<p>If you accrete a mass of <span class="math-container">$M$</span> the total binding energy will be <span class="math-container">$3GM^2/5R$</span>, which will at least partially turn into heat. If the melting temperature is <span class="math-container">$T$</span> and specific heat capacity <span class="math-container">$C$</span> we get the condition <span class="math-container">$$\frac{3GM^2}{5R}=CTM,$$</span> or <span class="math-container">$M/R&lt;5CT/3G$</span>. So if we use a low silicate rock melting point of 600 C and basalt thermal capacity then <span class="math-container">$M/R&lt;1.8313\cdot 10^{16}$</span> kg/m, while the upper range 1200 C gives <span class="math-container">$3.0899\cdot 10^{16}$</span> kg/m. So if we consider a basalt planetoid it will start to have some melt when cohering into one ball of radius larger than 1000 km. So, not much of a planet.</p>

CC BY-SA 4.0
2019-04-06T01:55:47.690Z
Dang. Thanks, though!
Daniel B
CC BY-SA 4.0
2019-04-05T21:23:15.310Z
2019-04-05T21:23:15.310Z
Anders Sandberg
<p>Based on what I know, the Earth accreted out of the solar nebula, had a period when it was entirely molten, and then slowly cooled. Could a planet form without ever passing through a molten phase? </p>

CC BY-SA 4.0
2019-04-05T19:51:16.727Z
I don't see how that could be possible; even the slowest collisions between large enough bodies would have enough kinetic energy to produce enough heat to cause thorough melting of the two bodies, and their mutual gravity would cause them to accelerate towards each other thus producing even more kinetic energy and heat.
BillDOe
<planetary-formation>
Could a planet form without a molten state?
Daniel B
# Could a planet form without a molten state?

(Asked by: username_0 on 2019-04-05)

Based on what I know, the Earth accreted out of the solar nebula, had a period when it was entirely molten, and then slowly cooled. Could a planet form without ever passing through a molten phase?

**Tags:** planetary-formation
> **Comments:**
> **username_1**: I don't see how that could be possible; even the slowest collisions between large enough bodies would have enough kinetic energy to produce enough heat to cause thorough melting of the two bodies, and their mutual gravity would cause them to accelerate towards each other thus producing even more kinetic energy and heat.  

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## 1 answers

### Answer by username_2 on 2019-04-05. Score: 5 | Accepted answer

If you accrete a mass of $M$ the total binding energy will be $3GM^2/5R$, which will at least partially turn into heat. If the melting temperature is $T$ and specific heat capacity $C$ we get the condition $$\frac{3GM^2}{5R}=CTM,$$ or $M/R<5CT/3G$. So if we use a low silicate rock melting point of 600 C and basalt thermal capacity then $M/R<1.8313\cdot 10^{16}$ kg/m, while the upper range 1200 C gives $3.0899\cdot 10^{16}$ kg/m. So if we consider a basalt planetoid it will start to have some melt when cohering into one ball of radius larger than 1000 km. So, not much of a planet.

> **Comments:**
> **username_0**: Dang. Thanks, though!  

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