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The atmospheric metallicity of a giant planet describes its atmospheric inventory of elements heavier than hydrogen and helium. It must specify a convention: an elemental abundance ratio relative to hydrogen, an enhancement relative to a reference composition, or a total heavy-element mass fraction are related but different quantities. A quoted enrichment also needs to identify its reference, such as the host star.

Atmospheric retrieval estimates molecular abundances, which must then be connected to elemental inventories through a model of chemical equilibrium or disequilibrium chemistry in an exoplanet atmosphere. Atmospheric condensate rainout can hide elements in particles below the observed levels. Thus an atmospheric enrichment need not directly equal the heavy-element fraction of the whole exoplanet interior.

Doppler spectroscopy detects an exoplanet through the host star's changing Doppler shift. Both bodies orbit their shared astronomical barycenter: the star undergoes stellar reflex motion even when the exoplanet itself is unseen. Its velocity along the line of sight shifts its spectral lines; at speeds small compared with the speed of light, $\Delta \lambda /\lambda \simeq v_r/c$, with positive $v_r$ for recession. Repeated measurements can fit a Kepler orbit, rather than merely detect one shifted spectrum. Starspots and other changes in stellar spectral lines must be distinguished from actual orbital motion.

For one companion in an isolated two-body problem, the stellar radial-velocity semi-amplitude isHere $G$ is the gravitational constant, $P$ the orbital period, $e$ the orbital eccentricity, and $M_{\star },M_p$ the star and exoplanet masses. The orbital inclination $i$ is measured relative to the sky plane: $i=0$ is face-on and $i=90^{\circ }$ is an edge-on orbit. The exact binary mass function measured from the fitted orbit isWith known $M_{\star }$ and $M_p\ll M_{\star }$, this is usually reported as $M_p\sin i$. Taking $\sin i=1$ gives the minimum companion mass; a smaller orbital inclination allows a larger mass. A detected exoplanet transit constrains $i$ close to $90^{\circ }$ for a compact planet orbiting well outside the star's surface, substantially resolving this ambiguity. Combining Doppler spectroscopy and exoplanet transit photometry then supplies a mass and radius for exoplanet interior studies.

For a computed circular example, let $q=M_p/M_{\star }=0.001$ and choose a relative orbital speed $V_{\mathrm{rel}}=100\mathrm{km}{\mathrm{s}}^{-1}$: this is the speed of the planet relative to the star, not its speed about the astronomical barycenter. Conservation of momentum givesThe barycentric velocities point in opposite directions, so their speeds add to $V_{\mathrm{rel}}$. Here $e=0$ and $K=V_{\star }\sin i$: $K=99.9001\mathrm{m}{\mathrm{s}}^{-1}$ at $i=90^{\circ }$, $49.9500\mathrm{m}{\mathrm{s}}^{-1}$ at $i=30^{\circ }$, and zero at $i=0$. The star still orbits in the face-on case, but its orbital velocity has no line-of-sight component. The plotted circular signal is $v_r(t)-\gamma =K\sin (2\pi t/P)$ for a chosen phase origin and constant system velocity $\gamma$.

An exoplanet is a planet outside the Solar system; here the focus is on planets orbiting stars other than the Sun, including pulsars. Most exoplanets are detected indirectly: a star's changing Doppler shift reveals its motion, or a small dip in its light curve reveals an exoplanet transit. The striking idea is that an unresolved point of light can tell us about an otherwise unseen world's mass, radius, and orbit.

The measurements answer different questions. Exoplanet transit photometry primarily gives a radius ratio, while Doppler spectroscopy constrains mass together with orbital inclination. Combining them with the host star's properties gives a mean mass density, ${\bar{\rho }}_p=3M_p/(4\pi R_p^3)$, useful for exoplanet interior models. Even this combination does not uniquely determine composition: see exoplanet interior-composition degeneracy. Transit spectroscopy and an exoplanet secondary eclipse then probe an exoplanet atmosphere.

The discovery history has two distinct milestones. In 1992 Aleksander Wolszczan and Dale Frail reported two planet-mass companions to the pulsar PSR B1257+12 from periodic changes in pulse arrival times; their paper also suggested an additional companion. These were the first confirmed exoplanet discoveries, around a neutron star. ^[ref]. Wolszczan's contemporary conference account, archived by NASA, likewise distinguishes the two reported companions from a possible third. ^[ref].

