Physics in Film

For my superhero movie, I chose to analyze the superman in the 2006 release of Superman. This movie is’nt horrible to watch and the updated special effects were better than the previous films. Along with the quality of the special effects, superman’s powers seem a bit boosted as well and develop as the story goes along. The three powers I will ananyze are 1) x-ray vision, 2) super strength 3) his ability to be bullet-proof. First let’s start with x-ray vision. In the film, superman can look within the human body, through multiple building floors, through houses, etc. He is also able to exactly control the penetrating depth of his x-ray vision so that he doesn’t look through what he wants to see. Superman’s x-ray vision seems to just be an alternate function of his normal eyesight, that is he uses no outside devices to help him view things. In the modern medical world x-rays are used routinely to peer into the human body. In these machines the strongest voltages used to produce x-rays are in the 150 kV range which requires adequate sheilding of at least 2.5 mm of lead for protected exposed organisms. We also must note that x-ray imaging isn’t direct imaging and that the x-rays much be shot through the patient then onto a special photographic plate so they can be viewed, much like a normal picture. So even if superman could shoot out x-rays, I’m not so sure that it would help him see anything, especially because the wavelength of x-ray light falls far below that of what is considered normally visible light. Power, to produce x-rays that could see through buildings and houses and other things at a distance, he would need an x-ray source many times stronger than the most powerful medical x-rays which use some 150,000 volts of electricity. In the movie he uses his x-ray vision several times to look at Louis for some reason or another. The put protective lead shielding on your vital organs when getting an x-ray for a reason. High amounts of x-ray exposure can be very damaging to tissue. Even at the meger levels produced by the medical applications, protection is required. So when superman is staring at Louis with his x-ray vision he might just be giving her cancer.  Now, onto his super strength abilities. It has been asserted that superman’s powers stem from the fact that gravity on his home planet was much stronger than the gravity here on earth, thus superman is much stronger her. Well this has been taken to the extreme in this movie where superman lifts a ship out of the water and then if that wasn’t enough, proceedes to tunnel into the ocean floor with laser vision to lift a large island out of the sea?  What I found interesting about this was what if we apply some simple newtonian mechanics here. Several times in the movie he is depicted tossing huge objects around with some strange effects. A good example here is when he tossed the kryptonite infested crystal island thing out into space. He flys up into space with this chunk of material that must have weighed conservatively millions upon millions of tons and shoves it tumbling off into space. What is odd here is that he doesn’t move backward! Newton says that an equal and opposite force would be experienced by superman.  That is if the 215 lb. superman exerted a force strong enough to move to send this giant piece of debris off into space then he should have experienced an equal force in the opposite dierction. Given that his mass is just a tiny fraction of that of the debris, we can presume that he should have been sent rocketing off in the opposite direction from the chunk at thousands of km/h. Funny also was the fact that superman’s cape was blowing around in the “space wind”. Now lastly, onto his apparent bullet-proof body. The film shows superman going after some bad guys who decide to start shooting him with a mini-gun in the chest. A blazzing trai of bullets can be seen hitting superman’s chest, some of their energy being absorbed by his chest turning it into a jelly like substance, the bullets would then be deflected of in another direction. well given that he is superman its viable that he has super tough skin that doesnt break and can absorb the energy of bullets with out harm. The key word here is absorb, in the next seen, when the guy runs out of belt-fed mini gun ammo, he pulls out a .45 caliber pistol and shoots superman in the eye, the eye doesnt deform to absorb energy like the chest, but instead the bullet just splatters and falls off. Since the eye didnt move at all, or the rest of superman’s head, we must assume that supermans eye must be extremely hard to be able to absorb all of that impact with out any damage or deformation.  How could he have what would need to be a very flexible membrane like the eye be made out of material that can resist bullet strikes, it seems that with such hardness you would also have equal rigidity which would mean no blinking for instance. It would appear that superman is made of some paradoxical material that is extremely hard but also very flexible, after all he is superman.

