The end of the world (again)
I originally started this journal to write about science and eschatology, so here's a nice doomsday-ish post for you:
I'm always harping on the dangers of asteroids, but I think a lot of people don't understand the risks involved. So let's engage in a little Gedankenexperiment:
Let's say you hopped in a rocket ship and traveled into empty space, away from any other planets, the equivalent of the distance from the Earth to the moon--about 384,000 km. Then you stop your rocket ship, and just let it fall back to the Earth, the way a ball falls to the ground.
When the rocket "lands" on Earth, the Earth will absorb the kinetic energy of the rocket. Let's simplify things and assume the rocket doesn't heat up and blow up in the atmosphere (like the Tunguska Event and that the Earth doesn't act like a big fluffy mattress and harmlessly absorb most of the impact. In this case, the energy of the explosion caused by the rocket hitting the earth will be equal to the kinetic energy of the rocket, or 1/2 X the mass of the rocket X the rocket's velocity squared (1/2*mv^2).
We can calculate what the rocket's velocity is when it hits earth, or even easier we can just calculate its potential energy at the point where it starts to fall, which will convert 100% to kinetic energy by the time of impact. The potential energy equals mass X acceleration due to gravity X distance from the earth (mgh). g is 9.8, and h is about 384,000,000 meters. We'll leave the mass variable for now, so the energy of the impact will be m*9.8*384,000,000, or 3.7x10^9 times the mass of the rocket.
The unit of the energy is in joules, but let's translate it into something more familiar. One ton of TNT yields 4.184x10^9 joules. As you can see already, if the rocket only weighs one kilogram, you're looking at an explosion equivalent to almost a ton of TNT. The bomb dropped on Hiroshima had a yield of about fifteen thousand tons of TNT.
Now let's say, instead of a rocket ship, you're sitting on a piece of space debris similar to an asteroid, except in this case it's got a really tiny orbit (Most asteroids orbit the sun at a distance greater than Earth, so they'll have a lot more energy. This is just a hypothetic example remember). Most asteroids are made primarily out of iron, which has a density of 5.5 grams/cubic centimeter or 5500 kilograms/cubic meter. But we'll be optimistic and assume this is a rockier asteroid with a density of 3000 kilograms/cubic meter.
So let's say the space debris is on cubic meter in volume--about the size of like a Geo Metro. That rock will hit earth with an impact of 3000 X 3.7x10^9 joules, or the equivalent of about 2600 tons of TNT--probably enough to level a city block. NASA's Near Earth Object Program considers an object with a diameter of less than 50 meters to be relatively harmless. If our hypothetical space rock were a sphere with a diameter of 50 meters, its volume would be 1962.5 cubic meters so its mass would be 5887500 kg. The energy of its impact would be five million tons of TNT, or a handful of modern atomic weapons. I don't know much about the conditions that cause nuclear winter so I can't say for sure that it will happen, but an impact that big would probably be capable of wiping a European country off the EArth, at least.
Will an impact like this happen any time soon? Who knows! Space is a big place, and we can't even see all the objects that are around us. But it's happened plenty of times before.
I'm always harping on the dangers of asteroids, but I think a lot of people don't understand the risks involved. So let's engage in a little Gedankenexperiment:
Let's say you hopped in a rocket ship and traveled into empty space, away from any other planets, the equivalent of the distance from the Earth to the moon--about 384,000 km. Then you stop your rocket ship, and just let it fall back to the Earth, the way a ball falls to the ground.
When the rocket "lands" on Earth, the Earth will absorb the kinetic energy of the rocket. Let's simplify things and assume the rocket doesn't heat up and blow up in the atmosphere (like the Tunguska Event and that the Earth doesn't act like a big fluffy mattress and harmlessly absorb most of the impact. In this case, the energy of the explosion caused by the rocket hitting the earth will be equal to the kinetic energy of the rocket, or 1/2 X the mass of the rocket X the rocket's velocity squared (1/2*mv^2).
We can calculate what the rocket's velocity is when it hits earth, or even easier we can just calculate its potential energy at the point where it starts to fall, which will convert 100% to kinetic energy by the time of impact. The potential energy equals mass X acceleration due to gravity X distance from the earth (mgh). g is 9.8, and h is about 384,000,000 meters. We'll leave the mass variable for now, so the energy of the impact will be m*9.8*384,000,000, or 3.7x10^9 times the mass of the rocket.
The unit of the energy is in joules, but let's translate it into something more familiar. One ton of TNT yields 4.184x10^9 joules. As you can see already, if the rocket only weighs one kilogram, you're looking at an explosion equivalent to almost a ton of TNT. The bomb dropped on Hiroshima had a yield of about fifteen thousand tons of TNT.
Now let's say, instead of a rocket ship, you're sitting on a piece of space debris similar to an asteroid, except in this case it's got a really tiny orbit (Most asteroids orbit the sun at a distance greater than Earth, so they'll have a lot more energy. This is just a hypothetic example remember). Most asteroids are made primarily out of iron, which has a density of 5.5 grams/cubic centimeter or 5500 kilograms/cubic meter. But we'll be optimistic and assume this is a rockier asteroid with a density of 3000 kilograms/cubic meter.
So let's say the space debris is on cubic meter in volume--about the size of like a Geo Metro. That rock will hit earth with an impact of 3000 X 3.7x10^9 joules, or the equivalent of about 2600 tons of TNT--probably enough to level a city block. NASA's Near Earth Object Program considers an object with a diameter of less than 50 meters to be relatively harmless. If our hypothetical space rock were a sphere with a diameter of 50 meters, its volume would be 1962.5 cubic meters so its mass would be 5887500 kg. The energy of its impact would be five million tons of TNT, or a handful of modern atomic weapons. I don't know much about the conditions that cause nuclear winter so I can't say for sure that it will happen, but an impact that big would probably be capable of wiping a European country off the EArth, at least.
Will an impact like this happen any time soon? Who knows! Space is a big place, and we can't even see all the objects that are around us. But it's happened plenty of times before.