We blow up asteroids, too . . . and ours are bigger. The following is based on a downloaded DivX vidcap of the episode, with a framerate of 15 fps.
In "Rise", Voyager comes to the aid of the Nisu. One of their colonies is being subjected to an asteroid bombardment. Their own attempts to vaporize the asteroids keep failing . . . fragments still impact against the surface. As the episode begins, we see a large asteroid tumbling toward the planet.
Tuvok: "The asteroid is fragmenting. But, most of the debris is still on a collision course with the planet."
Janeway: "Target the fragments. Destroy them."
Chakotay: "That asteroid should have been vaporized. What happened?"
Kim: "I'm not sure. Sensors showed a simple nickel-iron composition. We shouldn't be seeing fragments more than a centimeter in diameter."
(Sklar tells of the similar outcome of their own efforts on previous asteroids.)
Tuvok: "I've destroyed most of the debris, Captain. However, targeting scanners were unable to track two of the fragments. They have already entered the upper atmosphere.
(Tuvok's report comes at 1:10 in the episode, 28 seconds after the asteroid was first hit, and 20 seconds after Janeway's order to destroy the fragments.)
Four minutes into the episode, we learn something interesting from a Nisu scientist named Vadum, "our most prominent astrophysicist," as per the Ambassador's statements.
Vadum: "Ambassador, I've been analyzing the debris, and I've discovered disturbing evidence that the asteroids are not what they seem! They are composed of artificial materials. I must meet with you immediately . . ." (garbling, then transmission cuts out)
A few minutes later, we learn what he means, as Torres and Chakotay examine one of the fragments, with the Nisu Ambassador looking on.
Torres: "I've completed the mineralogical scans. The rock is composed of trioxine, olivine, . . . waitaminute. I'm reading a concentration of triatium."
Ambassador: "Triatium? Isn't that an alloy?"
Chakotay: "B'Elanna, give me a hand with this."
(Chakotay has used a pick to crack the outer layer. He and Torres now pull the two pieces apart, revealing the rock's technology-innards.)
Torres: "This doesn't look like any asteroid I've ever seen, but I'll bet it's the source of our triatium."
It is discovered that the asteroids were part of a ruse by another race to make the colony planet appear unsafe, leading to a Nisu evacuation. The planet thus unoccupied, the other race could then stake a claim. Naturally, Voyager saved the day. For our purposes, however, the most interesting part of the episode is the asteroid destruction in the beginning.
Obviously, to have an asteroid destruction scene in Star Trek is of interest, given the level of interest the asteroid destruction scene in Return of the Jedi garners from pro-Wars and pro-Trek debaters alike.
And so, with that history in mind, let's take a look at what we can learn about this scene. What we want is a firepower analysis . . . what we therefore need are details about the size of the asteroid, the composition of the asteroid, and so on.
In order to determine the size of the asteroid, we need something to scale from. In this case, we have ourselves a lovely little photon torpedo.
From here, scaling the torpedo is a simple matter. For the sake of being conservative, I will assume that Voyager's torpedo is fired in a portward direction (i.e. toward the observer) . . . this will have the effect of making the torpedo glow area smaller. It should be noted that it is pretty clear from the episode that Voyager was shooting roughly dead-ahead. However, making the torpedo appear to be smaller will have the effect of making the asteroid seem smaller, making this a conservative estimate.
Scaling off of Voyager's port side, and using the torpedo as it appeared two frames after being fired, the central glowing area of the torpedo (i.e. not including the streamers) is approximately 10 meters in diameter. Now, I shall take the asteroid as it appeared two frames before torpedo impact (image below). (The image one frame before impact shows an illumination of the asteroid surface, and I do not want my estimate thrown off as a result). I count the torpedo as being a grand total of four pixels wide, with the central glowing area constituting two pixels or so of width. The asteroid is sitting at an angle of about 45 degrees in the shot . . . tipping it so the long axis is vertical, we have an asteroid length of 78 pixels, with a width varying between 37 and 50 pixels. I shall treat the asteroid as if it were a rough cylinder.
