Planet occurrence

Planet occurrence is the astronomer's word for how common planets are: the average number of planets per star, or the fraction of stars that have any, inside a stated range of planet size and orbital period. It is never a raw count. Every survey method misses most of the planets that exist, so each rate is a detection count divided by the survey's sensitivity. Thirty years after the first planet was found around a Sun-like star ^[1], and with 6,372 planets confirmed as of 25 September 2026 ^[2], the answer is clear in outline: planets are the rule, most stars have several, and the kinds of planet a star gets depend strongly on its mass and its metal content.

Pax Abyssi gives planets to its stars at these measured rates. Every star in the game draws whether it has planets from a probability fitted to the surveys on this page, 96 per cent for red dwarfs and 89 per cent for a Sun-like star, adjusted for companions, metal content, age and the star's stage of life, and every star with real, catalogued planets keeps them. The numbers you meet as you travel, how many systems are empty and how many are full, are the numbers astronomers have measured.

What a rate means

Surveys see planets through narrow windows. A transit survey such as Kepler catches a planet only when its orbit happens to be edge-on, crossing the face of its star; for a circular orbit the chance of that alignment is roughly the star's radius divided by the orbit's size,

$$p_\mathrm{tr} \approx \frac{R_\star}{a}.$$

For Earth around the Sun that is 696,000 km divided by 149.6 million km, about 0.47 per cent, one viewing direction in 215. The radial-velocity method, which measures the star's wobble, has the opposite bias: it favours heavy planets close in. The star's speed amplitude is

$$K = 28.4\ \mathrm{m\,s^{-1}} \left(\frac{m_p \sin i}{M_\mathrm{J}}\right)\left(\frac{P}{1\ \mathrm{yr}}\right)^{-1/3}\left(\frac{M_\star}{M_\odot}\right)^{-2/3},$$

which gives 12.5 m/s for Jupiter tugging on the Sun and 9 cm/s for Earth, a signal at the edge of what the best spectrographs can reach.

To turn detections into a rate, each planet found is weighted by how unlikely it was to be found:

$$f = \frac{1}{N_\star}\sum_{i} \frac{1}{p_{\mathrm{tr},i}\,p_{\mathrm{det},i}},$$

where $N_\star$ is the number of stars searched and $p_{\mathrm{det},i}$ is the measured chance that the survey's software would have flagged that planet. A single Earth-like detection in a transit survey therefore stands for about 200 planets that were not aligned.

Two kinds of number come out, and they are easily confused. A planets-per-star rate counts planets; a host fraction counts stars with at least one. Planets clump into systems, so the two do not convert simply. If planets fell on stars independently, a mean of $\lambda$ planets per star would leave a fraction $e^{-\lambda}$ of stars empty. Kepler's close-in planets do not behave like that: about 30 per cent of Sun-like stars host a Kepler-like system of planets larger than Earth inside 400 days, and those systems average three planets each ^[3]. That is 0.9 planets per star in the window, but only 30 per cent of stars, where independent placement would have given 59.

How we know

Each method covers a different patch of the mass and distance plane, and the full picture is stitched together from all of them.

• Transits. Kepler watched about 150,000 stars for four years and produced most of the statistics for small planets inside about one AU. It found that planets between Earth and Neptune in size, which the Solar System lacks, are the commonest kind close to stars, and that their radii split in two with a gap near 1.5 to 2 Earth radii ^[4]. TESS extends the same census to bright, nearby stars of every type.
• Radial velocity. Decades-long wobble surveys of nearby stars measure giant planets out to a few AU and the frequency of planets around M dwarfs ^{[5] [6]}.
• Microlensing. When a star passes in front of a more distant one, its gravity briefly magnifies the background light, and a planet adds a blip. The method is most sensitive at 0.5 to 10 AU, beyond the reach of the other two, and it found that cold planets are common too ^[7].
• Direct imaging sees young giant planets tens of AU from their stars. About 9 per cent of stars heavier than 1.5 solar masses have a planet of 5 to 13 Jupiter masses at 10 to 100 AU, and such planets are rarer around Sun-like stars ^[8].

