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51 Pegasi b is the giant exoplanet whose 1995 discovery established a planet around a Sun-like star. It is a hot Jupiter: its roughly 4.23-day orbital period and about 0.05 astronomical unit separation differ markedly from Jupiter's distant orbit. Earlier confirmed exoplanets had already been found around a pulsar; the host category is part of this discovery's significance.^[ref]

Michel Mayor and Didier Queloz used the ELODIE spectrograph to measure periodic Doppler shifts in the host star's spectrum. The star's motion around the shared centre of mass produces alternating approaching and receding velocities even though the planet is unresolved. For a nearly circular orbit and a planet much less massive than its host,The measured velocity amplitude and period therefore constrain $M_p\sin i$, originally about half Jupiter's mass, rather than independently determining inclination and true mass. Checking spectral-line changes also helps distinguish orbital motion from changing stellar line profiles.^[ref]

An activity-period alias in radial-velocity sampling is an apparent period created when a stellar activity signal is measured at a restricted set of observing times. For observations exactly separated by $1/f_s$, a sinusoid of frequency $f$ is indistinguishable at those times from appropriate sinusoids at $|f\pm n{f}_s|$, with integer $n$. Thus a genuine stellar rotation signal can produce peaks at periods different from the rotation period.

Real observing times are irregular, so the aliases have different amplitudes and phases rather than being perfectly equivalent. Simulating a candidate signal at those same times helps test which observed peaks it predicts. The method applies to planetary signals as well as stellar noise; a periodogram peak alone does not identify a new exoplanet.^[ref]

Aleksander Wolszczan and Dale Frail discovered a planetary system around the millisecond pulsar PSR1257+12 through precise radio timing. The regular pulses supplied a clock whose observed arrivals varied periodically.

Those variations trace the changing light-travel time as the pulsar moves in response to its companions. Fitting the timing signal constrains the companions' orbital periods and minimum masses. The discovery established that the search for exoplanets could extend beyond ordinary main-sequence host stars.^[ref]

Andrew W. Howard measures the physical properties and population of exoplanets. In the 2013 study with Erik A. Petigura and Geoffrey W. Marcy, the team searched Kepler space telescope photometry and inserted synthetic exoplanet transits into real observations to measure transit survey completeness.^[ref]

Correcting missed detections changed the question from “how many candidates were found?” to the underlying exoplanet occurrence rate. For the study's 5–50-day orbital periods, the rising distribution flattened below about twice Earth's radius.

Atmospheric superrotation is circulation whose axial angular momentum per unit mass exceeds that of the underlying body's equator. An eastward equatorial jet is a common manifestation, but it requires a continuing source of equatorial momentum convergence rather than merely a local temperature difference.

In models of exoplanets under tidal locking, day-night heating excites large-scale Rossby waves and Kelvin waves. Their phase structure transports eastward momentum toward the equator and can maintain the jet against drag. This mechanism was demonstrated using an analytic model and numerical calculations of increasing complexity.^[ref] Such a jet can shift a bright atmospheric region eastward, affecting an exoplanet thermal phase curve, although a brightness offset alone does not uniquely measure a wind speed.

David Charbonneau detected atmospheric absorption in a transiting exoplanet by comparing the transit depth in different wavelength bands. His team's observations of HD 209458 b found extra dimming near the sodium resonance lines relative to adjacent spectral bands.

During an exoplanet transit, a small fraction of the stellar light passes through the planetary limb. Absorbing atmospheric gas therefore changes the apparent blocking area with wavelength. The observed feature was weaker than a particular cloud-free model predicted, illustrating why detecting an atmospheric species and uniquely determining the atmospheric structure are different inference problems.^[ref]

Dimitar Sasselov studies the physics of exoplanets and their atmospheres. With Sara Seager, he modeled how a transiting gas giant's atmosphere would imprint absorption features on the host star's radiation spectrum.