Contact (the movie) vs. Special Relativity

The 1997 film Contact is actually quite decent when compared to most action/sci-fi films out there. It has an interesting plot and is full of bits of real science. It was hard to tell this was a sci-fi film until well into the movie, when she first decodes the blueprints for a spaceship. Despite its good points, it has one complete contradiction to the accepted scientific theory of Special Relativity. In the film, Jodie Foster’s character is put aboard an alien machine built from blueprints received via radio telescope and is then quickly transported 25.3 light years and then back again in a very short period of time. This is itself is not so bad because wormholes are an interesting, theoretically not disproven, and debated topic in modern physics. What is a bit off is the depiction of dilated time for Foster and her friends on Earth. The movie assumes that through these wormholes she must be moving at relativistic speed, so they cleverly alter the experienced time length of her voyage and how long earthlings perceived her voyage to be. In the film, Foster is able to travel through the wormhole by being dropped in a pod through the spinning and glowing alien machine which opens up the wormhole allowing her in. She states that her 50.6 light year trip lasted 18 hours, as later reinforced with her 18hrs of camera static. From how long it takes the pod to fall through the alien machine, about 3 seconds, we get the earth based observers perception of the journey length. To prove that this part of the film is incorrect, we can use the following equation to plug in some values and see just how backward this movie science is. We can use the equation for relativistic time dilation here:

∆t = ∆t₀/ √1-(v² /c² )

Where ∆t = the dilated time earth observers would have seen due to Foster’s relativistic motion in respect to their earthbound inertial frame. (3 seconds)

∆t₀ = the proper time as measured by Foster in her reference frame. (18 hours or 64,800 seconds)

v = Foster’s velocity

c = 299,792,458 m/s

When you start to plug in numbers, it becomes evident that the movie’s portrayal of this time dilation wouldn’t work because, with the given constant variables, the equation cannot produce an accurate description of time dilation regardless of the value of the other variable, v. For example: because we know that Foster is moving in her reference frame at extreme velocities in relation to the inertial frame velocities of the earth based observers, the people on earth should ALWAYS perceive a longer interval of time compared to someone traveling at such speed. No matter what value is plugged in for v in the above equation, with the given variables, ∆t will always be larger than ∆t₀ , the exact opposite of what the film shows where she sees 18 hours and the earth sees 3 seconds. So no matter what, an earth based viewer WILL ALWAYS perceive her trip as being longer than she does because of her motion relative to theirs.

So, a somewhat more plausible scenario must exist. So what if we use the same equation as before, keep ∆t₀ as 18 hours and use a speed of .90c to see how much time would have passed on earth during what Foster saw to be an 18 hour journey. This yields a ∆t of 146,826 seconds or 40.79 hours, so traveling at 90% of the speed of light Foster only experiences 44% of the time that those in the inertial from of earth do. This could work in pretty easily to a sci-fi plot I would presume. The hero departs for what seems to be at least from earth a trip just shy of two days. The world eagerly awaits the return and upon reunion notice that their hero seems to have only been gone less than a day according to him and his on-board equipment. Surely an eyebrow raising event to those unfamiliar with Special Relativity and an interesting talking point or plot twist possibility in a movie. The closer you approach the speed of light with your velocity, you can further and further increase the time dilation, and at high enough speeds, in theory produce the possibility of something like forward time travel. Traveling at 99.999% the speed of light, those 18 hours traveling at that speed now become 167.7 days. So in theory your movie spaceship could leave earth early in Feb. of 2009 and fly off in space at v= .99999c for what would be only 18 hours to them, and return to earth sometime in late June 2009, truly having only aged 18 hours while the rest of the earth would be almost a half a year older. Interesting plot possibilities indeed.

I found that I liked this movie more than I expected. I watched this movie on my own and besides fast-forwarding through the mushy scenes, I found it quite compelling as a historical narrative, I just wished there could have been more in-depth history and science. The changing attitudes of the scientists on the project is indeed and interesting plot event. At first they are enthused about working on something that has never been done before. It is easy to understand their excitement, having been called away from their normal jobs, under the highest security clearance, taken to a secret location that “doesn’t exist”, being surrounded by the best minds in science, and having an opportunity to change history, it is no question that any scientist wouldn’t dare turn down an opportunity to be involved in such a thing. Their attitudes change though when the project starts to become a reality and no longer a theoretical adventure. Once the pieces start to fall into place that make the weapon functional, such as the implosion design and sufficient amounts of fissile material, some scientists begin to question the morality of dropping such a device on Japan with no warning or demonstration. Many of the scientists on the project and some other government officials like the Admiral are opposed to a no warning drop and suggest that the device be demonstrated. However approval from a very unlikely source, Oppenheimer, comes and the bomb is set to drop without a demonstration because he fears a) it might not work and they would appear foolish and give the Japanese more confidence, and b) a demonstration would require more material, leaving less for weapons. Though the scientists are afraid of the implications of the device they have created, they are indeed enthused as is Oppenheimer when the Trinity test is a success and the bomb is deemed a go. The drive of the general is strong and expected. Being charged with controlling and conducting the most massive and expensive government project in history, not to mention one that could potentially end a war thats outcome, at least at that time, was still very much uncertain. His unwavering ambition is not so hard to understand when you consider the tremendous responsibility he is untrusted with. Even with the news that Germany had no bomb he still pushed for the weapon and kept this news secret so that he might try and gain the United States the nuclear upper-hand on the rest of the world, which he did until a few years after the war when the soviets tested their first nuclear device. Lastly, on Oppenheimer’s “God Complex”, its not hard to realize why he may have felt god-like and why people may have viewed him as such. Here we are looking at one of the smartest scientists on the planet heading a project to build an epic never before seen weapon that could bring catastrophic devastation on a biblical scale. He is a single man, who with the work of his peers, could forever change the nature of warfare and who in the days the bomb was being built, held the lives of hundreds of thousands of Japanese in his hands. It is easy to see how someone with this sort of power could be seen as god-like and for someone of his status, it would not be unthinkable that there might be some arrogance that might cause others to view him as having such a complex.

