# How much energy released by the Theia-Gaia impact?

I read somewhere that the Chicxulub impact released the energy equivalent of anywhere from 100-300 teratons of TNT. That's an impressive amount of energy.

Assuming a head on collision (according to newer research), how would it compare to the impact that created our moon?

• It would be insignificant in comparison. – bon May 19 '17 at 16:42

Here's a quick-and-dirty estimate. The gravitational self-energy of a uniform-density sphere is $$U = \frac35 \frac{GM^2}R$$ Let's assume Theia had the same mass and density as Mars, and that Gaia contained the rest of the mass of the Earth-Moon system. The binding energies for the four bodies are then

theia/mars 4.82e+30 joules
gaia       1.90e+32 joules
earth      2.24e+32 joules
moon       1.24e+29 joules


You can see that Theia and the Moon contribute to the binding energy starting the third significant figure: moving the 90% of Theia's mass to Gaia, leaving us with the Earth and the Moon, must have released something like $0.3\times10^{32}\rm\,J$ of gravitational binding energy as heat.

Kinetic energies due to Earth's rotation and the Moon's orbit are irrelevant compared to Earth's binding energy --- the biggest contributor there is $0.25\times10^{30}\rm\,J$ associated with Earth's daily rotation. It's probably safe to assume the same about the progenitors.

Apparently a teraton of TNT is $4\times10^{21}\rm\,J$, if you insist on that comparison.

Note that I've assumed nothing about the geometry of the collision, whether it was head-on or glancing. I'm only making assumptions about the (well-known) final state and the (poorly constrained) initial state.

• That's about 10 zettatons of TNT. – Ethan722 Mar 20 '18 at 5:52