Could a 200GT TL destroy an asteroid the size of Texas?

[Admiral Valdemar]

A Texas-sized asteroid is headed toward Earth at 22,000 mph and the only way to save humanity is to to land a ragtag oil rig crew on its surface, drill an 800-foot-deep hole, plant a nuclear bomb on a convenient fault line, and split the asteroid in half, all of which has to be done in a mere 18 days. The crew is the usual lovable assortment of misfits and neurotics in a complete spectrum of shapes and sizes. They have no space flight experience and flunk their medical exams, but are supposedly the best people for the job thanks to their knowledge of oil well drilling. Of course, this knowledge cannot be conveyed to astronauts or NASA engineers.

One of the worst physics insults occurs after our plucky heroes are strapped into their shuttles and launched. They have to stop at the Mir space station and refuel. Evidently, one of the guys from the movie's accounting department pointed out that simulating apparent weightlessness would be expensive. In response, the moviemakers have the Russian on Mir throw a switch and create artificial gravity by rotating Mir. The station rotates fast enough to reach 1 g in less than 30 seconds, even though Mir's mass is about 124,340 kg.

The level of artificial gravity would be equal to the centripetal acceleration, which depends on the distance from the axis of rotation located in the center of Mir's main cylindrical-shaped section. As they walk around, the workers have their feet on one side of the axis of rotation and their heads on the other side. This means that their feet and heads would feel like they were being pulled in opposite directions. The artificial gravity level could not possibly seem constant unless they laid on the floor. Artificial gravity can only work in a gigantic space station where the height of a human is a small percentage of the radius of rotation. In such a situation astronauts would not feel the variation in artificial gravity between their heads and feet. Mir's highly variable artificial gravity would be disorienting and probably cause the workers to stumble and vomit.

If the rotation of Mir were set so that the inner wall of the main module had Earth-like artificial gravity (9.8 m/s2 centripetal acceleration), the outermost parts of Mir would experience about six times as much. This would be like attaching Mir to two freight train engines moving in opposite directions. Mir would be torn apart.

When our heroes land they find a hodgepodge of large, spike-like protrusions all over the asteroid. Evidently the spikes are supposed to make the place look scary. We would use the term silly. How could spikes possibly form? We're at a loss for an explanation or even an example of something like it somewhere else in the universe.

Our heroes have no problems walking or standing in an Earthlike way even though the gravity force would have been about a tenth of the gravity force on Earth. The low gravity cannot support an atmosphere and yet we see flames at the crash site of one of the space shuttles.

To get an idea of the asteroid's size, consider that Texas is 1,289,000 meters long from the eastern side to the western tip. Although the asteroid is misshapen, for convenience we'll assume it's spherical with a diameter of 1,289,000 meters. If it has the same density as Earth (5500 kg/m3), the asteroid would have a mass of about 6×1021 kg. A 243 meter (800 foot) deep hole seems awfully insignificant compared to the length of Texas.

We couldn't help thinking that a Texas-sized asteroid deserved a Texas-sized hole. This set our imaginations running about how to dig one. The answer hit us like a meteorite: bowling! Why not blast a hole in the asteroid with bowling balls? Each bowling ball's blast could come from its kinetic energy. With the asteroid headed toward Earth at 22,000 mph a space shuttle could head away from Earth at 22,000 mph straight toward the asteroid. This would give a closing speed of 44,000 mph or 19,678 m/s. A bowling ball rolled out the front of the shuttle would eventually strike the asteroid with so much kinetic energy that the ball would explode. We use the following equation to calculate the kinetic energy of each ball:

K = ½mv2

Where K is kinetic energy, m is mass, and v is the magnitude of velocity. If we assume each ball's mass is 8 kg, then the kinetic energy will be 1.5 billion joules, or the energy contained in 740 pounds of TNT. This would be a pretty big blast, but not enough for a Texas-sized hole. However, a space shuttle can carry a 29,545 kg payload, or in other words 3,693 bowling balls. Assuming that each ball blasted a 2-meter-deep hole, 3,693 bowling balls could create a hole 7,386 meters, or 24,350 ft, deep. Put another 3,190 on a second shuttle and the hole could be deepened to 45,385 ft (13,767.05 meters) or about 50 times deeper than the movie hole. This would still leave room on the second shuttle for a 9 megaton nuclear bomb (the biggest in the United States arsenal). Roll a ball every 4 seconds and the hole could be completed in 7.6 hours. Of course, this assumes that the balls land one after another in about the same place and that the explosion of one ball doesn't disrupt the others.

Surely Bob's bowling buddies would have even more appeal than a bunch of oil rig workers. Think of the possible misfits. Imagine a scene where NASA guys try to bowl and throw gutter balls as Bob's boys guffaw. Only Bob's boys could put that special spin and accuracy on the ball needed for proper blasting. The NASA guys would have to tear out Bob's lanes and redesign them for installation on the space shuttles, but that would add to the drama. Once in space, one of of Bob's boys could get space psychosis, think he was playing basketball, and waste a few bowling balls. Bob could reason that his mass was just enough to compensate for the missing bowling balls and become a hero by not letting go of the last bowling ball as he hurled it down the lane. He would fly kamikaze-style into the hole and successfully blast the last few feet of depth.

Unfortunately, Bob's bowling buddies would be subject to the same physical limitations as the oil drillers. By our calculations the asteroid was about 10 hrs away from Earth when the drillers landed on it. Allowing 8 hours to drill, the bomb could not have been detonated any more than 2 hours before the asteroid was supposed to impact. Given this detonation time, the asteroid halves need a separation velocity of 4,738 mph (2,119 m/s) to miss Earth by the 400 miles stated in the movie. Each asteroid half would acquire 6.7 × 1027 joules of kinetic energy when it reached the required velocity. The biggest nuclear bomb ever built was constructed in Russia and had a 100-megaton yield. To give the asteroid halves the required kinetic energy would require 64 billion of them. This assumes that no energy is needed to create the split and that about 50% of the bombs' blast energy goes into the kinetic energy of the asteroid halves. It also neglects the gravitational attraction force between the two asteroid halves, which would tend to slow their separation velocity.

Even if the bomb did split the asteroid, the halves would not translate outward as depicted in the movie. They would rotate as they moved apart since the bomb was located near the asteroid's center of mass. The force created by the bomb would create a torque or twisting action on each asteroid half. To visualize this effect, imagine splitting a peeled orange by pulling it apart on one side. The gap at the front of the orange would widen faster than the gap at the back, giving each half a slight rotational motion. For the asteroid halves, this rotational motion would add to the total kinetic energy requirement, meaning we would need an even bigger bomb.

According to the movie the asteroid starts rotating on three axes as it passes the Moon. Yet miraculously, the asteroid is lined up perfectly with Earth when the bomb detonates. What's more, the asteroid splits exactly in half, and the parts have no rotational motion.

Okay, let's assume that everything falls perfectly into place, and the core of the asteroid just happens to be a fissionable material which is exploded by the nuclear bomb. Even if the halves fly apart and miss Earth by 400 miles exactly as depicted, it's still going to be a tragedy. The gravitational force created by the asteroid halves as they pass Earth will be about 100 times higher than the gravitational force from the Moon, which causes tidal actions on Earth. Since most of Earth's population lives in coastal areas, most of the world's population will be destroyed in the resulting tidal surge. Sometimes there's just no way to have a happy ending.

-Source: http://www.intuitor.com/moviephysics/

[Asst. Asst. Lt. Cmdr. Smi]

And what about that 11G maneuver around the moon? The only way a nuke of that size could blow up the asteroid if the asteroid was mostly hollow, full of flammable gases, and made of weak materials, with the latter option being unlikely, considering there was iron in the asteroid. On another note, what would be the KE of this asteroid impact? What would happen to Earth?