I believe that in our current energy situation, we can obviously not be content on continuing to burn fossil fuels, that much is a given. However, with all the current infrastructure in place that is doing precisely that, it will be a massive effort to convert over to a new energy source once that is developed. We do however, already have nuclear power plants that have been safely producing power for many years. South Carolina alone has 7 power-producing nuclear reactors dispersed over 4 different powerplants. These sites produce 52% of the states electricity, the rest being left to oil, and natural gas powerplants. There are many pros and cons when it comes to nuclear power, that is exactly why the debate concerning its safety and operation has raged for years. First the pros: 1) nuclear power plants do not release CO2 into the atmosphere as a by-product of electric power generation. 2) it is cheaper to obtain the smaller amount of nuclear fuel needed to sustain a reactor than the many tons of fossil fuel needed for conventional powerplants. 3) nuclear power has thusfar proven itself to be very safe, to date there has yet to be a single fatality in the United States related to nuclear power generation. (there have been, however accidents such as Three Mile Island, in which there was a partial meltdown but little radiation escaped and no one was injured or made ill) Now for the bad side, 1) spent fuel disposal, once the material exhausted in the reactor, it will remain dangerously radioactive for a few thousand years, certainly something that must remain heavily guarded and cannot just be left lying around. For this, the government has arranged for the creation of nuclear depositories in areas such as the Yucca Mountain site in Nevada about 100 miles from Las Vegas. This area was selected based on both its topography and geology, and would be a safe haven for this material given the proper authorities watch over it and there was no mishandling. The problem is though, that this Yucca Mountain project has taken years to complete and is just now, in the next few years, going to be ready to start accepting nuclear waste. This is a huge problem because by the time this place is finished, there will be more waste to dispose of than the facility can handle, basically we’re building a doghouse to store an SUV. Additionally, our country has been around for 250 years, how can we then make plans for our government to regulate this waste for the next FEW THOUSAND years, when no single government authority has ever or will likely last that long. Also a con is the potential security risks involved in having large amounts of nuclear material located close to densely populated areas. Despite any measure taken to enhance security, there cannot ever be a completely secure facility and despite all efforts for safety and all the backup systems, its cannot be 100% safe simply do to the nature of the material. When it comes to the issue of nuclear power, I for one support the use of nuclear energy over that of fossil fuel burning. I believe that we should pursue a cleaner means of energy production with our existing nuclear infrastructure, all the while attempting to find a solution to the problem of waste disposal, which I believe is a smaller issue to deal with than the problems we may face if we decide to keep duping CO2 and pollution into the air.

Nuclear weapons have to date only been used in warfare twice, with devastating results. If I could choose, I would choose that those two detonations would be the last two detonations or such awesome weapons. Currently, thermonuclear bombs are the most powerful weapons that can be brought to the battlefield and therefore those who posses them, such as the United States and a handful of other nations would be reluctant to give them up if there still were a possibility that other nations would have them. It’s kind of like trading your pistol for a knife at a gun fight. I don’t believe that smaller tactical nuclear weapons are the answer either. Just using a smaller bomb doesn’t erase the stigma of a nuclear attack, dropping a nuclear weapon on a country is still dropping a nuclear weapon on a country regardless or it’s size or composition. Such an attack would not go unrecognized globally and would be a definite source or outrage and possibly retaliation. While I definitely don’t agree with the used of nuclear weapons, I don’t think that they will ever go away until something even more powerful and devastating is created. Since man has been able to create tools and weapons, we have been in a global arms race, first to take down game and then to battle amongst each other. First it was the stick, then the stone, bronze weapons, steel weapons, bows and arrows, gun powder, flintlock rifles, cannons, bolt action and single shot weapons, aircraft, the machine gun, chemical weapons, tanks, missiles, and now nuclear bombs. The world it seems will never be at peace when it comes to humanity, and one can expect that naturally, in order to win a fight, each side wants the most powerful tools at their disposal, whether as a threat or as a weapon.

