A roughly spherical asteroid with a diameter of 1 km, and a mean density of 4 g/cm^3, hits the Earth with a relative speed 1.5 times the orbital velocity of the Earth. Compute the amount of energy released upon the impact. Compare that with the energy released by a 10-Megaton thermonuclear bomb, which is about 4.2 x 10^27 erg. Contemplate the value of a search for Earth-crossing asteroids. Please be sure to enter your answer in units of ergs (the CGS unit of energy). Note: 1 Joule = 10^7 ergs.
Energy released upon impact:
If the question is this : Please be sure to enter your answer in units of 10-Megaton bombs:
The response correct is 49738.09523, because 2.089*10^28 is in ergios.
4/3*pi*50000^3 = sphere volume
4*1/1000= density passed to Kg.
(4/3*pi*50000^3)*(4*1/1000)= mass
Velocity 1.5*30km/s=45km/s*1000=45000m/s
Energy kinetic (Joule)(Kg.m/s)=1/2*mass*V^2=1/2*(4/3*pi*50000^3)*(4*1/1000)*(45000m/s)^2
(1/2*mass*V^2=1/2*(4/3*pi*50000^3)*(4*1/1000)*(45000m/s)^2)*10^7=Joule passed to Erg
Energy kinetic total=2.12058*10^28 Erg
Equivalent to 50489,88193 Thermonuclear Bomb of 10 Megatons exactly!