Size and shape of a celestial body, definition of a planet

TL;DR

This paper proposes a physics-based criterion for defining planets based on size and shape, linking celestial body shape to hydrostatic equilibrium and internal forces, challenging current arbitrary definitions.

Contribution

It introduces a new approach correlating size and shape of celestial bodies in hydrostatic equilibrium, removing arbitrary size criteria from planet definitions.

Findings

Only gas giants and Haumea can achieve fluid-like shapes in solid state.

Most nearly round bodies in the solar system formed before solidification.

Current planet definition criteria are inconsistent with physical principles.

Abstract

Experience shows that celestial bodies have a nearly round shape only from a certain size. At IAU resolution B5, item b, that shape serves as an indicator for a distinct mechanism of its forming, caused by a minimum of mass. Rigid body forces should have been overcome by self gravity and a hydrostatic equilibrium shape should have been achieved. A new approach to correlate the size and shape of a solid in hydrostatic equilibrium by balancing self gravity and rigid body forces leads to a real, not to an arbitrary lower limit of size. No arbitrary criterion is required as it is often the case. Above this limit the shape of a solid body is restricted by a maximum of its surface area, and this maximum vanishes only at infinite size. Therefore the shape like that of a related fluid in hydrostatic equilibrium can only be reached in the solid state, if its surface area is larger than this maximum. This applies only to the four giant planets and Haumea. All the known nearly round celestial bodies in the solar System cant have achieved their present shape while being solids. The dwarf Haumea is a questionable exception. The present shapes have been formed before solidification and are frozen. The gas giants are not solids at all and the terrestrial planets have at least partially melted in their thermal history for millions of years. The smaller nearly round objects such as asteroids and satellites were at least partially melted combined with internal differentiation and resurfacing of a mechanically unstable crust in their very early thermal history. No rigid body forces had to be overcome. Item b of the current planet definition is somewhat undetermined. All planets and dwarfs in the solar system match this requirement only at very generous interpretation. It should be completely deleted. The number of dwarfs could be restricted by an arbitrary minimum of mass.