What if an Asteroid Hit the Earth?

Problem:
Suppose a cylindrical asteroid 10 km in height x 10 km in diameter impacted the earth at 30,000 mph. Calculate the energy dissipated, in megatons of TNT, and the rate at which it is dissipated, in watts.

Solution:
Let the density of the asteroid, , be five times the density of water, i.e.,

= 5000 kg/m³.

Then, the mass of the asteroid is

(5000 kg/m³) x (5000 m)² x (10,000 m) = 4 x 10¹⁵ kg

and the kinetic energy, traveling at 30,000 mph (= 1 x 10⁴ m/sec) is

(1/2) x (4 x 10¹⁵ kg) x (1 x 10⁴ m/sec)² = 2 x 10²³ joule.

Now, one megaton of TNT delivers 4.2 x 10¹⁵ joule, so that the required energy in megatons of TNT is

5 x 10⁷ megatons

or 50 million megatons! The time for the asteroid to impact the earth is

(10,000 m)/(1 x 10⁴ m/sec) = 1 sec

so that the rate of energy dissipation in watts is

2 x 10²³ watts,

or 200 billion trillion watts!!!

Afterthought:
Such an object might have been responsible for causing the extinction of the dinosaurs at the end of the Cretaceous period. A layer of Iridium has been found in the Cretaceous-Tertiary (K-T) boundary, which appears to be world encircling (Alvarez, et. al.). Such a layer might have been deposited after an asteroid impact of great magnitude. In fact, the remains of a 65 million year old impact site have recently been found, providing an excellent candidate for the K-T event. From various geological survey data (originally intended to locate promising sites for oil drilling), the site is in the Yucatan.