# Proxima Centauri

Proxima Centauri is a small, low-mass star located 4.244 light-years (1.301 pc) away from the Sun in the southern constellation of Centaurus. Its Latin name means the "nearest [star] of Centaurus". This object was discovered in 1915 by Robert Innes and is the nearest-known star to the Sun. With a quiescent apparent magnitude of 11.13, it is too faint to be seen with the naked eye. Proxima Centauri is a member of the Alpha Centauri system, being identified as component Alpha Centauri C, and is 2.18° to the southwest of the Alpha Centauri AB pair. It is currently 12,950 AU (1.94 trillion km) from AB, which it orbits with a period of about 550,000 years.

Observation data Epoch J2000.0      Equinox J2000.0 (ICRS) Constellation Photograph taken from the Hubble Space Telescope near Earth in 2013 Centaurus /ˌprɒksɪmə sɛnˈtɔːraɪ/,[1][2] 14h 29m 42.94853s[3] −62° 40′ 46.1631″[3] 10.43 – 11.11[4] Main sequence red dwarf M5.5Ve[5] 14.21[6] 12.95[6] 11.13[6] 9.45[6] 7.41[6] 5.357±0.023[7] 4.835±0.057[7] 4.384±0.033[7] 1.26 1.82 1.68 2.04 0.522 0.973 UV Ceti ("flare star")[4] Radial velocity (Rv) −22.204±0.032[8] km/s Proper motion (μ) RA: −3781.306[9] mas/yr Dec.: 769.766[9] mas/yr Parallax (π) 768.5 ± 0.2[9] mas Distance 4.244 ± 0.001 ly (1.3012 ± 0.0003 pc) Absolute magnitude (MV) 15.60[10] Primary Alpha Centauri AB Companion Proxima Centauri Period (P) 547000+6600−4000 yr Semi-major axis (a) 8700+700−400 AU Eccentricity (e) 0.50+0.08−0.09 Inclination (i) 107.6+1.8−2.0° Longitude of the node (Ω) 126±5° Periastron epoch (T) +283+59−41 Argument of periastron (ω)(secondary) 72.3+8.7−6.6° Mass 0.1221±0.0022[8] M☉ Radius 0.1542±0.0045[8] R☉ Luminosity (bolometric) 0.0017[11] L☉ Luminosity (visual, LV) 0.00005[nb 1] L☉ Surface gravity (log g) 5.20±0.23[12] cgs Temperature 3042±117[12] K Metallicity [Fe/H] 0.21[13][nb 2] dex Rotation 82.6±0.1[16] days Rotational velocity (v sin i) < 0.1[16] km/s Age 4.85[17] Gyr Alpha Centauri C, CCDM J14396-6050C, GCTP 3278.00, GJ 551, HIP 70890, LFT 1110, LHS 49, LPM 526, LTT 5721, NLTT 37460, V645 Centauri[18] SIMBAD data ARICNS data

Proxima Centauri is a red dwarf star with a mass about an eighth of the Sun's mass (M), and average density about 33 times that of the Sun. Because of Proxima Centauri's proximity to Earth, its angular diameter can be measured directly. Its actual diameter is about one-seventh the diameter of the Sun. Although it has a very low average luminosity, Proxima is a flare star that undergoes random dramatic increases in brightness because of magnetic activity. The star's magnetic field is created by convection throughout the stellar body, and the resulting flare activity generates a total X-ray emission similar to that produced by the Sun. The mixing of the fuel at Proxima Centauri's core through convection, and its relatively low energy-production rate, mean that it will be a main-sequence star for another four trillion years.

