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Saturday, January 4, 2014

Asteroid Math -- January 3rd we had a Earth Entry, with nearly no warning

Kinetic Energy in a meteor

Note: I will use the carat symbol ^ to represent raising a number to a power. Thus, 100 = 10 squared = 10^2. Similarly, a million is 10^6.
Let's assume that the meteor is travelling at 30 km/sec = 30 x10^3 meters/sec = 3 x10^4 meters/sec.

(Where did I get this number? I pick it because it is the velocity of the Earth around the sun, and meteors are also going around the sun, so their velocity is similar.
How do I know this is the Earth's velocity around the sun. Either I can look it up, or calculate it by remembering that the distance from the earth to the sun is 93 million miles = 150 million km = 150 billion meters. The distance around the circular orbit is this number times 2 pi = (150 x10^9)x(6.28) = 942 x10^9 meters = (approximately) 1000 x10^9 meters = 10^12 meters.
The Earth takes a year to go around. To find the number of seconds in a year, take 365 days x 24 hours/day x 60 minutes/hour x 60 seconds/minute = 31600000 seconds = (approx) 3 x10^7 seconds.
Now divide the distance around by this many seconds, to get
velocity = (10^12 meters)/(3 x10^7) = 30000 m/sec (approximately)
The kinetic energy is given by
E = (1/2) m v^2

Let's calculate the energy of a 1 gram meteor. We must use mks units. So we set m = (1/1000) kg = 0.001 kg. v = 30 km/sec = 30,000 meters/sec. Plug into the equation:
E = (1/2) (.001) (30000)^2
= 450000 joules
To convert this to calories, divide by 4.18
= 100000 calories (approximately)
=100 Calories
CONCLUSION: A meteor has 100 times as much energy per gram as does TNT!
This is an amazing, surprising, yet simple result to remember.

Suppose the meteor were larger, and weighed a ton? What would its kinetic energy be? Every gram would have the energy of 100 grams of TNT.

So a ton of meteor would have the energy of 100 tons of TNT.

Suppose we had an asteroid that weighed a million tons? 

Then the kinetic energy would be equal to 100 million tons of TNT, or about 100 hydrogen bombs.

How heavy would an asteroid be if it were the size of San Francisco? 

Lets estimate 10 km x 10 km x 10 km = (10,000)^3 = 10^12 cubic meters. A cubic meter weighs about a ton, so the mass would be 10^12 tons = 10^6 megatons. The kinetic energy would be 100 times larger, or 10 million megatons = 10 million hydrogen bombs. 

The US and Russia together had about 10,000 hydrogen bombs.

Asteroids come in groups, a debrid field so to speak.

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