Adam, > Kinda. On one hand is the fact tht the overall energy > being delivered is spread out over several seconds. > On the other, the delay means that the asteroid has > some time to bleed off excess energy (not sure how to > quantify this though - Curtis? Mike?) We'd need to know the coefficient of heat conduction for likely asteroid compositions. Check physical chmeistry, geology or engineering textbooks. Find a volumetric heat conduction coefficient expressed in W / m / K (watts per metre per Kelvin). Call this number k. Say that P is the power of heat injection to the solid, ocurring within a cylindrical volume where the beam passes through. Let the length (depth) of penetration be "l" and the beam radius be "r". Let the radial temperature gradient within the material be "dT/dr". Does energy injection by the beam exceed heat removal by conduction? Yes, if P > 2 pi k r l (dT/dr). If this condition is satisfied then there will be a runaway buildup of heat in the cylindrical space where the beam intersects the rock. This condition ignores the possibility that the beam may not penetrate all the way through the material, and may be attenuated by heat loss into the matter that is closer to the beam's source. If we want to calculate how the distribution of heat within the rock evolves with time then we need to solve a set of differential equations. This is non-trivial. I might look into it and present the results of computer calculations one of these days. For the moment, is it sufficient to have a rough, rule-of-thumb idea? > I'd say the melting/vaporization figures are definite > upper limits though (for the reasons Brian and Curtis > elaborated on - if the beam delivered more than 60 kt > worth of energy in a second, the asteroid probably > would have vaporized Even the 10 kt figure could be > debatable, since the asteroid was not completely > molten but simply fragmented - molten debris would > look different from fragments and also would give off > some noticable luminesence.) > > Adam, Ah, I see that you mean that you want to divide the _energy_ requirement by a _time_ of 3 seconds, not a number 3. You want a power, not a fdged energy number. Curtis. On Thu, 24 Feb 2005, Adam Gehrls wrote: > Its not arbitrary. Its the time it takes to destroy > the asteroid. In other words, a sustained delivery of > energy rather than a single brief burst (like the TESB > TL). I merely suggested that as a generous upper > limit Wayne use melting/vaporization figures as upper > limits, adjusted for the "sustained" delivery of > energy.) > >> Wayne, Adam: >> >> Why do you want to divide some figure by an >> arbitrary factor of 3? Why >> not 10 or 30 or 100? I've missed part of this >> thread but this bit of >> methodolody seems questionable. > > > __________________________________________________ > Do You Yahoo!? > Tired of spam? Yahoo! Mail has the best spam protection around > http://mail.yahoo.com > > *AOTC:ICS rates the point defense guns at 6 megatons per shot (max). This > is about 25000 terajoules. This jives with Mike's estimate of a massless > beam rocking the Falcon in TESB http://www.stardestroyer.net/Empire/Tech/Beam/Calc1.html That is for the Acclimator, and right now I'd rather not put a max number on those guns yet. > *"The vaporized "cloud" that used to be an asteroid flashed from bright > luminescence to invisibility in one second." It has been a long time since > I did the turbolaser stuff, but IIRC, it was 1/4 second from contact to > total vaporization. Ok. I'll play it safe and say "less than one second." *If we look at that next anigif after that statement, it appears that the asteroid is only ~5-10 times greater in diameter than the TL bolt (eyeball). If you keep the Trek scaling, I'd add a comment about that somewhere - that these asteroids might be only 5-10 meters in diameter. Done. "The cannons vaporized asteroids from 10 meters to 40 meters in diameter in less than one second." > *I see that the small phaser took 3 seconds. What about the big one? I'll have to watch the scene again to be sure. The planetary disruptor spit a ball of energy at the asteroid, and it exploded on contact. > *Nice scaling image of the BoP. That's Sean's expert work! > *IIRC, in ST3, Sulu said that a BoP crew is "about a dozen." Of course, > that was a couple generations before this. Yeah, there a big controversy about the BoP and scaling, crew compliment, etc. > Also, I have the entire TNG series on DVD, if you need any images, video, > audio, etc. I have TNG DVD, but not seasons 5 and 6. I don't have any DS9. There are only a dozen episodes or so of that show that I'd be interested in, so I'm not going to pay $100 per season. Agreed 100% When you can get quality shows like "24" for less than $50 bucks, those Trek DVD prices are insulting. BTW Brian, do you like zombie movies? Brian Wayne, > I'll get some AOTC images, that can be scaled more precisely. http://www.babtech-onthe.net/download/wayne/ Here are 15 images from the AOTC asteroid chase (temporary link). A few of these are successive frames. Most of these are near misses, and show the scale next to Obi-Wan's fighter. One shows decent scale against Slave1. The fighter is about 8x4 meters, so some of these red-glowing asteroids are 10-15 meters in diameter, others are probably 5 or so (eyeball). Some asteroids fragmented, others vaporized. But these that are glowing red, and are still roughly spherical, satisfy the lower limits we calculate. 