Astronomy:50000 Quaoar

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Short description: Cold classical Kuiper belt object

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50000 Quaoar 🝾 (mostly astrological)
Quaoar-weywot hst.jpg
Quaoar with its moon Weywot imaged by the Hubble Space Telescope in 2006
Discovery[1]
Discovered by
Discovery sitePalomar Observatory
Discovery date4 June 2002
Designations
(50000) Quaoar
Pronunciation/ˈkwɑːwɑːr/, /ˈkwɑːoʊ.ɑːr/
Named afterQua-o-ar / Kwawar[2]
(deity of the Tongva people)
2002 LM60
Minor planet category
AdjectivesQuaoarian
Orbital characteristics[3]
Epoch 31 May 2020 (JD 2459000.5)
Uncertainty parameter 3
Observation arc65.27 yr (23,839 d)
Earliest precovery date25 May 1954
|{{{apsis}}}|helion}}45.488 AU (6.805 Tm)
|{{{apsis}}}|helion}}41.900 AU (6.268 Tm)
43.694 AU (6.537 Tm)
Eccentricity0.04106
Orbital period288.83 yr (105,495 d)
Mean anomaly301.104°
Mean motion0° 0m 12.285s / day
Inclination7.9895°
Longitude of ascending node188.927°
|{{{apsis}}}|helion}}≈ 11 February 2075[6]
±17 days
147.480°
Known satellites1 (Weywot)
Physical characteristics
Dimensions1,159±8 km (2023; equatorial)[7]
1,138+48
−34 × 1,036+44
−31 km (2013; equatorial and polar)[lower-alpha 1]
Mean diameter1,086±4 km (2023; area equivalent)[7]
1,110±5 km (2013; volume equivalent)[8]
Mean radius543±2 km (2023; area equivalent)[7]
555±2.5 km (2013; volume equivalent)[8]
Flattening0.12±0.01 (2023; projected)[7]
0.0897±0.006 (2013)[8]
Surface area3.83×106 km2[9]
Volume(7.16±0.10)×108 km3[lower-alpha 2]
Mass(1.20±0.05)×1021 kg[10](p3)
Mean density1.68±0.08 g/cm3[lower-alpha 3]
Equatorial surface gravity
0.26 m/s2
Equatorial escape velocity
0.54 km/s
Rotation period17.6788±0.0004 h[11][10]
Axial tilt13.6°[lower-alpha 4] or 14.0°[lower-alpha 5] to ecliptic (if coplanar with rings)
North pole right ascension258.47°±0.87°[10](p3) or 259.82°±0.23°[7](p4) (outer ring)
North pole declination+54.14°±0.11°[10](p3) or +53.45°±0.30°[7](p4) (outer ring)
Geometric albedo0.124±0.006[7]
0.109±0.007[8]
Physics≈ 44 K[13]
IR (moderately red)
B–V=0.94±0.01[14][15]
V−R=0.64±0.01[14]
V−I=1.28±0.02[15][16]
Apparent magnitude19.0[17]
Absolute magnitude (H)2.737±0.008[17]
2.4 (assumed)[3][1]
Angular diameter40.4±1.8 milliarcseconds[18]


Quaoar (minor-planet designation 50000 Quaoar) is a ringed dwarf planet in the Kuiper belt, a region of icy planetesimals beyond Neptune. A non-resonant object (cubewano), it measures approximately 1,086 km (675 mi) in diameter, about the size of Saturn's moon Dione or half the size of Pluto. The object was discovered by American astronomers Chad Trujillo and Michael Brown at the Palomar Observatory on 4 June 2002. Signs of water ice on the surface of Quaoar have been found, which suggests that cryovolcanism may be occurring on Quaoar. A small amount of methane is present on its surface, which can only be retained by the largest Kuiper belt objects.

Quaoar has one known moon, Weywot, which was discovered by Brown in February 2007.[19] Both objects were named after mythological figures from the Native American Tongva people in Southern California. Quaoar is the Tongva creator deity and Weywot is his son. In 2023, astronomers announced the discovery of two rings orbiting Quaoar outside its Roche limit, which defies theoretical expectations that these rings should not be stable.[7]

History

Discovery

Quaoar was discovered using the Samuel Oschin telescope at Palomar Observatory
Animation of three discovery images taken over a period of 4.5 hours, showing the slow movement of Quaoar (indicated by the arrow)[20]

Quaoar was discovered on 4 June 2002 by American astronomers Chad Trujillo and Michael Brown at the Palomar Observatory in the Palomar Mountain Range in San Diego County, California.[1] The discovery formed part of the Caltech Wide Area Sky Survey, which was designed to search for the brightest Kuiper belt objects using the Palomar Observatory's 1.22-meter Samuel Oschin telescope.[21] Quaoar was first identified in images by Trujillo on 5 June 2002, when he noticed a dim, 18.6-magnitude object slowly moving among the stars of the constellation Ophiuchus.[22][23] Quaoar appeared relatively bright for a distant object, suggesting that it could have a size comparable to the diameter of the dwarf planet Pluto.[24]

