Planets: Power Laws and Classification

TL;DR

This paper develops empirical power-law relationships for planetary radius, density, and surface gravity based on Solar System and exoplanet data, revealing three natural classes of planets by mass.

Contribution

It introduces a classification of planets into three groups based on power-law relations of their physical parameters with mass, using empirical data and least squares fitting.

Findings

Planets naturally separate into three classes by mass.

Power-law functions best fit radius, density, and gravity relations.

Distinct classes suggest different planetary formation or composition regimes.

Abstract

The study of the interior of the planets requires the knowledge of how certain parameters, as radius and mean density, vary according to the planet mass. The aim of this work is to use known data of the Solar System Planets and Transiting Exoplanets (specifically the radius and mass) to create empirical laws for the planetary radius, mean density, and surface gravity as a function of mass. The method used is to calculate with the available data, the mean density and surface gravity for the planets and adjusts, using the least squares method, a function with respect to the radius-mass, density-mass and surface gravity-mass relations. In the mass interval from 10E19 to 10E29 kg, the planets separate in a natural way into three groups or classes which I called class A, class B and class C. In all these classes and with all the functions (radius, median density and surface gravity) those best fits are power laws.