First compute the mass of the asteroid from its density and radius,r. Call it m.
m = (4/3)pi*r^3
Then compute E = G*M*m/R, where
R is the radis of the Earth
M is the mass of the Earth
m is the mass of the asteroid
G is Newton's universal constant of gravity
E is the energy of the collision,in Joules, assuming the asteroid approaches from infinity. Convert it to megatons of TNT using the specified conversion factor.
Consider an asteroid of radius 2 km and density 2,500 kgm3 impacting the Earth. When it collides with the surface its kinetic energy is, to a large extent, dumped into the environment, some as heat vaporizing rock and some as mechanical energy throwing rock to great distance and height. If the asteroid were released from rest a great distance from Earth (you can assume this is infinite) find its kinetic energy at impact. Express your result in megatons. These are units often used to measure nuclear weapon energy yields; a megaton is the energy released by one million tons of TNT and equals 4.2×1015 Joules. Round your answer to two significant digits.
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