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The mass-radius relation of exoplanets constrains internal composition, mantle mineralogy, and the presence of volatile-rich envelopes. Terrestrial exoplanets follow a tight sequence; super-Earths and mini-Neptunes show diversity indicating varied compositions (rocky, water-rich, or gas-dominated). Combined with atmospheric characterization, mass-radius measurements infer whether planets are terrestrial, ocean worlds, or mini-Neptunes.
From your study of exoplanet detection methods, you know that transit observations yield a planet's radius (from how much starlight it blocks) and radial velocity measurements yield its mass (from the gravitational wobble it induces in its star). When you have both measurements for the same planet, you can calculate its bulk density — and density is the key that unlocks interior composition. A dense planet must be made primarily of rock and metal; a low-density planet must contain substantial amounts of lighter material like water ice, hydrogen, or helium. The mass-radius relation is the systematic pattern that emerges when you plot thousands of exoplanets on a mass-versus-radius diagram.
For purely rocky planets — those made of iron cores and silicate mantles like Earth, Venus, and Mars — physics predicts a tight relationship between mass and radius. As you add mass to a rocky body, gravity compresses the interior, so radius increases more slowly than you might expect. A planet twice Earth's mass is only about 1.25 times Earth's radius if it has the same composition. This rocky planet sequence forms a well-defined curve on the mass-radius diagram, and planets that fall on or near it are confidently classified as terrestrial. Planets that plot above this curve — larger than expected for their mass — must contain lower-density material.
The most intriguing region of the mass-radius diagram is the super-Earth to mini-Neptune transition, spanning roughly 1.5 to 4 Earth radii and 2 to 20 Earth masses. Here, planets with similar masses can have dramatically different radii, revealing fundamentally different compositions. A planet of 5 Earth masses might be a rocky super-Earth with radius 1.5 R⊕, a water world with a deep ocean or high-pressure ice mantle at 2 R⊕, or a mini-Neptune with a thick hydrogen-helium envelope at 2.5 R⊕. The mass-radius measurement alone cannot always distinguish between these possibilities — this is the degeneracy problem, where different interior structures can produce the same bulk density. Breaking this degeneracy requires atmospheric characterization from spectroscopy, which can reveal whether a planet has a hydrogen-rich envelope, a water-dominated atmosphere, or a thin rocky-planet atmosphere.
A striking observational finding is the radius gap (also called the Fulton gap) — a deficit of planets between about 1.5 and 2.0 Earth radii. This gap separates bare rocky super-Earths below from gas-enveloped mini-Neptunes above, and is thought to result from atmospheric mass loss: planets that formed with thin hydrogen envelopes lose them to stellar radiation (photoevaporation) or internal heat (core-powered mass loss) if the envelope is not massive enough to resist stripping. Planets that retain their envelopes remain puffy mini-Neptunes; those that lose them shrink to bare rocky cores. The mass-radius relation thus encodes not just present-day composition but the entire history of atmospheric evolution — connecting planet formation, stellar irradiation, and interior physics into a unified picture of planetary diversity.