If the continuum assumption is adopted in metaphysics, we have to accept that heavenly bodies can only have two different shapes, a torus or a spherical shape.
NASA astronauts have done an amazing experiment with a body of water in nearly zero gravity. It shows clearly the behavior of a continuum in a void and the effects of mechanical forcing.
Heavenly bodies in quantum physics are always liquid and have no mass and no structural integrity. The bodies are shaped by the forces that act on their surface. Their continuous motion relative to the sun means that such types of bodies are subject to thermal forcing.
“Today, scientists use geodesy, which is the science of measuring Earth’s shape, gravity and rotation. Geodesy provides accurate measurements that show Earth is round. With GPS and other satellites, scientists can measure Earth’s size and shape to within a centimeter” – NASA 2017
From a mechanical point of view thermal forcing is a strong force that can cause motion of, mainly, the liquid atmosphere and water in the oceans.
Another important conclusion is that moving large quantities of dense matter from the core to the surface and the conversion of this matter into low density liquid matter and heat will have consequences for the geometry of the planet at sea level and for the (local) climate characteristics.