Estimate the kinetic energy (1/2 m v2) of a comet striking the Earth. Assume that the comet is a sphere 8 km in diameter, with the density of water and is traveling at 30 km s-1 when it hits the Earth. Use SI units throughout.
1 Megaton of TNT has an explosive yield of 4×1015 Joules. The entire nuclear arsenal of the world has been estimated at 5,000 Megatons. Estimate the diameter of a comet with a destructive power of 5,000 Megatons (with the same density and velocity as above).
Calculate the total mass of water needed to cover the entire surface of Mars to a depth of 30 meters. How many comets of average size (say, 2 km diameter) would it take to bring in this much water? What is the average time between impacts, if this number of comets struck Mars in the first billion years of the solar system?
What is the radius of an asteroid for which the escape velocity is 8 meters/sec? Assume the density of the asteroid is 3000 kg/m3. (At this low escape speed, a person could “run” off the asteroid.)
Volume of sphere=4/3 x Pi x r^3, r=radius
V =4/3 x 3.141592 x 4,000^3
V=268,082,517,333 cubic meters
Mass =268,082,517,333 kg
KE =1/2 x M x v^2
KE=1/2 x 268,082,517,333 x 30,000^2
KE=120,637,132,800,000,000,000 =~1.2 x 10^20 Joules
1 Megaton =4.2 x 10^15 Joules, therefore:
[1.2 x 10^20] / [4.2 x 10^15] =~28,723 Megatons of energy released.
Mass of the asteroid =m = 4.66667×10^10 kg.=Volume of the asteroid.
4.66667×10^10=4/3 x pi x r^3, solve for r
r=2,233m x 2 =4,466m =~4.5 km - diameter of the asteroid.
1) Find the surface area of Mars using: SA=4 x pi x r^2, r=radius + 30 meters.
2) Find the surface area of 1 asteroid
3) divide the answer in 1 by the answer in 2 =number of asteroids to cover Mars with water, 30 meters deep.
4) Divide the answer in 3 by 1 billion years to get the average time between impacts.
