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balanced cork extra credit

"The Laws of Physics in an Animation Universe."

Tom Austin
Physics 123
October 19 2011

Physics in the Film Armageddon

Armageddon is a live action film staring Bruce Willis as Harry Stamper, the best oil well driller on the planet; Ben Affleck as AJ, the son Harry never had; and Liv Tyler as Grace, the daughter Harry does have but who is in love with AJ. Tension is build early in the film when Harry finds AJ in bed with Grace. Not much much unexplained physics going on here, if you exclude Harry shooting at AJ with a shotgun while chasing him around an oil rig and not blowing anything up. The film is directed by Michael Bay, produced by Jerry Bruckheimer and released by Disney's Touchstone Pictures.

Unknown to Harry, AJ, and Grace is that the world is about to come to an end. A Texas sized asteroid  on a collision course with earth has just been discovered by NASA, and unless something is done all life on earth – down to the smallest bacteria – will be extinguished. The best plan NASA can come up with on short notice is to grab the best oil well driller on the planet and have him train a bunch of astronauts to use a space age oil drilling rig attached to a specially designed asteroid rover that luckily for mankind just happened to be available. OK, it wasn't just laying around. NASA had been planning or a mission to send it Mar and drill holes in the red planet. The astronauts have not been able to figure out why the rig won't work. Harry is familiar with the design because it was stolen from him and in two minutes figures out the problem. The astronauts have put it together backwards. Harry decides the only way this plan will work is if he uses his crew and decides that it is faster to train rough necks to be astronauts then to train astronauts to be rough necks.

NASA jumps at the chance to send a bunch of irreverent, loud talking, hard drinking, oil men in to space to save the earth. After two days of ultra-rigorous astronaut training the crew is ready and are loaded on board two special top secret space shuttles that also happened to be sitting around in case a Texas sized asteroid needed to be chased down and taught a lesson. The drill rigs have been attached to the giant mars rovers and loaded aboard  the shuttles that will carry the crew  to the drill site on the asteroid. What could go wrong?

Of course the movie is fun. How could it not be with a Texas sized asteroid heading straight for Earth. Texas is about 1300km square – not quite but close, and if we make it a sphere for this discussion and give it a 2000km diameter its size is close to that of Pluto. This is a big piece of rock. The asteroid is also very irregular in shape, very jagged with deep canons, and lots of stalagmites on its surface. Looking at the two figures of the asteroids, Eros and the one from the movie in figures 3 and 4 it is easy to see the two look nothing alike. In the premise the asteroid was dislodged by an impact with a comet so maybe there are bits of the comet stuck to its surface.

NASA who cooperated with the production has a notification in the credits disavowing any endorsement for the authenticity of the movie's physics. A website that evaluates movie physics states that NASA actually found 168 different violations. Only the three most obvious flaws will be studied for this paper. During the journey to the asteroid the two spacecrafts need to dock at the Russian Mir space-station to take on fuel. Apparently the space-station just happens to have extra on board. The Mir is put in to a spin with the space crafts docked at opposite ends of the stations axis of rotation to give the crew a little artificial gravity during their stay. I don't understand the need for this extravagance but suspect it had more to do with the difficulty of creating the illusion of zero gravity during filming then to help the plot. How the gravity is created and how it behaves as the astronauts move about the station will be analyzed.

After a series of catastrophic mistakes the crew manages to destroy the station while barely escaping with their lives and the one Russian astronaut that was on board when they arrived. Sorry Russia, but with the extermination of all life on the planet at stake what's the loss of one space-station. The two spacecraft are on their way to slingshot around the moon to accelerate to the 22,000 miles per hour they will need to catch up to the asteroid. Things don't get any better on the next portion of the trip. One of the spacecraft crash lands on the surface destroying every thing except for their rover, AJ (Ben Affleck), and two other members of the crew. The other ship manages to survive its landing but is miles off course and as luck would have it centered over a 50 foot thick layer of the hardest iron yet known to man. Looking at the physics while on the surface we see a good sequence where one of the astronauts pulls another off of a cliff to save him from an explosion. The fall will be analyzed to see how gravity behaves on the asteroid.

Tension builds as the crew from the other ship, the one with Harry (Bruce Willis) on board, begins to drill through the sheet of the hardest iron known to man and destroy drill bit after drill bit before finally burning up the transmission of the drilling rig. Just as it seems that all hope for mankind is lost, the second rover comes over the hill with AJ on board. Luckily it has a intact drilling rig and with determination equal to the hardest iron known to man cuts through to the required depth of 800 feet. About a tenth of the way to the center of the asteroid. The asteroid's description says it is Texas sized but maybe it is just a very thin slice of Texas. With the required depth reached, all that remains for our stalwart crew is to place the nuke, set the timer, fire up the spacecraft engines, and escape the nuclear blast. Unfortunately the timer is damaged and no one thought to bring a spare. Someone will have to stay behind and make the ultimate sacrifice for good of mankind.
AJ picks the short straw but Harry tricks him and pushes him back in to the air lock and heads off to steal all the glory. The question is how big does this blast need to be. It must be must split the rock in two with enough force to divert each halve to opposite sides of earth. Humanity did get a break because this one in a billion Texas sized asteroid is lined up to impact dead center with the earth. With a few assumptions I will attempt to figure out the forces required to move the two halves the required distance in the time remaining before the collision.

