second.
Here, then, are a few issues. The ISD scene would not have shown asteroidlets, either due to the targets being much smaller asteroids or, alternately, the asteroids were too distant and the asteroidlets too small. If you look at the Falcon asteroid destruction, you see an incredibly detailed explosion, while the ISD scene only has a non-descript gassy poof. As for the asteroidlets, one could argue that they were only seen in the Falcon scene due to the Falcon's passage through them . . . they were only barely seen immediately following the asteroids' destruction, compared to the asteroids they came from.
Another issue revolves around the notion that we ought to have seen molten or glowing fragments in the Falcon scene . . . but we don't. What we see instead is a partial vaporization coupled with fragmentation/shatter . . . but no glowing bits are seen. We might then assume that either the asteroids are not iron but, instead, something that is either vaporized or fragmented but not melted, or alternately that the special effects team simply chose not to add molten bits.
All this applied to the ISD scene would indicate that it is entirely likely that the asteroids popped by the turbolasers were not entirely vaporized. If the ISD scene asteroids were on the order of 20 meters in diameter, they could have been dismantled by around 23.2 GJ of energy. If the ISD scene asteroids were in the 10 meter range, they could have been dismantled by around 3.9 GJ of energy. If the ISD asteroids were in the 5 meter range, they could have been dismantled by a force of .2 GJ, or about 238 MJ. These estimates are actually rather high, considering the fact that they are based off of the Falcon scene (where the width of the asteroid was far less than the height). If they were lowered appropriately, we would have figures roughly 20-25% less. To ensure fairness, I shall use both the high and low estimates.
Converting this to watts, and assuming one-tenth of a second for both the Falcon scene and ISD scene impacts against asteroids, we get:
Power of a turbolaser bolt:
|20m||23.2 GJ||232 GW|
|10m||3.9 GJ||39 GW|
|5m||.24 GJ||2.4 GW|
|20m||17 GJ||170 GW|
|10m||3 GJ||30 GW|
|5m||.18 GJ||1.8 GW|
(Actually, considering the fact that UVD gives .225 to .3 seconds for the turbolaser bolts in the ISD scene to destroy the asteroids, these figures are also terribly high. To correct the appropriately lowered estimates, we'd find figures of 57-76 GW, 10-13 GW, and .6-.8 GW (600 to 800 MW) respectively.)
None of these figures, high or low, put the turbolaser cannons in the terawatt range, as some of the more vigorous pro-Wars debaters do. Indeed, these watt figures refer to the power of an individual turbolaser bolt . . . to determine the power output of a turbolaser cannon over sustained periods, we'd need to know the recharge time. From the "Turbolaser Commentaries" analysis of recharge time, we get the figure of two seconds. We thus find the following:
Sustained Power of a single TL Cannon::
|20m||23.2 GJ||11.6 GW|
|10m||3.9 GJ||1.9 GW|
|5m||.24 GJ||.12 GW|
|20m||17 GJ||8.5 GW|
|10m||3 GJ||1.5 GW|
|5m||.18 GJ||.09 GW|
Now the most important question that remains is, how big are the asteroids that the ISD was popping? This, unfortunately, can be a matter of serious contention. We are not given the camera's distance from either the ISD or the asteroids, nor are we given any idea of the camera's field of view. We do not know the distance from the ISD to the asteroids.
However, we do know a few things. We do know that, assuming the ISD is moving forward along her own orientation, the camera is not in the path of the ship. We do know that, assuming the ISD is moving forward along her own orientation, that the largest soon-to-be-popped asteroid visible (the one apparently closest to the camera) at the beginning of that scene is moving from port toward starboard, from the ISD's point of view (i.e. it's coming in from a 10 or 11 o'clock angle when it's popped). This is corroborated by the fact that, later, we see an ISD firing on the Millennium Falcon that is directly in front of her, and the ISD looks almost exactly the same insofar as angle and distance are concerned. The turbolaser bolts fired toward the Falcon are extremely thin from the camera's vantage point . . . the turbolaser bolts fired at the asteroids are much thicker. When we see the view from the Millennium Falcon directly astern, the beams appear much thicker. This either implies that turbolasers have power settings (low for MF, high for asteroids) that changed when the camera was looking back from the Millennium Falcon, or ( more likely in this case) that the ISD popping asteroids was firing more in the camera's direction, thus making thicker-looking bolts (just as the pencil-thin bolts appeared much thicker when viewed from a better angle).
We can try several things here. We can guess, based on the path of the asteroid and it's apparent closeness in the beginning of the ISD-pops-asteroids scene, what it's size is. Or, we can attempt to use the TL bolt that appears to have struck the Millennium Falcon's hull in the chase scene to determine the width of a turbolaser bolt. For the latter, assuming a 30-meter wide Falcon, we find that turbolaser bolts are, at best, 1-1.5 meters wide. This seems corroborated by the shot from the side with the pencil-thin TL bolts a few moments earlier.
Applying this width to the TL bolts in the popping scene, we find that the main asteroid is no more than three to five meters in diameter. This still leaves it at between ten and fifteen feet, roughly, which is none too shabby. This gives us a lower sustained firepower estimate for a turbolaser of 22-29 MW assuming a 3 meter main asteroid, 90-120 MW assuming a five meter asteroid. Of course, in both those ranges, the upper figures (29 and 120) are not appropriately lowered, as per previous statements.