Proxima Centauri has two confirmed planets and a third unconfirmed. In 2016, astronomers announced the discovery of Proxima Centauri b, a planet orbiting the star at a distance of roughly 0.05 AU (7.5 million km) with an orbital period of approximately 11.2 Earth days. Its estimated mass is at least 1.17 times that of the Earth.[19] The equilibrium temperature of Proxima b is estimated to be within the range of where water could exist as liquid on its surface, thus placing it within the habitable zone of Proxima Centauri, although because Proxima Centauri is a red dwarf and a flare star, whether it could support life is disputed. A super-Earth, Proxima c, orbiting roughly 1.5 AU (220 million km) away every 1,900 d (5.2 yr), was discovered in 2019 and confirmed in 2020 using archival imagery from 1995, making it the closest planet (and first) ever directly imaged. Candidate planet Proxima d was found in 2019 using radial velocity data, with an orbital period of 5.15 days.[19]

## Observation

In 1915, the Scottish astronomer Robert Innes, Director of the Union Observatory in Johannesburg, South Africa, discovered a star that had the same proper motion as Alpha Centauri.[20][21][22][23] He suggested that it be named Proxima Centauri[24] (actually Proxima Centaurus).[25] In 1917, at the Royal Observatory at the Cape of Good Hope, the Dutch astronomer Joan Voûte measured the star's trigonometric parallax at 0.755±0.028 and determined that Proxima Centauri was approximately the same distance from the Sun as Alpha Centauri. It was also found to be the lowest-luminosity star known at the time.[26] An equally accurate parallax determination of Proxima Centauri was made by American astronomer Harold L. Alden in 1928, who confirmed Innes's view that it is closer, with a parallax of 0.783″±0.005″.[21][24]

Stars closest to the Sun, including Proxima Centauri

In 1951, American astronomer Harlow Shapley announced that Proxima Centauri is a flare star. Examination of past photographic records showed that the star displayed a measurable increase in magnitude on about 8% of the images, making it the most active flare star then known.[27][28] The proximity of the star allows for detailed observation of its flare activity. In 1980, the Einstein Observatory produced a detailed X-ray energy curve of a stellar flare on Proxima Centauri. Further observations of flare activity were made with the EXOSAT and ROSAT satellites, and the X-ray emissions of smaller, solar-like flares were observed by the Japanese ASCA satellite in 1995.[29] Proxima Centauri has since been the subject of study by most X-ray observatories, including XMM-Newton and Chandra.[30]

In 2016, the International Astronomical Union organized a Working Group on Star Names (WGSN) to catalogue and standardize proper names for stars.[31] The WGSN approved the name Proxima Centauri for this star on August 21, 2016 and it is now so included in the List of IAU approved Star Names.[32]

Because of Proxima Centauri's southern declination, it can only be viewed south of latitude 27° N.[nb 3] Red dwarfs such as Proxima Centauri are too faint to be seen with the naked eye. Even from Alpha Centauri A or B, Proxima would only be seen as a fifth magnitude star.[33][34] It has an apparent visual magnitude of 11, so a telescope with an aperture of at least 8 cm (3.1 in) is needed to observe it, even under ideal viewing conditions—under clear, dark skies with Proxima Centauri well above the horizon.[35]

In 2018, a superflare was observed from Proxima Centauri, the strongest flare ever seen. The optical brightness increased by a factor of 68 to approximately magnitude 6.8. It is estimated that similar flares occur around five times every year but are of such short duration, just a few minutes, that they have never been observed before.[36]

On 2020 April 22 and 23, the New Horizons spacecraft took images of two of the nearest stars, Proxima Centauri & Wolf 359. When combined with Earth-based images, the result will be a record-setting parallax measurement.[37]

## Physical properties

Proxima Centauri is a red dwarf, because it belongs to the main sequence on the Hertzsprung–Russell diagram and is of spectral class M5.5. M5.5 means that it falls in the low-mass end of M-type stars.[17] Its absolute visual magnitude, or its visual magnitude as viewed from a distance of 10 parsecs (33 ly), is 15.5.[38] Its total luminosity over all wavelengths is 0.17% that of the Sun,[11] although when observed in the wavelengths of visible light the eye is most sensitive to, it is only 0.0056% as luminous as the Sun.[39] More than 85% of its radiated power is at infrared wavelengths.[40] It has a regular activity cycle of starspots.[41]

Comparative sizes of (from left to right) the Sun, Alpha Centauri A, Alpha Centauri B, and Proxima Centauri
The two bright points are the Alpha Centauri system (left) and Beta Centauri (right). The faint red star in the centre of the red circle is Proxima Centauri.

