Is there a practical calculation that would reveal how large an astronomical body could be and still form a lithosphere? The really large non-stellar bodies in this system appear to have no discernible “surface”, transitioning from gas to fog to mist to liquid over many vertical miles. It seems like a really large body would naturally differentiate into layers composed primarily of substances of progressive density (heavier inward). At some approximate threshold of gross mass, this differentiation would, I think, inhibit the body from forming a crust-like outer layer. Is there a fairly simple way to calculate how big a crusted planet-like body could be? Accounting, of course, for the balance of “metallicity” of the body.
And thus dies my dream of doing jumping jacks on the surface of Jupiter.
TLDR: Yes, but I do not know how to set it up.
The surface of a rocky planet would have to be too hot for the molten rock to solidify. Absent an atmosphere, the planet could simply orbit close enough to its star to maintain a surface temperature of over 800°C. But such close orbit may not even be stable. Alternatively, a very large dense atmosphere opaque to infrared radiation could keep the surface this hot. The atmosphere of Venus raises its surface temperature by about 200°C, and the surface of Mercury already heats up to over 400°C even without an atmosphere. So perhaps even Venus, were it orbiting a lot closer to the Sun that Mercury, could lack a lithosphere. On the other hand, Venus is likely too small to retain such hot atmosphere so close to the Sun for very long. So you really do need a larger planet.
I imagine the presence of natural satellites would matter as well, since a large-ish moon would flex the body of primary, adding some heat.
Aren’t you misunderstanding the question? I assume that the OP wants to know how large of a planet can have a solid, rigid rocky surface rather than being a gas giant of some sort with a gradual shading of gas to supercritical fluid to exotic crystalline solid.
So how big can a planet be without it being a gas giant, in other words.
Observations suggest that you can form rocky planets up to 17 times more massive than Earth, although the mechanism to do so is not understood, since such massive objects would normally trap massive atmospheres and become gas giants under current theory. Kepler 10c is one of a few mega-Earth examples. Perhaps it lost its atmosphere over a long period of time, since it’s hot and orbits close to its star.