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Hi! When I read or hear about asteroids, specifically about those that have impacted the earth at sometime in the past, I notice that the authors compare the force that the asteroid impacted the earth with to the strength of the atomic bomb. (Example: The asteroid that killed the dinosaurs impacted the earth with the force of several atomic bombs) Now I know to calculate the force of an object that would hit the earth (f=ma) (correct me if that is not how you calculate the force of an object that would impact earth - must I know the objects speed, etc?) but how do I compare that force to the explosion of an atomic bomb? It would be interesting to see, for example, How the impact of a 10-ton object made of a various material, and the destruction that such an object would produce,would compare to the destruction of an atomic bomb. I would assume that 1 atomic bomb would produce the kind of destruction seen in Japan during WW2? Thank you so much for your help, Happy New Year!
Question Date: 2009-12-30
Answer 1:

The people quoting statistics like that are using the word "force" incorrectly; the word they should be using is "energy". They also miscompare the amount of energy of atomic bombs, which vary a lot in explosive power.

The energy yield of the impactor at the Cretaceous-Tertiary (K-T) boundary 65 million years ago was equivalent to approximately 100 terratons (terra = trillion, or 1012) of TNT; we know this based on the size of the (200 km diameter) hole it blew in the Earth's crust in southern Mexico.

Based on the depth of the Earth's gravitational potential well, the minimum speed such an object would have acquired were it simply dropped out of space is about 16 km/second (which is equal to escape velocity). It probably was moving faster, but not by a whole lot; objects in the solar system mostly move at speeds in tens of kilometers per second. In order to have that much kinetic energy that could be released upon impact, the object could have had the density of rock and a diameter of roughly 10 kilometers. There is a question of how dense asteroids are, however; they may be giant piles of rubble, which would lower the density and thus necessitate a larger size as well. Of course, if the object were made of ice (a comet, instead of an asteroid), then it would have needed to be bigger as well, because ice is less dense than rock.

As of the mid 1990s, the combined nuclear firepower of the nations of the Earth added up to an estimated 20 gigatons (2 x 1010), roughly one five-thousandth of the energy needed to make the crater that the K-T impactor made. The bomb that destroyed Hiroshima had a yield of roughly 20 kilotons, a million times smaller yet. By contrast, the largest nuke ever detonated was a Soviet test of 60-something megatons, about one three-hundredth of the world's total estimated firepower.

In addition to creating a 100-mile wide hole in the Earth, the K-T impactor caused a roughly magnitude 10 earthquake along the eastern seaboard of North America. The quake wouldn't really have mattered as far as anyone living there would have been concerned, however, as the flash from the fireball would probably have ignited everything flammable within a thousand kilometer radius, like an atomic bomb - just much, much, bigger.

As for the global effects, that's still hotly debated. It's not even certain that the impact was responsible for the extinction of the non-bird dinosaurs, although most paleontologists agree that it probably contributed. There are massive outpourings of lava in India (the Deccan traps) at the same time (hundreds of thousands cubic kilometers of basalt), which would have released vast quantities of poisonous gasses into the atmosphere, enough volcanic ash to blot out the sun for some months even without the impact dust doing the same thing, and lastly amounts of carbon dioxide that make human greenhouse emissions seem insignificant in comparison. Nonetheless, based on some physical models, there is the theory that the impact ejects itself would have heated up the Earth's upper atmosphere upon re-entry and literally broiled the whole planet, causing a global firestorm and killing everything that could not get either underground or underwater. The problems with this hypothesis are (1) the K-T extinction hit marine life almost as hard as it hit life on land, and (2) there have been other large, although not as large, impacts that are not associated with mass extinctions in the fossil record.

A majority of paleontologists (myself included) seem to be gravitating toward what I call the "Murder on the Orient Express" theory concerning mass extinctions: you usually need several things to happen simultaneously in order to cause them. This appears to be true of the K-T, as well as a number of others, both larger and smaller.

Answer 2:

Actually its quite simple. The energy of the impact is given by 1/2 mv2 where m is the mass of asteroid (directly related to its size or characteristic length since we know the density of 'cosmic' materials : rho for ice, rock and metal (essentially Fe-Ni 90/10 ) are, 1000 kg/m3, 3000 kg/m3 and ~8000 kg/m3, respectively) and V is the RELATIVE VELOCITY between Earth and asteroid at the moment of impact. This velocity is minimally the escape velocity for Earth of 11.2 km/s and can reach up to about 70 km/s for a head on impact with a body such as acomet that moves on a retrograde orbit about the Sun. Typical impact velocities are in the range 15-50 km/s depending on orbital details.

So the KINETIC ENERGY is 1/2 mv2 so then there is only the conversion from JOULES which is what impact energy is and EQUIVALENT kg of TNT. That conversion is this: One ton of TNT (1000 kg=1t) = 4.2x109 Joules (J).

For comparison, the atomic bomb dropped on Hiroshima on August 6, 1945, exploded with energy of about 15 kilotons of TNT that is 15000 tons of TNT detonated all at once. The nuclear weapons currently in the arsenal of the United States range in yield from 0.3 kt (1.3 TJ) to 1200 kt.

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