While it may contain laughable science and a remarkably predictable plot, The Day After Tomorrow and like films carry influences that go beyond the silver screen. It would be hard to pack an auditorium full of teens, soccer moms, and average Joes to hear a scientific lecture about global climate change; however millions paid their 7 or 8 bucks per person to see this film. These films serve as sort of eye-openers to the general population, which seems at most minimally interested in scientific matters. While obviously the science here is completely bogus, the concept of climate change affecting our daily lives is not. People see these movies and are introduced to an idea or concept, while the movie may not have provided factual information; it provided a basis of interest for the general public. By doing this someone who would have before totally looked over a scientific issue might actually take some time to think about it. This sort of effect can be seen by the effect other movies have had. After the release of the two doomsday asteroid movies, Armageddon and Deep Impact, there was a voice of public interest in the subject of impactors from space, surely not something that most people think of often, or ever. These films spawned so much interest that people were asking NASA, what is the plan? A whole set of television shows came about relating to this subject and it was clear that people were interested, it only took a spark. When Al Gore’s An Inconvenient Truth came out in 2006, I remember this film being presented to us in high school as absolute truth, a scientific reality that we were all basically screwed, and it seemed more like a scare tactic than a science documentary. It is obvious that this film has done a lot more that spark public interest, and along with the global warming frenzy we hear about everyday, has really swayed public opinion. There is a huge movement in this country to ‘go green’ and reduce carbon emissions along with other forms of pollutants. Just about everywhere you look now, there is something new that is supposed to be greener and cleaner for the environment, a lot different than say 2 or 3 years ago. Gore’s film, despite having a few likely exaggerations and a bit of scaremongering, brought an important issue directly in front of the public with a huge response. This may have been good for the environment and society, but we can’t always be so quick to accept something we see in a film documentary, on the news, in the paper, or especially from the state as fact. Being a responsible person is about looking into things for yourself, doing your own research, in which you can draw from hopefully un-biased sources and create a much more effective position on the issue. Fact of the matter is, the government, media, celebrities, and others have agendas, often times the information they put out, while it may be factual, is shaped and molded to fit an agenda to get a certain idea across, the idea they want you to think. While, it may be less convenient to check out a science journal than the latest issue of Rolling Stone, your likely guaranteed a much less bias source than your radio or television can supply.

