<p>Here's a quick-and-dirty estimate.
The <a href="https://en.wikipedia.org/wiki/Gravitational_binding_energy" rel="nofollow noreferrer">gravitational self-energy</a> 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</p>

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

<p>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.</p>

<p>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.</p>

<p>Apparently a <a href="https://en.wikipedia.org/wiki/TNT_equivalent" rel="nofollow noreferrer">teraton of TNT</a> is $4\times10^{21}\rm\,J$, if you insist on that comparison.</p>

<p>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.</p>

CC BY-SA 3.0
2018-03-20T05:52:33.147Z
That's about 10 zettatons of TNT.
Ethan
CC BY-SA 3.0
2017-05-19T19:34:58.197Z
2017-05-19T20:12:08.590Z
2017-05-19T20:12:08.590Z
rob
<p>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. </p>

<p>Assuming a head on collision (according to <a href="http://newsroom.ucla.edu/releases/moon-was-produced-by-a-head-on-collision-between-earth-and-a-forming-planet" rel="nofollow noreferrer">newer research</a>), how would it compare to the impact that created our moon?</p>

CC BY-SA 3.0
2017-05-19T16:42:41.210Z
It would be insignificant in comparison.
bon
<earth-history><moon><earth-system>
How much energy released by the Theia-Gaia impact?
x0a
# How much energy released by the Theia-Gaia impact?

(Asked by: username_0 on 2017-05-19)

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](http://newsroom.ucla.edu/releases/moon-was-produced-by-a-head-on-collision-between-earth-and-a-forming-planet)), how would it compare to the impact that created our moon?

**Tags:** earth-history, moon, earth-system

> **Comments:**
> **username_1**: It would be insignificant in comparison.  

---

## 1 answers

### Answer by username_2 on 2017-05-19. Score: 3 | Accepted answer

Here's a quick-and-dirty estimate.
The [gravitational self-energy](https://en.wikipedia.org/wiki/Gravitational_binding_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](https://en.wikipedia.org/wiki/TNT_equivalent) 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.

> **Comments:**
> **username_3**: That's about 10 zettatons of TNT.  

---

