Question: What mass would a meteorite have to be to destroy the world

Mark Kennedy answered on 7 Nov 2016:

So, let’s start with something small. Imagine I give you a single atom of hydrogen – which is just a proton with a single electron orbiting it. If you wanted to separate the hydrogen into a proton and an electron, you’d have to hit the hydrogen with a minimum amount of energy to break it up. We call this minimum energy the binding energy, and for hydrogen it’s 13.6058 eV (which is 2.17e-18 J).

If we approximate the Earth to a sphere, and assume a certain density for the Earth, then we can calculate the binding energy of the Earth! In this case, it’s 2.24e32 J, which is a massive amount of energy!

Now assume a meteor hit the Earth, and that the meteor was travelling at 60 km/s (about the speed of a car). The kinetic energy of the meteor will have to be 2.24e32 J to break up the earth, so we just need to solve the equation:

E=1/2 m v*v

where E=2.24e32 J and v=60 km/s. The resultant mass is 1.24e23 kg! That’s 124,000,000,000,000,000,000,000 kg! The Earth has a mass of 5e24 kg! Which means you’d need a meteor which is 2% the mass of the Earth, which is a really REALLY big meteor.

If you look at the above formula, you could also work out how fast a meteor of a particular mass would have to be to destroy the Earth. For example, the comet Churyumov-Gerasimenko has a mass of about 1e13 kg. So solving

E=1/2 m v*v

where E=2.24e32 J and m=1e13 kg gives you v, which would be 6.6e9 m/s! Which is faster than the speed of light, which means this is impossible! So I think we’re pretty safe for the moment 🙂

(Edit: I changed the velocity of Churyumov-Gerasimenko, as originally, I forgot to take the square root!)