Thoughts within thoughts

Last year saw the discovery of Gliese 581g, the first (habitable) planet to exist within the habitable zone of its star. It is a super-earth, a planet 3.1 to 4.3 times as massive. We have no idea how big it is yet, therefore we cannot say for certain what its density or composition is. For the purpose of this argument we will assume it is the same density and composition as the Earth, therefore it is larger than the Earth.

Now, lets bring up plate tectonics. This is a very important process for life on Earth. The Earth has a molten core because it has decaying radioactive material heating the rock, but all planets and moons have (or had) this to some degree. Plate tectonics occur because the Earth has a sufficiently low surface area to volume ratio. The maths is beyond me but all we need know is the volume of a three dimensional object increases at a faster rate than its surface area. This means that land as well as radioactive materials are recycled. Continents are built, mountain ranges grow, seas vanish and reform. It also means the air is supplied with enough greenhouse gases, without which the Earth would actually freeze.

If we want to plot a simple graph we could the Moon, Mars and Earth. The Moon is roughly 1/4 the size of the Earth. It had early geological activity, we can see the result in the dark plains we call seas and oceans on the Moon. But the surface to volume ratio was too high. Whether or not the core of the Moon is active now there is no way for any internal forces to break out. Mars meanwhile is 1/2 the size of the Earth. Its surface is now geologically dead, just as the Moon is, but we see some primitive attempts at plate tectonics viz Mariner Valley.

What does this mean for possible planet 3-4 times bigger than the Earth? All other things being equal does that mean Gliese 581g is super-active?

One final thing, lets throw a curveball, something off the graph. Venus is roughly the same size as the Earth. It has ample evidence of volcanic activity, including strange high, flat mountains that remind scientists of pancakes. One truly bizarre fact, Venus is almost evenly peppered with impact craters, which, added up, suggests the entire surface of the planet is more or less the same age. What on Earth (or Venus) could cause the planet to turn itself inside out like that?