Image pendingFile:Planet_detection_windows_diagram.svgLog-log chart of planet mass against orbital distance with shaded regions for transit, radial-velocity, microlensing and imaging surveys and the Solar System planets plotted as points

What the surveys found

Small planets are everywhere close in. Around Sun-like stars the fraction hosting at least one planet of 0.5 to 10 Earth radii within 300 days rises steeply toward cooler stars: 32 per cent for an F2 dwarf, 57 per cent for a G2 dwarf like the Sun and about 96 per cent for a mid-K dwarf ^[9]. M dwarfs are richer still, with 2.5 ± 0.2 planets of 1 to 4 Earth radii per star inside 200 days ^[10], and a radial-velocity survey of 238 M dwarfs finds 1.44 ± 0.20 planets per star between 1 and 1,000 Earth masses inside 1,000 days, which implies that nearly every M dwarf has one ^[6]. At the hot end the trend continues: a search of 20,257 A stars with TESS found no reliable small close-in planet, which puts sub-Neptunes around A stars at fewer than about 9 per 1,000 stars, several times rarer than around the Sun's kind ^[11].

Hot Jupiters are rare. Giant planets orbiting in less than ten days, the first kind found around a Sun-like star ^[1], occur around 0.43 ± 0.05 per cent of stars in the Kepler field ^[12] and 1.2 ± 0.38 per cent of nearby F, G and K dwarfs in radial-velocity surveys ^[13]. The two samples were chosen differently and the gap between them is not fully explained. TESS finds 0.41 ± 0.10 per cent overall and 0.26 ± 0.11 per cent for A stars ^[14], and 0.27 ± 0.09 per cent for early M dwarfs ^[15].

Cold giants are about ten times commoner than hot ones. The Anglo-Australian Planet Search finds giant planets of more than 0.3 Jupiter masses on orbits longer than 100 days around 6.7 per cent of Sun-like stars, against 0.84 per cent for hot Jupiters in the same sample ^[5]. Combining Kepler and radial velocities, giant-planet occurrence rises with distance, peaks near 2 to 3 AU, close to where water freezes in a young planetary disc, and then declines; giant planets of 0.1 to 20 Jupiter masses anywhere between 0.1 and 100 AU number about 0.27 per Sun-like star ^[16]. Microlensing adds Neptune-mass and super-Earth planets at a few AU in large numbers, enough to conclude that stars have one or more bound planets as a rule ^[7].

Metal-rich stars make giants. The chance that a Sun-like star has a giant planet detectable by radial velocity grows as the square of its iron content,

$$P(\text{giant}) \approx 0.03 \times 10^{\,2.0\,[\mathrm{Fe/H}]},$$

about 3 per cent at solar metallicity, 12 per cent at twice the Sun's iron ([Fe/H] = +0.3) and 0.3 per cent at a third of it ^[17]. Small planets show no such dependence and form around stars across a wide range of metallicity ^[18].

Planets come in correlated families. Cold Jupiters are about three times more common around stars that host inner super-Earths, and about 90 per cent of cold-Jupiter hosts also have super-Earths closer in ^[19]. About half of hot-Jupiter systems, 51 ± 10 per cent, have a distant massive companion between 1 and 20 AU ^[20]. By these measures the Solar System, with nothing inside Mercury's orbit, is unusual: a population model fitted to Kepler finds fewer than about 8 per cent of planetary systems with no planet interior to Mercury ^[21].

Earth-like planets and eta-Earth

The number most often asked for is eta-Earth, $\eta_\oplus$: the average number of rocky, roughly Earth-sized planets in the habitable zone of a Sun-like star. Almost no such planets are detected directly, because a year-long orbit transits rarely and produces a tiny wobble, so eta-Earth is an extrapolation and its value depends on the definitions chosen. For planets of 0.5 to 1.5 Earth radii around stars of 4,800 to 6,300 K, the final Kepler data give 0.37 to 0.60 per star in the conservative habitable zone and 0.58 to 0.88 in the wider optimistic one, which would place the nearest such planet around a G or K dwarf about 6 parsecs away on average ^[22]. An earlier estimate for planets of 1 to 2 Earth radii with periods of 200 to 400 days found 5.7 per cent ^[23]. For M dwarfs the conservative figure is 0.16 Earth-size planets per star ^[10]. None of these numbers says anything about whether such planets are habitable in practice.

Notable numbers

See also

• Planetary system archetypes
• Star system generation
• Habitable zone
• Radius valley
• Hot Jupiter
• Mini-Neptune
• Super-Earth
• Red dwarf
• Orbit

References

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