Keeping track of all the physics and general science blunders that take place in The Core is not a short task. I will list a few of the things I noticed in the film and some others pointed out by the ISMP movie review. First of all, like most of these ‘end of the world action type movies’ there is a young genius college professor or some other hot shot that the government brings in to save the day. In this movie it’s Doctor Keyes, a young geologist, who is scooped up from class by some government agents and taken to a secret meeting to determine the cause of 32 mysterious deaths in Boston. There it takes him about 2 minutes to explain the death’s of 32 people as an EM pulse that affected their pacemakers. The general in charge wants to know if it was caused by a weapon, Keyes says no, and is immediately dismissed, with no further investigation into the matter. Later Keyes discovers with his grad. students that the core of the earth has stopped spinning and that earth’s magnetic field is evaporating. This is a perfect example of bad physics. Even if the core did loose its driving force that caused its rotation, it wouldn’t just stop instantly and take the magnetic field with it. Conservation of angular momentum would suggest that such a huge mass of material moving so quickly would take a very long time to slow down, not the year or so the movie suggests. But surely he would be the only one in the world to notice such an impossible thing since he must have the only compass on earth. Anyway this is about where things start to get really bad, now that we know the earth is in danger Keyes shares his discovery with another famous scientist (Zimsky) who then dismisses it but later presents it as his own to the government. Keyes suggests that since the magnetic field is gone, earth will now be vulnerable to the sun’s deadly microwave radiation and that if the core isn’t restarted the planet will fry. This is a huge blunder by the moviemakers; first of all, the magnetic field of the earth has no affect on microwave radiation. Magnetic field or not, the same amount of microwave radiation would hit the earth anyway. Thankfully the amount of microwave radiation is small, not enough to cause any health risks, certainly not enough to melt the Golden Gate Bridge( and by the way what a cheesy target for a random beam of energy through a magnetic field hole, out of every other object on earth these sorts of things just seem to target famous architecture, much like the complete destruction of Rome later on, seriously come on) So now the government calls in both Keyes and Zimsky and asks them what to do, even though factually, it wouldn’t seem that there even is a problem.  But anyway, the plan is to make a manned mission to the core of the earth to drop off some nukes to restart the core. As the ISMP text noted the rational energy of the inner core is about equal to 340 200- megaton bombs. In the movie the plan is to use 5 200-megaton weapons to ‘re-spin’ the core, so even if the energy of the five bombs could be totally converted to a rotational force on the core they would still be 68000 megatons of energy short of spinning the core back up to speed. Also there is no way that an exploding bomb or bombs could create a torque on the core to cause it to spin, an explosion would simply act on its center of mass creating no torque or spin. It gets worse and worse from here on out, to get to the core they will need an impossible craft. The craft will have to be able to withstand extreme heat and pressure for extended periods of time while being able to plow through the earth at extremely high speed to reach the core, all while having a cooling system that could keep essentially a large metal tube (the ship) at around room temp inside, while its thousands of degrees outside. The solution to this is making a caterpillar looking ship that is made of ‘unobtanium’, a tungsten-titanium super cooled matrix or something fake, but scientific sounding like that, that is basically indestructible at any heat or pressure and actually gets stronger as it gets hotter? O.K. well it also has the magical ability to generate electricity when subjected to heat and pressure! There are even more problems with the ship, to plow through the earth, it uses laser/ultrasonics? I’m not sure what kind of spinning laser pointer/ultrasonic array would be able to instantly vaporize tens or hundreds of meters of rock per second in front of the ship to keep it moving quickly down through the crust, if it were at all possible surely such a device would need a heck of a lot more electricity than a single, small on-board nuclear reactor could produce. If the ship itself is impossible, so is the time-line, all of this goes together within 3 months and is ready for launch, making it a government record for speed on any project ever I would assume, not to mention that this would be the most challenging mission ever undertaken by mankind. As the ship enters the earth we have more crazy science, when going through the mantle the crew of the ship dodges state-sized diamonds and is at one point trapped inside a giant void which turns out to be a massive geode. That’s right, amidst the extreme pressure of the mantle there exists a giant empty space full of huge crystals that gets the ship stuck. Even with the intense heat and pressure that would have to exist in this impossible void, the crew can safely walk around outside the ship in their Halloween looking spacesuits. Strangely, even though it’s 9000 F outside, nothing is glowing brightly or even appears hot, minus the lava, and the super-space type suits seem to be unaffected. Even as the ship continues on apparently straight down towards the core, the crew can still walk around horizontally within the ship? That would be like walking up the isle of a commercial jet that was diving straight down. With all of this going on under the surface, other wild and impossible things are going on up on the surface. Apparently a loss of the magnetic field causes huge electrical storms with lightning bolts capable of destroying stone and metal structures. I’m not sure why, but these lightning bolts seem to be a blend of electricity and TNT, as they cause everything they hit to violently explode, including streets, and large stone buildings, we even have numerous cars being blown up and tossed into the air, and to put icing on the cake, several bolts converge to completely destroy the Coliseum in Rome. I have personally never seen lightning make things explode, surely purely bad science. Also the whole extremely dramatic bird scene, here apparently because the magnetic field is vanishing, birds have no idea what to do and begin violently suicide dive bombing everything in London. Even though birds may use the magnetic field to migrate and such, I’m sure they would be able to still remain airborne without it. I noticed during the film that the birds caused some pretty extreme damage to windows and vehicles and such and questioned the physics myself. Indeed ISMP noted this as well and suggests that even at top speed these pigeons wouldn’t even be able to break most windows. O.K., so back to the ship, after they finally make it to the core, the find out that they will need 40 percent more explosive energy to restart the core because the material isn’t dense enough. So the solution is to just grab some plutonium from the reactor and lay it next to the bomb to compensate. Wrong, using plutonium would create fission in the first place not a thermonuclear explosion like the other bombs. Even if the other bombs did cause the few pounds of plutonium to undergo explosive fission, this would be a drop in the bucket compared to the energy of the other bombs, certainly not 40 percent more. Even the scene of the plutonium extraction is laughably wrong. Keyes walks into the reactor compartment and with out even his helmet on, takes the raw plutonium reactor rods out and is not even phased by they presumably lethal radiation. Here this scene is mistake after mistake; they couldn’t even get the chain breaking scene right. I noticed from just casually watching the movie that the chain holding the rods, which melts from heat, seems to just melt like butter but doesn’t glow at all first, aren’t most chains made of steel? Or as they ISMP review joked, it must have been made of lead. There are many things that the ISMP text noticed that I didn’t and it went into pretty good detail in most of the cases I did notice. All in all the science used in this movie is totally bogus minus a few factual details about the structure of earth. This is a horrible depiction of real physics and general science as a whole, and to boot the story is lame and the acting sucks, pretty much two thumbs down no matter how you look at it.