In 2002, optical interferometry with the Very Large Telescope (VLTI) found that the angular diameter of Proxima Centauri is 1.02±0.08 mas. Because its distance is known, the actual diameter of Proxima Centauri can be calculated to be about 1/7 that of the Sun, or 1.5 times that of Jupiter. The star's mass, estimated from stellar theory, is 12.2% M, or 129 Jupiter masses (MJ).[42] The mass has been calculated directly, although with less precision, from observations of microlensing events to be 0.150+0.062
−0.051
M
.[43]

Lower mass main-sequence stars have higher mean density than higher mass ones,[44] and Proxima Centauri is no exception: it has a mean density of 47.1×103 kg/m3 (47.1 g/cm3), compared with the Sun's mean density of 1.411×103 kg/m3 (1.411 g/cm3).[nb 4]

A 1998 study of photometric variations indicates that Proxima Centauri rotates once every 83.5 days.[45] A subsequent time series analysis of chromospheric indicators in 2002 suggests a longer rotation period of 116.6±0.7 days.[46] This was subsequently ruled out in favor of a rotation period of 82.6±0.1 days.[16]

Because of its low mass, the interior of the star is completely convective,[47] causing energy to be transferred to the exterior by the physical movement of plasma rather than through radiative processes. This convection means that the helium ash left over from the thermonuclear fusion of hydrogen does not accumulate at the core, but is instead circulated throughout the star. Unlike the Sun, which will only burn through about 10% of its total hydrogen supply before leaving the main sequence, Proxima Centauri will consume nearly all of its fuel before the fusion of hydrogen comes to an end after about 4 trillion years.[48]

Convection is associated with the generation and persistence of a magnetic field. The magnetic energy from this field is released at the surface through stellar flares that briefly increase the overall luminosity of the star. These flares can grow as large as the star and reach temperatures measured as high as 27 million K[30]—hot enough to radiate X-rays.[49] Proxima Centauri's quiescent X-ray luminosity, approximately (4–16) × 1026 erg/s ((4–16) × 1019 W), is roughly equal to that of the much larger Sun. The peak X-ray luminosity of the largest flares can reach 1028 erg/s (1021 W).[30]

Proxima Centauri's chromosphere is active, and its spectrum displays a strong emission line of singly ionized magnesium at a wavelength of 280 nm.[50] About 88% of the surface of Proxima Centauri may be active, a percentage that is much higher than that of the Sun even at the peak of the solar cycle. Even during quiescent periods with few or no flares, this activity increases the corona temperature of Proxima Centauri to 3.5 million K, compared to the 2 million K of the Sun's corona,[51] and its total X-ray emission is comparable to the sun's.[52] Proxima Centauri's overall activity level is considered low compared to other red dwarfs,[52] which is consistent with the star's estimated age of 4.85 × 109 years,[17] since the activity level of a red dwarf is expected to steadily wane over billions of years as its stellar rotation rate decreases.[53] The activity level also appears to vary with a period of roughly 442 days, which is shorter than the solar cycle of 11 years.[54]

Proxima Centauri has a relatively weak stellar wind, no more than 20% of the mass loss rate of the solar wind. Because the star is much smaller than the Sun, the mass loss per unit surface area from Proxima Centauri may be eight times that from the solar surface.[55]

A red dwarf with the mass of Proxima Centauri will remain on the main sequence for about four trillion years. As the proportion of helium increases because of hydrogen fusion, the star will become smaller and hotter, gradually transforming into a so-called "blue dwarf". Near the end of this period it will become significantly more luminous, reaching 2.5% of the Sun's luminosity (L) and warming up any orbiting bodies for a period of several billion years. When the hydrogen fuel is exhausted, Proxima Centauri will then evolve into a white dwarf (without passing through the red giant phase) and steadily lose any remaining heat energy.[48]