Of course, we do not know how long a turbolaser cannon can continue engaging in sustained fire, firing a bolt every two seconds. We do know, however, that there are sixty such turbolaser cannons aboard an ISD, according to many various sources. Assuming that forty of these, on average, can be trained on any one vessel at any one time, we find that a Star Destroyer is capable of between 880 MW and 3600 MW (3.6 GW) sustained fire on a target, assuming that all bolts hit their mark.
These estimates are also quite high, considering the fact that we have assumed asteroids of solid iron. The Official Star Wars Web Site states that "The dangerous asteroid belt in the Hoth system was formed billions of years ago by the collision of two planets. Millions of boulders and rocky asteroids careen through space in orbit together, forming a deadly swarm and a menace to navigation."
This would seem to imply that the asteroids are predominately composed of rock, not pure metal. We do not know the composition of this rock, unfortunately, but if one were to guesstimate the density of this rock by using the density of the entire moon as an example, we'd have asteroids less than half as dense as iron (3300 kg/m3 as opposed to the 7924.5 kg/m3 used for iron).
Let us, then, estimate the required energy to produce the shatter and partial vaporization of various sized asteroids, assuming they are made of rock and not iron:
Turbolaser Bolt power, assuming a hit of .3 seconds:
|20m||9.7 GJ||32 GW|
|10m||1.6 GJ||5.3 GW|
|5m||.1 GJ||.3 GW|
|20m||9.7 GJ||4.9 GW|
|10m||1.6 GJ||.8 GW|
|5m||.1 GJ||.05 GW|
And now, assuming 40 turbolaser cannons could be fired at a vessel and all bolts would hit, we have a sustained power of between 2 GW and 200 GW. However, using the previous argument that the ISD's main visible asteroid was between 3 and 5 meters in diameter, we find that the sustained firepower of an ISD is 2 GW or below . . . perhaps as low as 800 MW for the whole ship.
Of course, this is based on the density of Earth's moon. In fact, that density might be far too high. To our own local asteroids, we have sent a NASA probe. This probe's data shows that one asteroid, 253 Mathilde, has a density of only 1.3 g/cm^3, or about 1300 kg/m^3. As a C-type asteroid, this is to be expected . . . it's predominately carbon. The asteroid 433 Eros, S-type, has a density of about 2600 kg/m3. It is predominately composed of high concentrations of silicate materials and metal. An estimate of average asteroid density might be 2000 kg/m3.
So, let's go at it again . . . this time just sustained firepower:
|20m||5.9 GJ||3 GW|
|10m||.99 GJ||.5 GW|
|5m||.06 GJ||.03 GW|
And now, using the five-meter ISD main asteroid hypothesis, coupled with the forty-TL on one target figure, we find that the firepower of a Star Destroyer against a target is on the order of 1.2 GW . . . if the asteroid was three meters, then the Star Destroyer would have something like 500 MW per forty turbolasers, all bolts of which must hit the target.
Meanwhile, pro-Wars debaters float theories and calculations suggesting that the asteroid was larger and completely vaporized in an instant (despite the contradiction with physical laws) with lower-limit *per bolt* estimates of 31,000 terajoules! The maximum I could come up with was a mere 23.2 gigajoules, making their estimates * 1.3 million times* my own. That's preposterous.
Even if we grant the erroneous assumption made by some pro-Wars debaters (based on one interpretation of the non-canon TNG Technical Manual) that the dorsal phaser array on the saucer of the Enterprise-D is only capable of directing 1.02 GW against shields, that array alone is about as powerful as a Star Destroyer's turbolaser complement, if not more powerful.
Something worth noting here, though, is the fact that the phase cannons aboard Enterprise NX-01 are rated at 500 gigajoules per shot, according to Reed in "Silent Enemy"[ENT]. Even allowing for larger asteroids of solid iron, phasers are much more powerful than turbolasers.
Update: Many Warsie debaters will try to claim asteroid sizes greater than 20 meters. However, this cannot be so. Take a look at the following two screen caps:
As you can see, the Falcon is being fired on in the first shot. The scene makes it clear that the Falcon is almost directly in front of the ISD. The Falcon's size is generally estimated to be a maximum of 40 meters in length. The scene which features the ISD firing on the asteroids has the ISD at almost exactly the same lateral angle from our perspective (look at the starboard point compared to the forward point in both images), but firing more toward the camera (about 30 degrees off the forward axis). The firing angle, plus the trajectory of the asteroid, plus the distance of the asteroid from the ship, plus the thickness of the beam, all serve to make it readily apparent that the ISD is firing much further toward her port side than in the forward-shooting Falcon chase.
Therefore, the chase scene constrains the possible size of the asteroid to less than forty meters, since it could not possibly have appeared as large as the Falcon did when it was in front of the ISD.
More on this issue will come soon.
Normal lightning bolts are rated at between 1 and 10 gigajoules, though a very significant fraction of that energy is radiated by the heat, light, and shockwave before it ever hits the ground.
Back to ST-SW intro.