If one pixel equals five meters, this gives the asteroid an approximate length of 390 meters, with a width varying between 185 and 250 meters.
Treating the asteroid as a cylinder, and using 210 meters as a rough width (the actual midpoint between the widths is 217.5), we arrive at an asteroid volume of 13,508,063 m3.
Several statements about the composition are made. Ensign Kim refers to the asteroid as having a "simple nickel-iron composition". Vadum, on the other hand, implies that the asteroids are composed of artificial materials. The tricorder scan performed by Torres would seem to unite the two ideas . . . the asteroid contained olivine, a common constituent of nickel-iron asteroids, but also contained triatium, an artificial alloy. (I have no idea what 'trioxine', the other mentioned substance, could be. A Google search for that word only came up with some sort of new medicine.)
The extremely dark and mottled coloring of the asteroid is a bit odd, but not unreasonably so. From what we know of the asteroid based on Kim's scans, it should fall within the parameters of an M-type . . . S-type if the olivine was common throughout, and not simply present on the surface, for example. The specimen collected by Voyager was obviously solid, and easy to crack. Judging by the color and composition, though, it would not seem to be representative of most of the asteroid. For our purposes, then, the average Sol system asteroid density of 3,000 kg/m3 seems fair to use here, as well.
This density, taken with the volume, gives us a total asteroid mass of 40,524,189,000 kilograms, or 40,524,189 metric tons.
In order to make this an absolute lower limit, I shall ignore the fact that it would require more energy to vaporize a lower-density asteroid than it would if it were solid iron, due to heat expansion and fragmentation effects. Further, I will calculate only based on iron (nickel has similar properties), and assume that it constitutes 60% of the mass of the asteroid, leaving us to deal with a mere 24,314,513,400 kilograms.
In effect, I am leaving plenty of room for Harry's comment that "we shouldn't be seeing fragments more than a centimeter in diameter" by estimating only 60% vaporization of the asteroid. Of course, some would argue that I should not claim any vaporization at all, but that's absurd . . . it's a photon torpedo, not a space blender. There's no way it can dice the asteroid into one-centimeter fragments without vaporizing the vast majority of the asteroid, minus those little less-than-a-centimeter escapees. (Indeed, even to assume that the remaining 40% of the asteroid would end up diced in such a fashion stretches believability.)
If we assume that the asteroid started out at 200 Kelvin, and that it would therefore take 7.6 megajoules to vaporize one kilogram of iron, we are still left with a necessary energy figure of 184,790,301,840 megajoules. That's 184,790 TJ, or 44 megatons, as an absolute I-bent-over-backward lower limit.
Now, let's take a look at the asteroid as the more rabid of my opponents look at theirs, so we can get something closer to an upper limit. First, the density will have to be bumped up from 3,000 to 7,000 kg/m3. This gives us a mass of 94,556,441,000 kilograms. Let's assume that the iron (and/or similar nickel) constitute 90% of the asteroid's mass, or 85,100,796,900 kilograms. At 7.6 megajoules per kilogram, this works out to 646,766,056,440 megajoules. That's almost 650,000 TJ, or 154.5 megatons. Then again, given that all this energy must be deposited into the asteroid in a fraction of a second by an explosive device, this, too, is probably a low-end figure.
As it happened, the asteroid was not vaporized in the episode as
everyone expected it to be, due to the fact that it wasn't exactly a normal
asteroid. Of course, this is irrelevant for our purposes since we know
what was expected, but it is interesting nevertheless. I may try to work
up some sort of acceleration parameters on the large pieces (the
biggest is ~100m) that are flung
off to the right at impressive speed (750 m/s minimum for the ~100m
fragment). Note also that the asteroid is shattering violently in the
first image, which is one frame (1/15th of a second, or .067s) after
100 megatons (420,000 terajoules) would appear to be an extreme but fair low-end figure for this scene's photon torpedo yield. It can't really be any lower, and is much more likely to be higher. Given other incidents of starships versus asteroids (the moon-sized object in "This Side of Paradise"[TOS], the wormhole scene of ST:TMP, and Dukat's efforts in "Return to Grace"[DS9]) and planets ("Skin of Evil"[TNG]), this fits in well. The Motion Picture actually could be used to provide a higher yield, given that the torpedo disappears completely from our view (implying a larger asteroid), but that example becomes an odd one to use, due to the wormhole and any unexpected effects it might have.
