What if an Asteroid Hit the Earth?

Let's compare the energies involved in earthquakes, bomb explosions, and asteroid collisions.

Bomb Explosion

If a bomb containing 110 kg of plutonium (1.43 x1026 atoms) is detonated, and this material undergoes fission, each atomic fission reaction releases 2.88 x 10-11 Joules of energy.  The total amount of energy released in this explosion is:

Ebomb = (1.43 x1026 atoms) x (2.88 x 10-11 J/atom)
Ebomb = 4.12 x 1015 J
If one megaton (= one million tons =106 tons) of TNT releases 4.16 x 1015 J,  what size warhead (in megatons) would this 110 kg plutonium bomb correspond to?
Ebomb = 4.12 x 1015 J / (4.16 x 1015 J/megaton) = 0.99 megaton
Asteroid Impact

Assume a 1 km radius, spherical asteroid hits the earth. What is the volume of the asteroid?

V = 4/3 pi R3 = 4/3 pi (103 m)3 = 4.19 x 109 m3


If the asteroid is made of normal rock, with an average density of 3500 kg per cubic meter, what is the mass of the asteroid?

M = density x volume = 3500 kg/m3 x 4.19 x 109 m3=  1.47 x 1013 kg
The comet that hit Jupiter in July, 1994 impacted at a velocity of 60 km/sec! If the asteroid hits Earth at a velocity of 30 km/sec, what is the kinetic energy of the collision? [Note that  KE = 0.5 M v2, where M is the mass and v is the velocity of the impacting body.] [gm cm/s will give ergs; kg m/s will give Joules]
Eimpact = 0.5 x (1.47 x 1013 kg) x (30 x 103 m/s)2
Eimpact = 6.6 x 1021 J
If we convert this to megatons, this is equivalent to 1.6 Million megatons.

An earthquake

The energy in an earthquake is usually calibrated on what we know of as the Richter scale. This is written algebraically as

log E = -2.22 + 2.57m,
where E is the energy (J) and m is the magnitude of the earthquake.   We can rewrite this as
E = 10-2.22+2.57m.
For example, a magnitude 1 earthquake would release
Equake=1 = 100.35 =  2.2 J.


How much energy is released by a magnitude 8 (m = 8) earthquake?

Equake=8 = 10-2.22+2.57x8 = 1018.34
Equake=8 = 2 x 1018 J
How much energy is released by a magnitude 3 earthquake (m=3)?
Equake=3 = 10-2.22+2.57x3 = 105.49 = 3.1 x 105 J
If there are 50,000 third magnitude earthquakes every year, and only one magnitude 8 earthquake every year, how does Earth release most of its seismic energy, in big or small quakes?
In 50,000 magnitude 3 quakes, the energy released would be 5 x 104 x 3.1 x 105 J = 1.5 x 1010 J, so a single large quake releases much more energy than an enormous number of smaller ones.
A comparison: Bombs, Earthquakes and Impacts

The 1945 Atomic Bomb explosion at Hiroshima released 7.9 x 1013 = 1013.9 , or just less than 1014 J.  We can translate this energy release into an equivalently energetic earthquake:

We  can simply solve the magnitude equation for m:
13.9 = -2.22 + 2.57 x m
m = (13.9+2.22)/2.57 = 6.27
so the Hiroshima explosion released as much energy as a magnitude 6.27 earthquake (of course, it also released much of this energy as heat, causing lots of damage from fires and also released lots of  radioactive particles; so the damage from this bomb wasn't strictly related to the amount of energy released in the explosion).
Compare these three events
Eimpact = 6.6 x 1021 J
Equake=8 = 2 x 1018 J
EHiroshima = 7.9 x 1013 J
The asteroid impact is 3,300 times more energetic than the magnitude 8 earthquake (it is equivalent to a magnitude 9.35 earthquake), while the bomb explosion produces only a miniscule amount of energy compared to either the earthquake or asteroid impact.