### Distance and motion

Based on a parallax of 768.5004±0.2030 mas, published in 2018 in Gaia Data Release 2, Proxima Centauri is about 4.244 light-years (1.301 pc; 268,400 AU) from the Sun.[9] Previously published parallaxes include: 768.13±1.04 mas, in 2014 by the Research Consortium On Nearby Stars;[56] 772.33±2.42 mas, in the original Hipparcos Catalogue, in 1997;[57] 771.64±2.60 mas in the Hipparcos New Reduction, in 2007;[3] and 768.77±0.37 mas using the Hubble Space Telescope's Fine Guidance Sensors, in 1999.[10] From Earth's vantage point, Proxima is separated from Alpha Centauri by 2.18 degrees,[58] or four times the angular diameter of the full Moon.[59] Proxima also has a relatively large proper motion—moving 3.85 arcseconds per year across the sky.[60] It has a radial velocity toward the Sun of 22.2 km/s.[8]

Distances of the nearest stars from 20,000 years ago through 80,000 years in the future. Proxima Centauri is in yellow.

Among the known stars, Proxima Centauri has been the closest star to the Sun for about 32,000 years and will be so for about another 25,000 years, after which Alpha Centauri A and Alpha Centauri B will alternate approximately every 79.91 years as the closest star to the Sun. In 2001, J. García-Sánchez et al. predicted that Proxima will make its closest approach to the Sun in approximately 26,700 years, coming within 3.11 ly (0.95 pc).[61] A 2010 study by V. V. Bobylev predicted a closest approach distance of 2.90 ly (0.89 pc) in about 27,400 years,[62] followed by a 2014 study by C. A. L. Bailer-Jones predicting a perihelion approach of 3.07 ly (0.94 pc) in roughly 26,710 years.[63] Proxima Centauri is orbiting through the Milky Way at a distance from the Galactic Centre that varies from 27 to 31 kly (8.3 to 9.5 kpc), with an orbital eccentricity of 0.07.[64]

Orbital plot of Proxima Centauri as presently seen from Earth

Ever since the discovery of Proxima, it has been suspected to be a true companion of the Alpha Centauri binary star system. Data from the Hipparcos satellite, combined with ground-based observations, were consistent with the hypothesis that the three stars are a bound system. For this reason, Proxima is sometimes referred to as Alpha Centauri C. Kervella et al. (2017) used high-precision radial velocity measurements to determine with a high degree of confidence that Proxima and Alpha Centauri are gravitationally bound.[8] Proxima's orbital period around the Alpha Centauri AB barycenter is 547000+6600
−4000
years with an eccentricity of 0.5±0.08; it approaches Alpha Centauri to 4300+1100
−900
AU
at periastron and retreats to 13000+300
−100
AU
at apastron.[8] At present, Proxima is 12,947 ± 260 AU (1.94 ± 0.04 trillion km) from the Alpha Centauri AB barycenter, nearly to the farthest point in its orbit.[8]

Such a triple system can form naturally through a low-mass star being dynamically captured by a more massive binary of 1.5–2 M within their embedded star cluster before the cluster disperses.[65] However, more accurate measurements of the radial velocity are needed to confirm this hypothesis.[66] If Proxima was bound to the Alpha Centauri system during its formation, the stars are likely to share the same elemental composition. The gravitational influence of Proxima might also have stirred up the Alpha Centauri protoplanetary disks. This would have increased the delivery of volatiles such as water to the dry inner regions, so possibly enriching any terrestrial planets in the system with this material.[66] Alternatively, Proxima may have been captured at a later date during an encounter, resulting in a highly eccentric orbit that was then stabilized by the galactic tide and additional stellar encounters. Such a scenario may mean that Proxima's planetary companion has had a much lower chance for orbital disruption by Alpha Centauri.[15]

Six single stars, two binary star systems, and a triple star share a common motion through space with Proxima Centauri and the Alpha Centauri system. The space velocities of these stars are all within 10 km/s of Alpha Centauri's peculiar motion. Thus, they may form a moving group of stars, which would indicate a common point of origin,[67] such as in a star cluster.

