Could a planet form without a molten state? 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?
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 $M/R&lt;5CT/3G$. So if we use a low silicate rock melting point of 600 C and basalt thermal capacity then $M/R&lt;1.8313\cdot 10^{16}$ 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.