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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].

In transit spectroscopy, starlight passes tangentially through the planet's terminator atmosphere during primary transit. Wavelength-dependent opacity changes the effective occulting radius. For a thin atmosphere with an absorption feature spanning $N_H$ atmospheric scale heights,Here $\mu$ is the mean particle mass in units of $m_H$, not a chemical potential. Large planets with warm low-gravity, low-molecular-weight atmospheres against small stars have larger signals. A spherical isothermal atmosphere has tangential column enhancement of order $\sqrt{2\pi R_p/H}$ over a vertical column, explaining sensitivity to tenuous high-altitude gas. Molecular bands, atomic lines, scattering slopes and clouds constrain the terminator, but cloud opacity, reference pressure and abundance-temperature degeneracies limit unique retrievals.^[ref]

Occultation spectroscopy instead subtracts the star-only spectrum during secondary eclipse from the star-plus-planet spectrum immediately outside eclipse. It measures the dayside planet/star flux ratio. In the blackbody approximation the thermal eclipse depth isLonger infrared wavelengths generally improve contrast for a cooler planet; molecular absorption or emission depends on the vertical temperature gradient. At optical wavelengths reflected light can dominate, with full-phase contrast $A_g(\lambda )(R_p/a{)}^2$, where $A_g$ is geometric albedo. Eclipse spectra therefore probe dayside emission or reflection, rather than the transit's slant absorption. Clouds and temperature inversions affect interpretation.^[ref]

For either measurement, the photon-limited signal-to-noise ratio scales as the spectral feature amplitude times $\sqrt{N_{\gamma }}$, with a penalty for subtracting finite in- and out-of-event samples. Finer spectral bins reduce photons per bin; bright hosts, repeated events and stable instruments improve sensitivity. Detector systematics, telluric absorption for ground observations, and variable starspots can limit the practical gain. Space observations remove telluric contamination, not stellar variability or instrumental drift. Neither technique directly measures a unique bulk composition or samples all longitudes of the planet.

Transit spectroscopy infers the properties of an exoplanet atmosphere from the wavelength dependence of an exoplanet transit. Its measured product is an exoplanet transmission spectrum, while an annulus model for transmission spectroscopy connects the spectrum to atmospheric optical depth. The observing technique is described by NASA.