To ascertain Quaoar's orbit, Brown and Trujillo initiated a search for archival precovery images. They obtained several precovery images taken by the Near-Earth Asteroid Tracking survey from various observatories in 1996 and 2000–2002.[20] In particular, they had also found two archival photographic plates taken by astronomer Charles T. Kowal in May 1983,[23] who at the time was searching for the hypothesized Planet X at the Palomar Observatory.[25][26] From these precovery images, Brown and Trujillo were able to calculate Quaoar's orbit and distance. Additional precovery images of Quaoar have been later identified, with the earliest known found by Edward Rhoads on a photographic plate imaged on 25 May 1954 from the Palomar Observatory Sky Survey.[1][3]

Before announcing the discovery of Quaoar, Brown had planned to conduct follow-up observations using the Hubble Space Telescope to measure Quaoar's size.[27] He had also planned to announce the discovery as soon as possible and found it necessary to keep the discovery information confidential during the follow-up observations.[28] Rather than submitting his Hubble proposal under peer review, Brown submitted his proposal directly to one of Hubble's operators, who promptly allocated time to Brown.[28][29] While setting up the observing algorithm for Hubble, Brown had also planned to use one of the Keck telescopes in Mauna Kea, Hawaii, as a part of a study on cryovolcanism on the moons of Uranus.[28] This provided him additional time for follow-up observations and took advantage of the whole observing session in July to analyze Quaoar's spectrum and characterize its surface composition.[30][28]

The discovery of Quaoar was formally announced by the Minor Planet Center in a Minor Planet Electronic Circular on 7 October 2002.[23] It was given the provisional designation 2002 LM60, indicating that its discovery took place during the first half of June 2002.[23][31] Quaoar was the 1,512th object discovered in the first half of June, as indicated by the preceding letter and numbers in its provisional designation.[lower-alpha 6] On that same day, Trujillo and Brown reported their scientific results from observations of Quaoar at the 34th annual meeting of the American Astronomical Society's Division for Planetary Sciences in Birmingham, Alabama. They announced Quaoar was the largest Kuiper belt object found yet, surpassing previous record holders 20000 Varuna and 2002 AW197.[21][27] Quaoar's discovery has been cited by Brown as having contributed to the reclassification of Pluto as a dwarf planet.[28] Since then, Brown has contributed to the discovery of larger trans-Neptunian objects, including Haumea, Eris, Makemake and Gonggong.

Name and symbol

Upon Quaoar's discovery, it was initially given the temporary nickname "Object X" as a reference to Planet X, due to its potentially large size and unknown nature.[28] At the time, Quaoar's size was uncertain, and its high brightness led the discovery team to speculate that it may be a possible tenth planet. After measuring Quaoar's size with the Hubble Space Telescope in July, the team began considering names for the object, particularly those from local Native American mythologies.[28] Following the International Astronomical Union's (IAU) naming convention for minor planets, non-resonant Kuiper belt objects are to be named after creation deities.[31] The team settled on the name Kwawar, the creator god of the Tongva people indigenous to the Los Angeles Basin, where Brown's institute, the California Institute of Technology, was located.[25]

According to Brown, the name "Quaoar" is pronounced with three syllables, and Trujillo's website on Quaoar gives a three-syllable pronunciation, /ˈkwɑː.oʊ(w)ɑːr/, as an approximation of the Tongva pronunciation [ˈkʷaʔuwar].[22] The name can be also pronounced as two syllables, /ˈkwɑːwɑːr/, reflecting the usual English spelling and pronunciation of the deity Kwawar.[27][32][33]

In Tongva mythology, Kwawar is the genderless[32] creation force of the universe, singing and dancing deities into existence.[2] He first sings and dances to create Weywot (Sky Father), then they together sing Chehooit (Earth Mother) and Tamit (Grandfather Sun) into existence. As they did this, the creation force became more complex as each new deity joined the singing and dancing. Eventually, after reducing chaos to order, they created the seven great giants that upheld the world,[22][27] then the animals and finally the first man and woman, Tobohar and Pahavit.[22]

Upon their investigation of names from Tongva mythology, Brown and Trujillo realized that there were contemporary members of the Tongva people, whom they contacted for permission to use the name.[28] They consulted tribal historian Marc Acuña, who confirmed that the name Kwawar would indeed be an appropriate name for the newly discovered object.[22][32] However, the Tongva preferred the spelling Qua-o-ar, which Brown and Trujillo adopted, though with the hyphens omitted.[28] The name and discovery of Quaoar were publicly announced in October, though Brown had not sought approval of the name by the IAU's Committee on Small Body Nomenclature (CSBN).[28] Indeed, Quaoar's name was announced before the official numbering of the object, which Brian Marsden—the head of the Minor Planet Center—remarked in 2004 to be a violation of the protocol.[28][34] Despite this, the name was approved by the CSBN, and the naming citation, along with Quaoar's official numbering, was published in a Minor Planet Circular on 20 November 2002.[35]