For this exercise I will present a plan to save the world from destruction by a large impactor similar to the asteroid in Armageddon. I will use a situation similar but not identical to the one in the film Armageddon, using similar velocities but a smaller impactor and much more time to react to the situation. I used an asteroid 6 miles in diameter as apposed to the over 700 mile wide asteroid depicted in Armageddon. This would be similar to the size of the asteroid that impacted near Chicxulub in the Yucatan Peninsula 65 million years ago, the supposed Dinosaur killer. The velocity remains the same, with the asteroid closing in on earth at 22,000 mph, or 9,834.88 m/s. I guessed that the asteroid might be able to be detected once it reached a distance equal to about the distance from our planet to Uranus or so. I calculated this distance using Uranus’s average orbital diameter of 2,876,679,082 km, dividing that by 2 to get its average orbital radius of 1,438,339,541km. With this we can then subtract the orbital radius of Earth from the orbital radius of Uranus so that we get the actual distance from the asteroid to the earth and not from Uranus to the sun. This works out to be 1,438,339,541km-74,798,943.75km= 1,363,540,597km or 1,363,540,597,000m. Using this distance, can then divide the 1,363,540,597,000m by the 9,834.88 m/s (speed of the asteroid) to get the amount of time before its impact with earth. This works out to be 138,643,338.5 seconds, about 1605 days or a little under 4.5 years. This sort of time would enable at least some organization of an attempt to intercept this asteroid, at least hopefully.

The plan I came up with to divert the asteroid is to launch an intercepting spacecraft toward the asteroid. The spacecraft would meet with the asteroid, attach itself with its thrusters aiming perpendicular with the asteroid’s line of fire with Earth, fire the thrusters continuously and hopefully push the asteroid far enough off course that is would miss the earth entirely. To understand how this would work we need to understand a few of the basic concepts involved. First, we must take into account how long it would take our lander to actually intercept the asteroid, This time subtracted from the total time until impact would tell us exactly how much time our thrusters would have to push on the asteroid once it gets there. If we have the total distance between the spacecraft and asteroid(assuming the craft is launched from Earth), 1,363,540,597,000m we can then develop a ratio between the two velocities, the velocity of the spacecraft away from Earth (16,000m/s [this value being derived from the avg. velocity of the Voyager 1 spacecraft, the furthest reaching space vehicle yet launched by mankind])and 9,834.88 m/s the velocity of the asteroid toward earth. We can then from this ratio, find the point at which our spacecraft would meet the asteroid in between Earth and the asteroid’s initial position of discovery. 1,363,540,597,000m(.626862758), using this ratio, our spacecraft would meet up with the asteroid when it is 8.338 x10^11 m from Earth. Using this number we can divide 8.338 x 10^11 by the velocity of the asteroid (9,834 m/s) to get the actual amount of time our thruster will have to work on the asteroid before it impacts the planet. This yields 86,910,345.55 seconds, or 1005.91 days, about 2 and three quarters of a year left to try and steer the asteroid away from the planet. For our thruster to push the asteroid far enough away from Earth it would have to push our massive asteroid 6,378.1km (the radius of Earth) or 6,378,100 m away from the planet in a time of less than 2 3/4 years. To see just how far we would be able to move the asteroid we must first come up with some estimated qualities of the objects involved. First, if we assume that our asteroid would be spherical in nature we can use the formula V=4/3Πr³ to find its volume this equation using a 6 mile in diameter asteroid would yield a volume of 4.714102585 x 10^11 m³. From this volume we can then assume and multiply an Earth-like density of 5500kg/m³ to yield 2.59277 x 10^15 kg’s, the mass of the asteroid.