5 meters- ~4 terajoules (1 kiloton) 10 meters- ~30 terajoules (7 kilotons) 15 meters- ~106 terajoules (25 kilotons) It is possible that we undercalculated this for the ICS, or some of the larger ones may have been hit twice. Things happen so fast, it's hard to tell even frame by frame. But the scaling here is more reliable than most of the ones in TESB, they all either fragmented or vaporized (most of them), and this is fighter-scale weaponry. These things make it a better comparison to Trek. Two asteroids in TESB must be on the order of 40 meters: http://www.stardestroyer.net/tlc/Power/bigasteroid.jpg http://www.stardestroyer.net/tlc/Power/asteroids9.jpg These both turned white-hot, remained roughly spherical (limited fragmentation), and vaporized. That would take at least 2000 terajoules (475 kilotons). Brian ----- Original Message ----- From: "Brian Young" To: Sent: Thursday, February 24, 2005 9:55 AM Subject: Re: Asteroid Calcs > Wayne, > >> I'll get some AOTC images, that can be scaled more precisely. > > http://www.babtech-onthe.net/download/wayne/ > Here are 15 images from the AOTC asteroid chase (temporary link). I added a video clip of the scene too. These are temporary links only. I'm going in now to do some scaling on the more significant ones (I'm out sick today). These are all quick and rough. I'm not doing Pythagoras today, just placing a circle around the ships, and measuring the circle. Image 10, asteroid between ships: fighter is about 26 pixels wide in foreground, Slave1 is about 65 pixels long in background. The smallest dimension of the white/yellow glowing area of the asteroid is the height, and is about 44 pixels. Width is about 67 pixels. Thus, we have an lower limit of about 6.75x10.3 meters, and an upper limit of about 14.6x22 meters. This asteroid vaporized in just over 1/2 second. Assuming the lower limit of ~6.75 meters in diameter, we're looking at at least 9.6 terajoules (2.3 kilotons). Note though, that I can't see this asteroid before it is hit. One is hit on the far side of it, then we see this one. Either the one on the far side is this one, and expanded to many times its original volume, or this asteroid was very dark. Image 13, asteroid between ships: fighter is about 32 pixels wide in foreground, Slave1 is about 95 pixels long in background. The asteroid is about 65x70 pixels. Lower limit ~8x8.75 meters, upper limit ~14.7x16 meters. Assuming the lower limit of ~8 meters in diameter, we're looking at a minimum of 16 terajoules (3.8 kilotons). This asteroid vaporized in about 1/2 second. Image 14, asteroid between ships: fighter is about 48 pixels wide, Slave1 is about 118 pixels long, asteroid is about 100 pixels diameter. Lower limit ~8.3 meters, upper limit ~18.2 meters. This one is close enough to Slave1 to illuminate the hull. As far as I can tell, none of the three glowing asteroids here are visible in the next 5 frames or so, thus were vaporized. Just assume for a moment that the real size is the mean of the upper and lower limits (it was close enough to illuminate both hulls). We'd have an asteroid ~13.25 meters in diameter, requiring about 73 terajoules to vaporize (17.4 kilotons). That is more than the total energy released by the "Little Boy" bomb on Hiroshima, leveling 60,000 buildings, IIRC. There were many, many more, including some seen through Kenobi's canopy. Brian http://science.nasa.gov/headlines/y2001/ast30nov_1.htm Explosions on the Moon NASA Science News During the 2001 Leonid meteor storm, astronomers observed a curious flash on the Moon -- a telltale sign of meteoroids hitting the lunar surface and exploding. November 30, 2001: Vivid, colorful streaks of light. A ghostly flash. Strange crackling noises and twisting smoky trails. Add to those a cup of hot cocoa, and you have all the ingredients for a delightful meteor shower .. on Earth. The recent Leonids were a good example. On Nov. 18th our planet plunged into a debris cloud shed by comet Tempel-Tuttle. Sky watchers saw thousands of meteors -- each streak of light a tiny bit of comet dust disintegrating in the atmosphere. A quarter of a million miles away, another Leonid shower was happening. But the recipe was different: Blinding flashes of light. Flying debris and molten rock. Sizzling craters. And certainly no hot cocoa! That's what the Leonids were like ... on the Moon. "Like Earth, the Moon also plowed through comet Tempel-Tuttle's debris field on Nov. 18th," says Bill Cooke of the NASA Marshall Space Flight Center. But, unlike Earth, the Moon doesn't have an atmosphere where meteoroids harmlessly disintegrate." Instead, lunar Leonids hit the ground and explode. David Palmer, an astrophysicist at the Los Alamos National Laboratory, saw just such an explosion from his backyard in White Rock, New Mexico. The 2001 Leonids were well underway when Palmer trained his 5-inch Celestron telescope and a low light video camera on the