## Planetary system

The Proxima Centauri planetary system[68][69][70][71][19][72]
Companion
(in order from star)
Mass Semimajor axis
(AU)
Orbital period
(days)
d (unconfirmed) ≥ 0.29±0.08 M 0.02895±0.00022 5.168+0.051
−0.069
b ≥ 1.173+0.087
−0.090
M
0.04857+0.00029
−0.00029
11.18418+0.00068
−0.00074
0.109+0.076
−0.068
0.8–1.5[73] R
c 7±1 M 1.489±0.049 1928±20 0.04±0.01 133±1°
RV-derived upper mass limits of potential companions[74]
Orbital
period

(days)
Separation
(AU)
Maximum
mass[nb 5]
(M)
3.6–13.8 0.022–0.054 2–3
< 100 < 0.21 8.5
< 1000 < 1 16

Proxima Centauri b, or Alpha Centauri Cb, is a planet orbiting the star at a distance of roughly 0.05 AU (7.5 million km) with an orbital period of approximately 11.2 Earth days. Its estimated mass is at least 1.3 times that of the Earth. Moreover, the equilibrium temperature of Proxima b is estimated to be within the range where water could exist as liquid on its surface; thus, placing it within the habitable zone of Proxima Centauri.[68][75][76]

The first indications of the exoplanet Proxima Centauri b were found in 2013 by Mikko Tuomi of the University of Hertfordshire from archival observation data.[77][78] To confirm the possible discovery, a team of astronomers launched the Pale Red Dot[nb 6] project in January 2016.[79] On August 24, 2016, the team of 31 scientists from all around the world,[80] led by Guillem Anglada-Escudé of Queen Mary University of London, confirmed the existence of Proxima Centauri b[81] through a peer-reviewed article published in Nature.[68][82] The measurements were performed using two spectrographs: HARPS on the ESO 3.6 m Telescope at La Silla Observatory and UVES on the 8 m Very Large Telescope at Paranal Observatory.[68] Several attempts to detect a transit of this planet across the face of Proxima Centauri have been made. A transit-like signal appearing on September 8, 2016 was tentatively identified, using the Bright Star Survey Telescope at the Zhongshan Station in Antarctica.[83]

Prior to this discovery, multiple measurements of the star's radial velocity constrained the maximum mass that a detectable companion to Proxima Centauri could possess.[10][84] The activity level of the star adds noise to the radial velocity measurements, complicating detection of a companion using this method.[85] In 1998, an examination of Proxima Centauri using the Faint Object Spectrograph on board the Hubble Space Telescope appeared to show evidence of a companion orbiting at a distance of about 0.5 AU.[86] A subsequent search using the Wide Field Planetary Camera 2 failed to locate any companions.[87] Astrometric measurements at the Cerro Tololo Inter-American Observatory appear to rule out a Jupiter-sized planet with an orbital period of 2−12 years.[88] A second signal in the range of 60 to 500 days was also detected, but its nature is still unclear due to stellar activity.[68]

Proxima c is a Super-Earth about 7 times as heavy as Earth, orbiting at roughly 1.5 astronomical units (220,000,000 km) every 1,900 days (5.2 yr)[89]. Due to its large distance from Proxima Centauri, the exoplanet is unlikely to be habitable, with a low equilibrium temperature of around 39 K[90]. The planet was first reported by Italian astrophysicist Mario Damasso and his colleagues in April 2019.[90][89] Damasso's team had noticed minor movements of Proxima Centauri in the radial velocity data from the ESO's HARPS instrument, indicating a possible additional planet orbiting Proxima Centauri.[90] In 2020, the planet's existence was confirmed by precovery images from Hubble c. 1995, making it the first and closest planet ever to be directly imaged.[91] The detected source is too bright for a planet of Proxima c's mass and age, implying that the planet may have a ring system with a radius of around 5 RJ.[92]