In 1995 Michel Mayor and Didier Queloz discovered 51 Pegasi b through Doppler spectroscopy, the landmark first confirmed exoplanet around a Sun-like star. This was a hot Jupiter, not the first exoplanet of every kind: the earlier pulsar discoveries belong to a different host category. ^[ref]. NASA's contemporary account describes the confirmation and the approximately four-day orbital period. ^[ref].

An exoplanet bulk-composition ternary diagram represents three component mass fractions by one point inside a triangle. If the components have fractions $x_1,x_2,x_3$, then $x_i\ge 0$ and $x_1+x_2+x_3=1$. Each vertex is a pure component, an edge excludes the opposite component, and the centre corresponds to equal thirds. The fractions are barycentric coordinates relative to the vertices.

For an illustrative iron-rock-water model, measured mass and radius restrict the allowed part of the triangle through an exoplanet interior calculation. They need not select a unique point, making exoplanet interior-composition degeneracy visible. The diagram is conditional on the chosen three components: an unmodelled hydrogen-helium envelope cannot automatically be interpreted as more of one of those solid components.

An exoplanet interior is the structure and composition beneath the layers directly sampled by observations. Mass and radius constrain the mean mass density, but a physical model also needs hydrostatic equilibrium, an equation of state, and assumptions about composition and thermal history. Dense material can be concentrated in a core or mixed into surrounding layers.

Solid-planet calculations show how iron-, silicate- and water-rich bodies occupy different broad mass-radius relations, with compression preventing one constant-density scaling from applying to every mass.^[ref] A light gas envelope can substantially alter the observed radius. Exoplanet interior-composition degeneracy therefore remains even when both mass and radius are measured precisely.

HD 149026 b is a transiting, roughly Saturn-mass exoplanet whose small measured radius made it an early test of giant-planet composition. The discovery combined Doppler spectroscopy at two observatories with ground-based exoplanet transit photometry: the first constrains mass, the second radius and orbital inclination. The original exoplanet interior models required a substantial inventory of elements heavier than hydrogen and helium to reproduce the measured compactness.^[ref]

The inferred concentration of heavy material is a model result, rather than an image of a planetary core. Its partition between a central core and the surrounding envelope depends on the assumed equation of state, age, and temperature; this illustrates exoplanet interior-composition degeneracy.

A hot Neptune is an exoplanet in approximately the Neptune mass or radius range receiving strong stellar irradiance. The name describes size and heating; it does not imply that its exoplanet interior or exoplanet atmosphere matches Neptune. A molecular hydrogen-rich envelope can supply a large fraction of the measured radius while containing a much smaller fraction of the mass.

Short orbital periods make repeated exoplanet transit photometry and Doppler spectroscopy practical. Comparing the inferred mass density with exoplanet interior models helps distinguish a retained gas envelope from a denser body. Strong irradiation also makes atmospheric escape relevant: losing a light envelope can substantially change radius without removing most of the solid material.

A Love number measures a body's tidal response to an applied potential. The degree-two potential response $k_2$ is sensitive to radial density structure and central concentration, and can complement mass and radius constraints on an exoplanet interior. Inferring it from orbital precession requires separating other contributions and assumptions about rotation and the tidal response.

At fixed mass, three broad controls of a super-Earth-sized body's observed radius are:

Bulk composition, envelope fraction/composition, and thermal/irradiation history are three independent controls. If mass is not fixed, the mass itself is an additional major variable. The label super-Earth does not ensure a rocky composition or an Earth-like atmosphere, and a radius alone does not determine which of these effects dominates.

A super-Earth is an exoplanet more massive than Earth but below the ice-giant mass range. The label does not guarantee a rocky exoplanet interior, a specific radius, or habitability. Radius-based usage can overlap the sub-Neptune population.

A departure of transit arrival times from a constant-period ephemeris can reveal gravitational interactions with other bodies. Dynamical fits may constrain an exoplanet mass independently of transit depth, providing a mass to combine with radius for exoplanet interior models.