Quaoar was given the minor planet number 50000, which was not by coincidence but to commemorate its large size, being that it was found in the search for a Pluto-sized object in the Kuiper belt.[35] The large Kuiper belt object 20000 Varuna was similarly numbered for a similar occasion.[36] However, subsequent even larger discoveries such as 136199 Eris were simply numbered according to the order in which their orbits were confirmed.[31]

Planetary symbols are no longer much used in astronomy, so Quaoar never received a symbol in the astronomical literature. A symbol ⟨🝾⟩, used mostly among astrologers,[37] is included in Unicode as U+1F77E.[38] The symbol was designed by Denis Moskowitz, a software engineer in Massachusetts; it combines the letter Q (for 'Quaoar') with a canoe, and is stylized to recall angular Tongva rock art.[39]

Orbit and classification

Ecliptic view of Quaoar's orbit (blue) compared to Pluto (red) and Neptune (white). The approximate perihelion (q) and aphelion (Q) dates are marked for their respective orbits.
Polar view of Quaoar's orbit (yellow) along with various other large Kuiper belt objects

Quaoar orbits the Sun at an average distance of 43.7 astronomical unit|AU (6.54 billion km; 4.06 billion mi), taking 288.8 years to complete one full orbit around the Sun. With an orbital eccentricity of 0.04, Quaoar follows a nearly circular orbit, only slightly varying in distance from 42 AU at perihelion to 45 AU at aphelion.[3] At such distances, light from the Sun takes more than 5 hours to reach Quaoar.[22] Quaoar has last passed aphelion in late 1932 and is currently approaching the Sun at a rate of 0.035 AU per year, or about 170 meters per second (380 mph).[40] Quaoar will reach perihelion around February 2075.[6]

Because Quaoar has a nearly circular orbit, it does not approach close to Neptune such that its orbit can become significantly perturbed under the gravitational influence of Neptune.[4] Quaoar's minimum orbit intersection distance from Neptune is only 12.3 AU—it does not approach Neptune within this distance over the course of its orbit, as it is not in a mean-motion orbital resonance with Neptune.[1][4] Simulations by the Deep Ecliptic Survey show that the perihelion and aphelion distances of Quaoar's orbit do not change significantly over the next 10 million years; Quaoar's orbit appears to be stable over the long term.[4]

Quaoar is generally classified as a trans-Neptunian object or distant minor planet by the Minor Planet Center since it orbits in the outer Solar System beyond Neptune.[1][3] Since Quaoar is not in a mean-motion resonance with Neptune, it is also classified as a classical Kuiper belt object (cubewano) by the Minor Planet Center and Deep Ecliptic Survey.[4][5] Quaoar's orbit is moderately inclined to the ecliptic plane by 8 degrees, relatively high when compared to the inclinations of Kuiper belt objects within the dynamically cold population.[28][41] Because Quaoar's orbital inclination is greater than 4 degrees, it is part of the dynamically hot population of high-inclination classical Kuiper belt objects.[41] The high inclinations of hot classical Kuiper belt objects such as Quaoar are thought to have resulted from gravitational scattering by Neptune during its outward migration in the early Solar System.[42]

Physical characteristics

Artist's impression of Quaoar with its ring and its moon Weywot

Quaoar's albedo or reflectivity could be as low as 0.1, similar to Varuna's albedo of 0.127.[43] This may indicate that fresh ice has disappeared from Quaoar's surface.[44] The surface is moderately red, meaning that Quaoar is relatively more reflective in the red and near-infrared spectrum than in the blue.[45] The Kuiper belt objects Varuna and Ixion are also moderately red in the spectral class. Larger Kuiper belt objects are often much brighter because they are covered in more fresh ice and have a higher albedo, and thus they present a neutral color.[46] A 2006 model of internal heating via radioactive decay suggested that Quaoar may not be capable of sustaining an internal ocean of liquid water at the mantle–core boundary.[47]