Now that we have the mass of the asteroid we can use Newton’s Second Law of Motion to see just how far the thruster could push the asteroid away from Earth. To figure this out though we will first need to find a value for the thrust of our rocket, or its force on the asteroid. For this value, I used the thrust of the initial stage of the massive Saturn V rockets that propelled the Apollo missions to the moon. Combined between all its thrusters, it had an initial liftoff thrust of 7,648,000 ft./lbs. This value converted to joules of energy works out to be 10,369,158.40 J. To find just how much one of these rockets could push the asteroid away from its collision course with Earth, we can use the equation a=F/m to find the acceleration of the asteroid due to the force of the thrusters acting on it. Because we know that the force of the rockets thrusting away is equal to the force that the thrusters exert on the asteroid, we can simply determine the acceleration of the asteroid by dividing the force of 10,369,158.40J by the asteroids mass of 2.59277 x 10^15, this yields a perpendicular acceleration of the asteroid of 3.99926 x 10 ^-9 m/s² . If we then plug in our remaining seconds before impact (86,910,345.55) into this result, we are left with the asteroid being diverted by 30,208,034m or about 30,208 km, a distance of nearly 5 times the diameter of the Earth, a near miss, but we should be safe.

We of course assume in this that the effects of gravity are ignored, the asteroid is perfectly spherical and has earth-like density, the thruster has a constant thrust that continually accelerates the asteroid without running out of fuel, and that the interceptor would be launched almost immediately after detection, also it may or may not be so that we could spot such a relatively small body at the distance assumed in the calculations, basically I had to give Earth a fair shot.