crescent Moon. "It was twilight," says Palmer. "Even so, the flash was bright enough to detect." He had spotted a Leonid crashing down near Sinus Media -- a lava plain on the lunar equator. Far from New Mexico, observers on the east coast of the United States saw it, too. Using 8 inch telescopes equipped with video cameras, David Dunham in Maryland and Tony Cook in Virginia independently recorded the flash -- a double confirmation. "We estimate it was as least as bright as a 4th magnitude star," says Dunham, director of the International Occultation Timing Association. This marks the second year Dunham and Palmer have seen lunar Leonids. They and others video-recorded six meteoroid impacts on the Moon during the 1999 Leonid meteor storm. The brightness of those flashes ranged from 7th to 3rd magnitude. "Actually, we've known for many years that Leonids hit the Moon," notes Cooke. "Between 1970 and 1977, Apollo seismic stations detected impacts during the Leonids and several other annual meteor showers. What's new since 1999 is that we're actually seeing the explosions from Earth." The first reports of bright lunar Leonids two years ago puzzled many scientists. Their calculations suggested that a Leonid hitting the Moon would need to mass hundreds of kilograms to produce an explosion visible through backyard telescopes. Yet there was little evidence for such massive fragments in the Leonid debris stream. Hundred-kilogram meteoroids hitting Earth's atmosphere would produce sensational fireballs, brighter than any sky watchers actually saw. Furthermore, lunar seismic stations operating for years had detected nothing larger than 50 kg. To solve the mystery, Jay Melosh, a planetary scientist at the University of Arizona's Lunar and Planetary Lab and an expert on planetary impact cratering, teamed up with Ivan Nemtchinov, a Russian physicist skilled in computer simulations of nuclear explosions. Experience with bombs came in handy solving this problem, says Melosh: "Leonid impacts aren't as potent as a nuclear warhead, but they are powerful. They hit the Moon traveling 72 km/s or 160,000 mph -- that's 240 times faster than a rifle bullet. In fact, the energy per unit mass in a Leonid strike is 10,000 times greater than a blast of TNT." Using computer programs designed to study bomb blasts, Melosh and Nemtchinov discovered that Leonids didn't have to be so massive to produce flashes as bright as those detected by Dunham and Palmer. Impactors massing only 1 to 10 kg could do the job. "That's more like it," says Cooke. "We occasionally see kg-sized fragments burning up in Earth's atmosphere. They appear as very bright fireballs that disintegrate completely before hitting the ground." On the Moon, of course, there's nothing to stop them from reaching the surface. According to Melosh, here's what happens when the Moon and a 10 kg Leonid collide: Much of the ground within a few meters of the impact point would be vaporized, and a cloud of molten rock would billow out of a growing crater. "At first the cloud would be opaque and very hot, between 50,000 K and 100,000 K," explains Melosh. "But the temperature would drop rapidly. Milliseconds after the initial blast, the cloud would expand to a few meters in diameter and cool to 13,000 K. That's the critical moment," he says, "when the vapor becomes optically thin (transparent); then, all the photons rush out and we can see a flash of light from Earth." An astronaut watching the event on the Moon, perhaps a hundred meters or so from the impact, would be momentarily blinded by the Sun-bright explosion. There wouldn't be a deafening report, however, and onlookers wouldn't be knocked down. "There's no air on the Moon to carry shock waves," explains Melosh. "Even so, you might have to pry some nasty bits of molten rock out of your space suit." Fortunately for future Moon colonists, there's little chance of being hit. Cooke explains: "During an intense Leonid meteor storm like the one Earth experienced in 1966, the lunar flux of meteoroids more massive than 10-5 gm would be 1 per square-km per hour. If we assume really chubby or bulky astronauts with a cross-sectional area of 0.5 square-meters, then the probability of being hit by a 10-5 gm Leonid is only 0.00025." Such tiny particles carry enough energy to puncture a spacesuit, but the astronaut inside would remain mostly intact, says Cooke. "The probability of being hit by something that might totally vaporize you -- like a 10 kg fragment -- is a billion times less." So ... lunar Leonid meteoroid showers might not be as scary as they sound. Future denizens of the Moon might even take up a new astronomical hobby: ground watching. "I saw a hundred puffs of moondust every hour," they might say after a good spate of Leonids. "And, ooh that fireball ... what a blast!" Editor's Note: After this article was published, a second lunar flash was confirmed for the 2001 Leonid shower. Video tapes recorded by Roger Venable from eastern Georgia (USA) and David Dunham of Maryland reveal a lunar Leonid on Nov. 18, 2001, at 23:19:16 UT near Tranquillitatis. AOTC:ICS rates the point defense guns at 6 megatons per shot (max). This is about 25000 terajoules.