Exoplanet Classification Explorer: Mass, Radius, Density and Interior

What is plotted. Mass and radius are the two numbers a planet hunter measures (radial-velocity or transit-timing mass, transit depth for radius). Their ratio gives the bulk density ρ = 5.514 g/cm³ × (M/M⊕) / (R/R⊕)³, the first clue to what a planet is made of: iron and rock above about 3.5 g/cm³, water-rich bodies near 2 g/cm³, hydrogen-helium envelopes below 1.5 g/cm³. Surface gravity g = GM/R², escape speed v = √(2GM/R) and the equilibrium temperature T_eq = 278.5 K × (1 − A)^1/4 L^1/4 / √a (a in AU, L in solar luminosities, full heat redistribution, no greenhouse) follow directly.

Classes. The size thresholds are the working ones used in exoplanet surveys: below 1.25 R⊕ terrestrial, 1.25 to 1.6 R⊕ super-Earth (the radius valley near 1.5 to 2 R⊕ separates mostly rocky planets from those holding a gas envelope), 1.6 to 4 R⊕ mini-Neptune, 4 to 8 R⊕ ice giant, above 8 R⊕ gas giant; a gas giant with T_eq above 1000 K is called a hot Jupiter. They are conventions, not sharp physical boundaries.

Interior model (solid mode). For planets up to 30 Earth masses the radius can be computed rather than typed in: hydrostatic equilibrium dP/dr = −ρg with dm/dr = 4πr²ρ is integrated outward from a trial central pressure, which is bisected until the integrated mass equals the chosen mass. Three layers are stacked by mass (iron core, MgSiO₃ mantle, water-ice shell) and each uses a cold Murnaghan equation of state ρ(P) = ρ₀(1 + K′P/K₀)^1/K′. The cut-away disc and the density profile come from this same integration.

Empirical median curve. The dashed curve is the broken power law of the Chen and Kipping (2017) probabilistic forecaster: R = 1.008 M^0.279 up to 2.04 M⊕, 0.808 M^0.589 up to 131.6 M⊕, then 17.74 M^−0.044. It is a fit to observed planets, with typical scatter of 10 to 20 %; real planets sit above or below it (inflated hot Jupiters, dense iron-rich worlds).

Honest simplifications. Temperature is ignored in the interior (cold curves); there is a single high-pressure phase per material, so planets below about 0.3 Earth masses come out about 8 % too small; no light elements in the core, no iron in the mantle, no melting or phase changes; the Murnaghan form is accurate to a few percent only up to roughly 10 to 20 Earth masses; above 30 Earth masses, or whenever the radius is typed in, composition is not inferred beyond a water-fraction or iron-fraction estimate for solid planets. The scale height uses T_eq and a mean molecular weight of 2.3 (H/He) or 29 (air-like), and the transit signal 2HR_p/R_s² uses typical stellar radii (1, 0.73, 0.29, 0.12 solar). Planet textures are artistic, baked in Blender; the colour of a real exoplanet is unknown.

Checks. (1) bulk densities of five Solar System bodies from mass and radius against the NASA fact sheet; (2) the interior model against Earth, Mars and the iron-ball limit, with mass conservation of the integrator; (3) continuity and anchor values of the empirical curve plus its agreement with the independent interior model on the rocky branch (0.5 to 2 Earth masses); (4) T_eq of Earth, Jupiter and Venus and the escape speeds of Earth and Jupiter.