-Matt Sanders

The 1996 Film “Eraser” is a classic example of bad Hollywood physics. The writers choose some existing technology that the general public knows little about and then transform it with their own set of physics laws so it becomes the perfect weapon. In the film, a rail gun is used to shoot through objects and blast people tens of meters upon impact. Rail gun technology actually does exists and has been tested successfully on a large scale (though velocities are nothing close to the movie values), they don’t come in a convenient shoulder fire weapon like Arnold uses. The U.S. Navy has tested such weapons with successful firing, only the energy it produces when fired destroys the weapon after every shot, and the weapon itself is building sized and uses an incredible amount of electricity for every shot. A rail gun in principle works by passing an electric current through a projectile placed between two conducting rails, the current forms a force in the direction of the end of the barrel, and basically fire projectiles at high velocities. To get an idea of just how bad the physics are we need only to apply a little math. To properly explain the situation we need to have some decent physical estimates of the objects involved. First: the bullet, to give a familiar example, in my calculations I used a standard sized .30cal bullet made from aluminum. A standard lead .30cal round from the 30-06 cartridge has a mass of about 12 grams or .012kg. the same sized round made of aluminum (as stated in the film) would weigh 2.86g or .00286kg, this is based on the fact that lead has a density of 11.34g/cm³ and aluminum has a density of 2.7g/cm³ so given that the bullets have the same volume we can presume, using division that an aluminum .30cal round will have a rest mass of .00286kg, we will need this when determining is momentum. Along with the mass of the bullet we will need to find it’s velocity to be able to calculate it’s momentum. In the film it says that the round is traveling nearly the speed of light or something to that effect, so I will as the movie physics text used, use a velocity of 90% of the speed of light. So c=299,792,458 m/s, then our velocity is V= c ( .90), therefore our velocity equals v= 269,813,212.2 m/s. It is interesting to note that even as the movie states these bullets are traveling at more than six hundred and four million miles per hour, they are able to be seen flying across the screen with their blue vapor trails. Anyway, due to the extreme speeds involved, we will not be able to use the simple P=mv when determining the bullets momentum, we will instead need to use one of Einstein’s equations. According to this equation, when an object’s velocity is approaching the speed of light we must use a value termed the Larentz factor in the equation to produce an accurate momentum, this is because as objects approach the speed of light their mass actually decreases. The equation P=mv then becomes P= γm_ou where γ is the Larentz factor and m_o is the object’s mass at rest. The Larentz factor is not a given value and must also be calculated using γ= 1/(1-U²/C²)^1/2 U is the objects velocity. We then have γ=1/[1-.90C)²/C²]^1/2 , this yields a Larentz factor value of 2.294. We can now use this to determine the bullets momentum. P= γm_ou is then P= 2.294(.00286kg)(269,813,212.2 m/s) this equation yields a bullet momentum of 1,770,201.315 kg/_m/s .This is enough momentum to give the bullet extremely high kinetic energy. To calculate just how much energy a round like this would have we must also use Einstein’s relativity equations due to the high velocity of the object in motion. To correct for these speeds, E_k =mv² becomes where p is the objects momentum, m is the object’s mass at rest and c is the speed of light in a vacuum. If we substitute in our know values for momentum, mass, and speed of light we are left with E_k = 3.326 x10¹⁴ Joules of energy about the equivalent of 79.49 kilotons of TNT. Therefore the impact of this bullet would have an explosive energy of about 5.5 times the energy of the atomic bomb dropped on Hiroshima during World War II. A far cry from simply blasting people back a few meters. We now have the bullet’s momentum and have found its kinetic energy, now we will determine both the recoil momentum of the weapon and the then the shooter and weapon together. The law of conservation of momentum states that if the bullet has a forward momentum of 1,770,201.315 kg/_m/s then the gun firing that bullet must experience an equivalent force in the other direction. If we already know that the rifle’s momentum will be equivalent to the bullets we can then determine the rifles recoil velocity by dividing the rifles recoil momentum by its weight in kg, by doing this the kg’s cancel and we are left with a recoil velocity in m/s. For this calculation I assumed a rifle mass of 40 pounds, this is about equivalent to a small sized machinegun much the same size as the rail gun used in the film, this works out to 18kg for the sake of our equation. So we now have 1,770,201.315 kg/_m/s / 18kg, this yields a rifle recoil velocity of 98,344.5 m/s or about 219,990m.p.h., this would of course blow the shooters arm right off. This is in drastic comparison to the slight wobble Arnold experiences when firing two of these weapons repeatedly, each in one hand, during the film. If somehow Arnold was invincible (in the Eraser he seems at least to be) and the rifle recoil did not blow through him, we can figure out how fast he should have been blown back by the firing the rail gun. As before, we will use the same recoil energy as before but use a larger mass when determining the recoil velocity of Arnold plus his rail gun. If we take 18k and 107kg (Arnolds weight at the peak of his muscleman career) and add them we get 125kg, the combined mass of Arnold plus his weapon. We then simply divide our momentum, 1,770,201.315 kg/_m/s by 125kg, and again kg units cancel, and we are then left with a backwards velocity of 14,161.61 m/s or 31,608 m.p.h. for Arnold and his weapon. Note again that during the movie Arnold barely moves a muscle when blasting several rounds at his enemies. By now using the recoil velocity of Arnold plus his gun we could then determine their momentum as well, their combined momentum, according to the law of conservation of momentum should be equal to the momentum of the fired bullet, given that friction is not taken into account and Arnold doesn’t absorb any recoil energy.The last issue to deal with on the surface of the rail gun problem is what happens to the victims who are hit by its projectiles. In the movie, when someone is hit by the rail gun, their chest lights up and they are merely thrown back sometimes as much as 10 meters or more. We have shown above that any impact of a projectile with such energy as the rail gun round would cause a massive explosion devastating an area miles around it, vaporizing the shooter and everyone else. Also, while the victim was simply blown back a great distance they didn’t seem to have any massive wounds. It can be seen from real world evidence that even a relatively low velocity .50cal machinegun round at only 900 or so m/s has been know to blow human bodies violently apart. Calculating the backward momentum of the victim ignoring the massive explosion and vaporization would be a little more difficult. Conservation of momentum suggests that a projectile, unless it experiences no resistance when passing through an object will impart some of it’s momentum to the object it strikes, therefore preserving the total momentum of the system. To know the backwards momentum of the victim we would need to find out how much energy was transferred from the bullet to the victim upon impact. This isn’t possible from watching the movie screen unless you were to take into account an estimate of how far they flew backwards, their angle of launch and exactly how much energy it would take to launch them that distance. This would be possible with a lower speed projectile in real life by observing the bullets speed and momentum prior to and after impact with the victim. The initial momentum of the bullet, minus it’s post victim momentum would leave you with the momentum force experienced by the victim, then one need only account for the victims mass in determining how far he or she would be blown back. All in all the physics of most of Eraser is bogus, especially every aspect of the rail gun, hopefully I have shown that this sort of weapon is not only unlikely, but physically IMPOSSIBLE. -Matt Sanders

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