Rabid Warsies will undoubtedly sneer at the 100 megaton figure. However, their own high-end estimates of the highest turbolaser firepower seen in the canon (Mike Wong's 250 TJ and 1500 TJ figures, as well as another person's 701 to 2863 TJ) don't come anywhere close to even 100 megatons (420,000 TJ), much less the 200 gigatons (836,800,000 TJ) from their non-canon.
Not that I find that surprising.
also that the "Rise" asteroid is not the largest asteroid we've seen destroyed by torpedoes, or
the densest. "Cost of Living"[TNG] shows the Enterprise-D
using two torpedoes to destroy an asteroid, and the first torpedo is not even
visible for most of the second torpedo's trip.
This asteroid is shattered, not vaporized. The asteroid was large enough, however, to have a differentiated core composed of "densely compressed nitrium and chrondite", and the remaining core was of sufficient size and density to cause planetwide damage to the planet below. Even if we merely assume a 10-15 megaton blast similar to Tunguska, that's still an asteroid of tremendous size, tremendous density, or both (at somewhat less tremendous levels). Data concluded that another torpedo would be unlikely to damage the core, but was able to shatter the core with a technobabble particle beam from the deflector. Judging by the beam, the core remnant was the size of the secondary hull of the Enterprise. The remaining core fragments no longer posed a danger, and were then flown through by the Enterprise on her way out of the system:
1. If Chakotay was able to tap a piece of the asteroid open with a little pick-axe, the asteroid must have been brittle. If it was made of such brittle materials, Voyager's torpedo should have done more damage.
There's a profound difference between taking a sharp pick against a solid rock and vaporizing it with a photon torpedo explosion. First, a rock has characteristics such as cleavage and fracture. That is, in fact, one of the ways rocks are identified.
Torres identifies olivine as one of the substances in the rock. You'll note that olivine has a brittle, conchoidal (shell-like) fracture. In other words, it breaks easily into curved fragments, not unlike glass does. Also pay attention to the fact that it is rather hard, but with a low density. Something hard, low density, and brittle is going to be easy to crack.
Compare this with iron, which they thought the asteroid was made of. It's softer, and thus more malleable. It has a higher density, and a jagged, torn fracture. Now, let's say you fire a bullet at a wall made of olivine. You'll probably end up with a hunk of broken fragments flying away, and might even get cracks running from the point of impact. Do the same to an iron wall, and if the bullet penetrates more than a dent's worth, you'll get torn metal.
Detonate a thermonuclear weapon next to that wall, and the olivine wall will probably shatter. The more resilient iron wall may either tear wide open, or just sit there and melt, et cetera, depending on various factors.
This would assume, of course, that the entire asteroid was olivine, and not nickel-iron with a couple of oddball chunks of olivine. Given the fact that it fragmented in the way it did without vaporizing as expected, that isn't a bad hypothesis. But, then, the Nisu astrophysicist dude mentioned in his transmission that the asteroids were composed of artificial materials . . . whether he had simply found evidence that triatium alloy was part of the asteroid, or had found that sensor signals were being distorted, or found that the majority of the asteroids were literally artificial is not clear.
In any event, the brittleness of a material is no indication that it will be easier to vaporize . . . indeed, it is far more likely to fracture uncontrollably, and in this case unexpectedly.
2. Voyager didn't actually destroy the asteroid, therefore you can't claim firepower off of this episode.
Why not? The crew fully believed that they had an iron-nickel asteroid before them, and that it could be vaporized by photon torpedo. The fact that it wasn't vaporized does not negate their belief that they could have done so. Further, a 100m chunk and a smaller, perhaps 50 meter chunk flew toward the planet. Another chunk of about 40 meters flew off to the left. There was also a bunch of other crap flying around, but it's too small (and the vidcap is too low-res) for me to get much more out of it. Let's say, for the sake of argument, that an extra 50m asteroid's worth of material made it out of the torpedo blast.