During an exoplanet transit, a small fraction of the stellar light passes through gas above the planetary limb. Strong atomic absorption can therefore make the apparent blocking area depend on wavelength. Their calculation identified promising sodium, potassium and helium features and emphasized the role of cloud height in interpreting the signal.^[ref]

Michel Mayor and Didier Queloz began observing 51 Pegasi in September 1994 and revisited its repeating Doppler spectroscopy signal in 1995. Their circular fit used 35 measurements: orbital period $4.2293\pm 0.0011$ days, stellar radial-velocity semi-amplitude $59\pm 3\mathrm{m}{\mathrm{s}}^{-1}$, and residual scatter $13\mathrm{m}{\mathrm{s}}^{-1}$ after epoch-dependent velocity offsets. Apparently stable comparison stars checked the instrumental zero point. Low chromospheric stellar activity and an inferred roughly 30-day stellar rotation period argued against starspots; light curves and the spectral line bisector tested stellar pulsation. These checks favoured orbital motion but had finite sensitivity. The reported $M_p\sin i=0.47\pm 0.02$ Jupiter masses was not a true mass. Stronger upper bounds used stellar-spin information and assumed spin–orbit alignment, limiting a nearly face-on binary star interpretation conditionally.^[ref]

The hot Jupiter matters both for planetary migration and for how exoplanets are found. At fixed small companion mass, orbital inclination and orbital eccentricity, the stellar radial-velocity semi-amplitude scales as $K\propto P^{-1/3}$. Comparing chosen orbital periods of $4$ days and $12$ years gives an amplitude ratio of about $10.3$: a close companion can be much easier to detect and complete many orbits during one observing season. Finding a giant planet close to its star also asks how its present orbit relates to where it formed. Doppler spectroscopy supplies a dynamical constraint; it does not by itself establish a formation pathway or measure the exoplanet's radius.

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 $\gamma$.

A dwarf planet, in the International Astronomical Union's 2006 Solar-system definition, is a body that orbits the Sun, has enough self-gravity to assume a nearly round hydrostatic equilibrium shape, has not cleared its orbital neighborhood, and is not a natural satellite. The classification combines a body's physical shape with its dynamical environment; it is not defined by size alone.^[ref]

Pluto illustrates why both aspects matter: it is rounded but belongs to the trans-Neptunian population rather than being dynamically dominant in its orbital region. Ceres provides another example, in the asteroid belt. A rounded Moon does not become a dwarf planet, because the satellite exclusion is explicit. Under this terminology, planet and dwarf planet are distinct categories.^[ref]

Clearing does not mean that literally no other object shares the region. It concerns orbital dominance over the surrounding population. Nor does the rounding requirement supply one universal diameter threshold: resistance to deformation depends on composition, internal structure and rotation. Observations of shape and mass therefore address one part of the definition, while orbital-population information addresses another. The cited resolution is explicitly about the Solar system; applying the same wording to an exoplanet population requires an additional convention.

Earth is a rocky planet whose surface couples a gaseous atmosphere, liquid ocean, solid crust and regions of ice. Its mean radius is about $6371\mathrm{km}$ and its mean mass density about $5.51\times 10^3\mathrm{kg}{\mathrm{m}}^{-3}$. These bulk quantities constrain, but do not uniquely specify, its differentiated interior.^[ref]

Seismic waves probe material beneath the surface, plate tectonics describes the moving outer shell, and the geodynamo explains the origin of the large-scale planetary magnetic field. At the surface, radiative transfer and ocean circulation redistribute solar energy. Earth therefore provides a nearby setting in which measurements can test coupled planetary processes that are much harder to separate in an unresolved exoplanet.

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 atmosphere is the gaseous outer region of an exoplanet, where gravity, radiative transfer, chemical reactions and fluid motion jointly determine what emerges into space. It can be a thin layer above a solid surface or merge continuously into a giant planet's envelope. Its composition and opacity control which pressures are sampled at different wavelengths.

Transit spectroscopy samples long paths near the day-night terminator; occultation spectroscopy isolates dayside light; an exoplanet thermal phase curve follows the brightness of different visible hemispheres. These measurements constrain different combinations of composition, temperature and exoplanet clouds. Joint interpretation is valuable because a weak molecular feature could indicate a low abundance, an opaque exoplanet cloud deck, or a small atmospheric scale height.

An exoplanet passes in front of its host star as seen by an observer and blocks part of the stellar flux. Exoplanet transit photometry infers geometry and radii from the resulting light curve. A true alignment involves the true anomaly, not generally the mean anomaly.