There are three questions to be asked and answered. The first: Is the centripetal force generated by the spinning of the Mir space station with the two space crafts attached consistent with the laws of physics and if not offer an explanation. The second: is the falling action of two astronauts on the surface of the asteroid consistent with the physical laws of gravity of a Texas sized asteroid and if not offer an explanation of how the laws of physics have changed on its surface. The Third: is analyze the amount of force required to divert two half Texas sized chunks of rock away from a collision with earth and if this force is reasonable with our understanding of force, mass, and acceleration; or offer an explanation of how this might be accomplished.

After the spacecrafts have been attached to the Mir station docking arms rockets are fired that cause it to spin about its axis. The plan is to create enough centripetal force to simulate the effects of earth gravity.  It  assumed that the axis for the rotation of the station is aligned with  its center of the mass. The act of spinning the station seems to work because we witness the Russian astronaut on board ceasing to float in space and get pulled toward the floor. He must have been attached to a hidden tether so the station could exert a force on him and increase his angular momentum. Centripetal force is effected by two things; the period of rotation and the radius of the rotating object experiencing the force. Figure 1 illustrates the centripetal effects on a rotating body under the real laws of physics. It shows that as you move toward the center of rotation for a given rotation period the simulated gravity effects are reduced. So out at the ends of the arms where the spacecrafts are docked to the Mir the gravitational forces would be greatest but would diminish as the crew travel to toward the center of the station. This does not happen. The forces on the crew are the same no matter where in the station they are. The laws of motion would have to be altered in the station to fit the graph shown in figure 2. The force is constant, independent of the radius, and only affected by the velocity of the spin. A confusing factor in this scene is ithe direction of the line of gravity. The crew runs all over the station and always seem to have their feet planted on the pathways. A competing theory that would resolve the gravitational behavior could have the rotation of the station creating a field that pulls the feet of the crew toward whatever walkways they find them selves on.

After landing on the Asteroid erratic effects of gravity still seem to plague the crew. They have special suits with down thrusting rockets to help hold them to the surface. These would work and with the correct computer control even compensate for walking, jumping, and running. They must also have small hidden thrusters on their bodies because when walking in the ship with their suits off they still experience earth level gravity. The asteroid, approximately the size of Pluto, has a gravitational pull of 1/12 that of earth. In the scene Harry pushes horizontally on the face of a cliff and the two slowly drift toward the surface of the asteroid as if in slow motion. Their down thrusting rockets are of no help because of their positions. The falling action is not too bad. The problem is that the parabola is very similar to that on earth. The lower gravity would effect the vertical acceleration and increase the time it would take to hit the earth but the horizontal velocity would not change. The horizontal distance they would travel would be much greater on the asteroid because of the extra time taken to hit the ground. A possible explanation is that the plate of the hardest Iron known to man effects horizontal velocity slowing down motion in the horizontal direction very much like someone filming a falling person on earth and showing it in slow motion. A competing theory could be that the Iron plate actually alters time of falling objects.

We need to Assume that the magic depth to split a 2000km thick asteroid down the middle  is 800 feet and that applying enough  forces equally against its two halves would send them to opposite sides of the earth. For this discussion the motion toward the earth will be called forward motion and motion perpendicular to it side motion. Even if a force could be generated to accelerate the rock halves to the sides fast enough in time to miss the earth a problem exists with where the charge is placed. If the charge is not at the center then the halves would spin about the center and not add appreciable velocity to the side motion.  So the answer must be that the center of the asteroid is just 800 feet below the surface and they are drilling along its axis in the direction of forward motion. It is the hardest Iron known to man or what they thought to be iron it is actually a very dense material that is a thousand time heavier then the rest of the planet and the crew was lucky to find a very thin layer that allowed them to drill to the center of mass of the asteroid. Now to tackle the force issue. The asteroid is traveling at 22000 miles per hour. The distance from earth when the blast occurs is about 8000 miles which will take a quarter of an hour for impact to happen. The halves need to travel half that far in the side direction (half the diameter of the earth) so the halves need to reach a velocity of 11000 miles per hour in 15 mins. That would be an acceleration of 11000miles per hour /.25 hour or

44000miles per hour/hour or 30 feet per sec/sec, or about 10 m/s². This would require 10 neutons per kilogram. The mass of Pluto is 1.3 x 10²²  requiring 1.3 x 10²³ newtons per meter of distance traveled and we need to travel about 6500 km which is about about 8.5 x 10²⁶ newton meters. A one megaton bomb generates 4 x10 ¹⁵ newton-meters. So we need a bomb that is about 2 x10¹¹ megatons. That's a big bomb. Greater then the combined arsenal of the whole world. So either the asteroid is either incredibility light or made up of fissionable material which assists in its annihilation.

In conclusion the laws of physics must get be bent to large degrees to accommodate this film. It does not take away from the success of the movie. It has grossed almost a billion dollars since its release. The action is well timed and is quick enough to hide the flaws in physics, unless one has taken Physics 123 and then it is laughable. The best alternative is that the NASA faked the whole thing to cover up cost over runs on its other programs and nothing in the film actually happened but that would be a totally different movie. 

 

Figure 1. Centripetal force. In Our world. (from the www.yesican-science.ca website)

 

Figure 2. Centripetal force. In the Armageddon world. (modified from Figure 1)

 

 

Figure 3 The Asteroid Eros from NASA

 

Figure 4 the Asteroid from the film Armegeddon.