If all that is correct, then it means 688,410 m3 of debris was left over by the torpedo blast. For an asteroid that started out at 13,500,000 m3, that ain't half bad, given the unexpected nature of what occurred.
3. Hey, I saw those two pieces flying off to the right, and when they hit the planet they weren't nearly that big.
I disagree. First, you're assuming that Tuvok is stupid, and would not have tried to take out the largest pieces headed toward the planet first. Second, and more importantly, those two pieces that depart the asteroid are flying away from one another at a 30-45 degree angle. The chances of them magically coming back together to become the two pieces that hit within kilometers of one another are staggering, to say the least. It would basically have to be a Q-inspired trajectory.
4. You scaled the asteroid wrong. First, torpedo glow doesn't increase after the torpedo exits the launcher. Second, you scaled the torpedo when it was at the greatest distance from the launch point, and you can't know how big the asteroid is from that.
The scaling is correct, within a reasonable margin of error. First, torpedo glow does indeed increase . . . it's a shield after all, and we can't assume it's raised to full strength the nanosecond the torpedo exits the tube.
In regards to the notion that I should've scaled the torpedo off of an earlier pic, let's take a look, using the "Hutt" methodology:
In the last pic above, there are two small squares and an itty-bitty square. The top-most two are, from the left, the frame they think I should have used, and the frame I did in fact use to scale the torpedo. Both have been reduced in size so that all the torpedoes are all the same size. Below the left frame, you can see a perspective-free schematic drawing of the 130-meter-wide Voyager, roughly (and conservatively) scaled to the navigational deflector of the scene above it. The width of the ship is 22 pixels . . . the length of the asteroid is (still) 78 pixels. Though the margin for error is greater using this method (especially given the small number of pixels we're dealing with), we still come up with a figure of 460 meters, 70 meters more than my figure. It would be even larger with a less conservatively-scaled schematic view. And, if torpedoes do not in fact seem to increase in size, and if we used the itty-bitty frame on the right for scaling, we'd end up with an asteroid a kilometer in length . . . and remember, the firepower would scale with the volume. Thus, we could quite easily end up beyond the 500 megaton "Skin of Evil"[TNG] territory, up into the 1.4 gigaton range.
So, what do you say we leave the scaling alone, and keep the conservative 100 megaton figure?
(After all, the "photonic torpedoes" deployed on Earth Starfleet ships in the early 2150's were capable of putting "a three kilometer crater into an asteroid"(Reed, "The Expanse"[ENT2]). Estimates of the yield from this example vary between 20 and 40 megatons, but either is more than sufficient to allow us to grant 100 megaton warheads 220 years later.)
And besides, given the torpedo's travel to the asteroid, the scaling I've used has to be accurate. First, let's look at the torpedo two frames after departing the launcher (at 15fps):
Now, let's look at it a full two frames later:
Thirteen frames later (after we see the asteroid alone for a bit), the torpedo comes into view at this point:
One single frame later, the torpedo reaches this point:
Six frames later:
Now, it takes an additional 11-12 frames after the above frame for the torpedo to hit the asteroid, depending on whether one wishes to call the impact the first of the below frames, or the second:
Now, would someone please explain to me how that could be an itty bitty non-Voyager-size asteroid, given the torpedo travel time? Even if you assume that Voyager fired the torpedo in a direction so that it would've grazed the 'camera', the thing still had to have travelled about 100 meters within four frames. And then, it still took 32-33 additional frames for the torpedo to reach the asteroid. Even if we ignore the obvious torpedo acceleration, that still implies that the torpedo has to travel a great distance to reach the target.
How could it not be Voyager-sized?
Thanks to the peculiarly-named "Slobba the Hutt" for the original scaled image from which my comparison above was made.
Special thanks to J.G. for providing the screencaps from "Cost of Living"[TNG]