Exoplanet transit photometry measures the decrease in a star's observed radiative flux during an exoplanet transit. Define $F_0$ as the unobscured star's observed radiative flux and $F(t)$ as the value at time $t$. For a dark, opaque exoplanet crossing a uniformly bright circular stellar disc, a fully superimposed planetary disc blocks exactly the fractionHere $R_p$ and $R_{\star }$ are the planet and star radii. This exoplanet transit depth determines a radius ratio, $R_p/R_{\star }=\sqrt{\delta }$; an absolute planet radius requires an independently estimated stellar radius. For $R_p/R_{\star }=0.10$, $\delta =0.010$: a one-percent dip, with $F_{\mathrm{full}}/F_0=0.990$. Halving the radius ratio to $0.05$ reduces the exoplanet transit depth to $0.0025$, a quarter as much.

For the central exoplanet transit illustrated below, the transit impact parameter is $b=0$. Write $k=R_p/R_{\star }<1$ and let $z$ be the projected centre-to-centre separation in units of $R_{\star }$. The light curve is $F/F_0=1-A(z)/\pi$, where $A(z)$ is the overlap area of circles of radii $1$ and $k$. There is no overlap when $z\ge 1+k$; the planetary disc is fully inside when $z\le 1-k$, giving $A=\pi k^2$. Between those limits, the overlap area grows or shrinks continuously. Thus even a uniform star has curved ingress and egress, with a flat bottom only during full overlap. The illustration uses approximately constant transverse velocity over the short crossing, so $z=|ut|/R_{\star }$ with mid-transit at $t=0$. Analytic models also handle limb darkening. ^[ref].

The simple exoplanet transit depth formula assumes constant stellar brightness, no limb darkening or starspots, negligible light from the exoplanet, and no transit dilution by other light. It describes full overlap in a non-grazing exoplanet transit, requiring $b<1-k$ for a full-overlap interval. A grazing exoplanet transit never hides the whole planetary disc against the star, and limb darkening weights different blocked areas differently. Repeating dips are valuable evidence, but eclipsing binary stars and starspots can imitate parts of the signal, so confirmation and joint modelling matter.

Geoffrey W. Marcy worked on the radial velocity method for finding exoplanets, including precision iodine-cell Doppler calibration. His paper with R. Paul Butler combined a wide recorded stellar radiation spectrum with reference absorption lines introduced directly into the stellar beam.

Measuring a small Doppler shift requires distinguishing real stellar motion from instrumental changes. The superimposed reference constrains the spectrograph's wavelength scale and point spread function during the exposure, allowing the stellar shift to be fitted with those effects included. The paper reported year-long tests of the technique on three solar-type stars.^[ref]

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.

Heather A. Knutson mapped the thermal emission of the exoplanet HD 189733 b from its changing infrared brightness over part of an orbit. Different viewing phases expose different fractions of the hot dayside and cooler nightside.

The measured phase dependence constrained the longitudinal brightness distribution rather than producing a spatially resolved photograph. The relatively modest day–night contrast implied efficient redistribution of absorbed stellar energy, while the displaced brightness maximum supplied evidence about atmospheric transport. Inferred brightness temperatures apply to the observing band and adopted emission model.^[ref]

A hot Jupiter is a giant exoplanet with a short orbital period and strong stellar irradiance, typically orbiting much closer to its star than Mercury orbits the Sun. Large radius and short orbital period make these bodies favourable for exoplanet transit photometry; large mass and small orbital separation also increase the stellar radial-velocity semi-amplitude.

Strong external heating makes an exoplanet atmosphere very different from that of Jupiter. Tidal locking can maintain nearly permanent illuminated and dark hemispheres, creating a large driving force for day-night heat redistribution. HD 209458 b illustrates transit spectroscopy, while HD 189733 b illustrates an exoplanet thermal phase curve. Their proximity to their stars also motivates planetary migration models: present orbital location need not be the location of formation.

Hot-Jupiter radius inflation is the unexpectedly large radius of some strongly irradiated giant exoplanets compared with ordinary cooling and contraction models at the inferred age. A giant planet loses internal energy through its exoplanet atmosphere; slowing that loss or depositing additional energy sufficiently deep can keep its interior hotter and more extended.

Atmospheric opacity and day-night heat redistribution affect the boundary condition seen by the interior. Analytic irradiated-atmosphere work shows why deep temperatures depend on global transport as well as incident power, while also illustrating the difficulty of explaining observed radii by simple opacity changes alone.^[ref] An expanded radius is thus a constraint on the thermal history, rather than direct evidence for one unique heating mechanism.