In 2017, a team of astronomers using the Atacama Large Millimeter/submillimeter Array reported detecting a belt of cold dust orbiting Proxima Centauri at a range of 1−4 AU from the star. This dust has a temperature of around 40 K and has a total estimated mass of 1% of the planet Earth. They also tentatively detected two additional features: a cold belt with a temperature of 10 K orbiting around 30 AU and a compact emission source about 1.2 arcseconds from the star. There was also a hint at an additional warm dust belt at a distance of 0.4 AU from the star.[93] However, upon further analysis, these emissions were determined to be most likely the result of a large flare emitted by the star in March 2017. The presence of dust is not needed to model the observations.[94][95]

In 2019, a team of astronomers revisited the data from ESPRESSO about Proxima b to refine its mass. While doing so, the team found another radial velocity spike with a periodicity of 5.15 days. They estimated that if it were a planetary companion, it would be no less than 0.29 masses of the Earth.[19] The discovery was released in 2020.

### Habitability

Pale Red Dot is an international search for an Earth-like exoplanet around the closest star Proxima Centauri.

Prior to the discovery of Proxima Centauri b, the TV documentary Alien Worlds hypothesized that a life-sustaining planet could exist in orbit around Proxima Centauri or other red dwarfs. Such a planet would lie within the habitable zone of Proxima Centauri, about 0.023–0.054 AU (3.4–8.1 million km) from the star, and would have an orbital period of 3.6–14 days.[96] A planet orbiting within this zone may experience tidal locking to the star. If the orbital eccentricity of this hypothetical planet is low, Proxima Centauri would move little in the planet's sky, and most of the surface would experience either day or night perpetually. The presence of an atmosphere could serve to redistribute the energy from the star-lit side to the far side of the planet.[97]

Proxima Centauri's flare outbursts could erode the atmosphere of any planet in its habitable zone, but the documentary's scientists thought that this obstacle could be overcome. Gibor Basri of the University of California, Berkeley, mentioned that "no one [has] found any showstoppers to habitability". For example, one concern was that the torrents of charged particles from the star's flares could strip the atmosphere off any nearby planet. If the planet had a strong magnetic field, the field would deflect the particles from the atmosphere; even the slow rotation of a tidally locked planet that spins once for every time it orbits its star would be enough to generate a magnetic field, as long as part of the planet's interior remained molten.[98]

Other scientists, especially proponents of the rare-Earth hypothesis,[99] disagree that red dwarfs can sustain life. Any exoplanet in this star's habitable zone would likely be tidally locked, resulting in a relatively weak planetary magnetic moment, leading to strong atmospheric erosion by coronal mass ejections from Proxima Centauri.[100]

## Future exploration

The Sun as seen from the Alpha Centauri system, using Celestia

Because of the star's proximity to Earth, Proxima Centauri has been proposed as a flyby destination for interstellar travel.[101] Proxima currently moves toward Earth at a rate of 22.2 km/s.[8] After 26,700 years, when it will come within 3.11 light-years, it will begin to move farther away.[61]

If non-nuclear, conventional propulsion technologies are used, the flight of a spacecraft to a planet orbiting Proxima Centauri would probably require thousands of years.[102] For example, Voyager 1, which is now travelling 17 km/s (38,000 mph)[103] relative to the Sun, would reach Proxima in 73,775 years, were the spacecraft travelling in the direction of that star. A slow-moving probe would have only several tens of thousands of years to catch Proxima Centauri near its closest approach, and could end up watching it recede into the distance.[104]

Nuclear pulse propulsion might enable such interstellar travel with a trip timescale of a century, inspiring several studies such as Project Orion, Project Daedalus, and Project Longshot.[104]

Project Breakthrough Starshot aims to reach the Alpha Centauri system within the first half of the 21st century, with microprobes travelling at 20% of the speed of light propelled by around 100 gigawatts of Earth-based lasers.[105] The probes would perform a fly-by of Proxima Centauri to take photos and collect data of its planets' atmospheric compositions. It would take 4.22 years for the information collected to be sent back to Earth.[106]

From Proxima Centauri, the Sun would appear as a bright 0.4-magnitude star in the constellation Cassiopeia, similar to that of Achernar from Earth.[nb 7]

## Notes

1. ^ From knowing the absolute visual magnitude of Proxima Centauri, ${\displaystyle \scriptstyle M_{V_{\ast }}=15.6}$ , and the absolute visual magnitude of the Sun, ${\displaystyle \scriptstyle M_{V_{\odot }}=4.83}$ , the visual luminosity of Proxima Centauri can therefore be calculated: ${\displaystyle \scriptstyle {\frac {L_{V_{\ast }}}{L_{V_{\odot }}}}=10^{0.4\left(M_{V_{\odot }}-M_{V_{\ast }}\right)}=4.92\times 10^{-5}}$
2. ^ If Proxima Centauri was a later capture into the Alpha Centauri star system then its metallicity and age could be quite different to that of Alpha Centauri A and B. Through comparing Proxima Centauri to other similar stars it was estimated that it had a lower metallicity, ranging from less than a third, to about the same, of our Sun's.[14][15]
3. ^ For a star south of the zenith, the angle to the zenith is equal to the Latitude minus the Declination. The star is hidden from sight when the zenith angle is 90° or more, i.e. below the horizon. Thus, for Proxima Centauri:
Highest latitude = 90° + −62.68° = 27.32°.
See: Campbell, William Wallace (1899). The elements of practical astronomy. London: Macmillan. pp. 109–110. Retrieved August 12, 2008.
4. ^ The density (ρ) is given by the mass divided by the volume. Relative to the Sun, therefore, the density is:
 ${\displaystyle \rho }$ = ${\displaystyle {\begin{smallmatrix}{\frac {M}{M_{\odot }}}\cdot \left({\frac {R}{R_{\odot }}}\right)^{-3}\cdot \rho _{\odot }\end{smallmatrix}}}$ = 0.122 · 0.154−3 · (1.41 × 103 kg/m3) = 33.4 · (1.41 × 103 kg/m3) = 4.71 × 104 kg/m3

where ${\displaystyle {\begin{smallmatrix}\rho _{\odot }\end{smallmatrix}}}$  is the average solar density. See:

• Munsell, Kirk; Smith, Harman; Davis, Phil; Harvey, Samantha (June 11, 2008). "Sun: facts & figures". Solar system exploration. NASA. Archived from the original on January 2, 2008. Retrieved July 12, 2008.
• Bergman, Marcel W.; Clark, T. Alan; Wilson, William J. F. (2007). Observing projects using Starry Night Enthusiast (8th ed.). Macmillan. pp. 220–221. ISBN 978-1-4292-0074-5.
5. ^ This is actually an upper limit on the quantity m sin i, where i is the angle between the orbit normal and the line of sight, in a circular orbit. If the planetary orbits are close to face-on as observed from Earth, or in an eccentric orbit, more massive planets could have evaded detection by the radial velocity method.
6. ^ Pale Red Dot is a reference to Pale Blue Dot, a distant photo of Earth taken by Voyager 1.
7. ^ The coordinates of the Sun would be diametrically opposite Proxima, at α= 02h 29m 42.9487s, δ=+62° 40′ 46.141″. The absolute magnitude Mv of the Sun is 4.83, so at a parallax π of 0.77199 the apparent magnitude m is given by 4.83 − 5(log10(0.77199) + 1) = 0.40. See: Tayler, Roger John (1994). The Stars: Their Structure and Evolution. Cambridge University Press. p. 16. ISBN 978-0-521-45885-6.

## References

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2. ^ Compare to the pronunciation for Centauri in the Alpha Centauri entry:
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