The presence of methane and other volatiles on Quaoar's surface suggest that it may support a tenuous atmosphere produced from the sublimation of volatiles.[13] With a measured mean temperature of ~ 44 K (−229.2 °C), the upper limit of Quaoar's atmospheric pressure is expected to be in the range of a few microbars.[13] Due to Quaoar's small size and mass, the possibility of Quaoar having an atmosphere of nitrogen and carbon monoxide has been ruled out, since the gases would escape from Quaoar.[13] The possibility of a methane atmosphere, with the upper limit being less than 1 microbar,[8][13] was considered until 2013, when Quaoar occulted a 15.8-magnitude star and revealed no sign of a substantial atmosphere, placing an upper limit to at least 20 nanobars, under the assumption that Quaoar's mean temperature is 42 K (−231.2 °C) and that its atmosphere consists of mostly methane.[8][13] The upper limit of atmosphere pressure was tightened to 10 nanobars after another stellar occultation in 2019.[48]

Mass and density

Because Quaoar is a binary object, the mass of the system can be calculated from the orbit of the secondary. Quaoar's estimated density of around 2.2 g/cm3 and estimated size of 1,110 km (690 mi) suggests that it is a dwarf planet. American astronomer Michael Brown estimates that rocky bodies around 900 km (560 mi) in diameter relax into hydrostatic equilibrium, and that icy bodies relax into hydrostatic equilibrium somewhere between 200 km (120 mi) and 400 km (250 mi).[49] With an estimated mass greater than 1.6×1021 kg, Quaoar has the mass and diameter "usually" required for being in hydrostatic equilibrium according to the 2006 IAU draft definition of a planet (5×1020 kg, 800 km),[50] and Brown states that Quaoar "must be" a dwarf planet.[51] Light-curve-amplitude analysis shows only small deviations, suggesting that Quaoar is indeed a spheroid with small albedo spots and hence a dwarf planet.[52] The IAU itself has called Quaoar a dwarf planet in a 2022–2023 annual report.[53]

Planetary scientist Erik Asphaug has suggested that Quaoar may have collided with a much larger body, stripping the lower-density mantle from Quaoar, and leaving behind the denser core. He envisioned that Quaoar was originally covered by a mantle of ice that made it 300 km (190 mi) to 500 km (310 mi) bigger than its present size, and that it collided with another Kuiper belt object about twice its size—an object roughly the diameter of Pluto, or even approaching the size of Mars.[54] This model was made assuming Quaoar actually had a density of 4.2 g/cm3, but more recent estimates have given it a more Pluto-like density of only 2 g/cm3, with no further need for the collision theory.[8]

Size

EarthMoonCharonCharonNixNixKerberosStyxHydraHydraPlutoPlutoDysnomiaDysnomiaErisErisNamakaNamakaHi'iakaHi'iakaHaumeaHaumeaMakemakeMakemakeMK2MK2XiangliuXiangliuGonggongGonggongWeywotWeywotQuaoarQuaoarSednaSednaVanthVanthOrcusOrcusActaeaActaeaSalaciaSalacia2002 MS42002 MS4File:EightTNOs.png
Artistic comparison of Pluto, Eris, Haumea]], Makemake, Gonggong, Quaoar, Sedna, Orcus, Salacia, 2002 MS4, and Earth along with the Moon. [v · d · e]
Size estimates for Quaoar
Year Diameter (km) Method Refs
2004 1,260±190 imaging [18]
2007 844+207
−190 		thermal [55]
2010 890±70 thermal/imaging [44]
2013 1,074±138 thermal [56]
2013 1,110±5 occultation [8]
2023 1,086±4 occultation [7]
Quaoar compared to the Earth and the Moon
Hubble photo used to measure size of Quaoar

Quaoar is thought to be an oblate spheroid around 1,110 km (690 mi) in diameter, being slightly flattened in shape.[8][48] The estimates come from observations of stellar occultations by Quaoar, in which it passes in front of a star, in 2013 and 2019.[8][48] Given that Quaoar has an estimated oblateness of 0.0897±0.006 and a measured equatorial diameter of 1,138+48
−34 km, Quaoar is believed to be in hydrostatic equilibrium, being described as a Maclaurin spheroid.[8] Quaoar is about as large and massive as (if somewhat smaller than) Pluto's moon Charon.[lower-alpha 7] Quaoar is roughly half the size of Pluto.[28]

Quaoar was the first trans-Neptunian object to be measured directly from Hubble Space Telescope images, using a method comparing images with the Hubble point spread function (PSF).[18] In 2004, Quaoar was estimated to have a diameter of 1,260 km (780 mi) with an uncertainty of 190 km (120 mi), using Hubble's measurements.[18][58] Given its distance Quaoar is on the limit of Hubble's resolution of 40 milliarcseconds and its image is consequently "smeared" on a few adjacent pixels.[18] By comparing carefully this image with the images of stars in the background and using a sophisticated model of Hubble optics (PSF), Brown and Trujillo were able to find the best-fit disk size that would give a similar blurred image.[18] This method was also applied by the same authors to measure the size of the dwarf planet Eris.[55]

At the time of its discovery in 2002, Quaoar was the largest object found in the Solar System since the discovery of Pluto.[28] Quaoar's size was subsequently revised downward and was later superseded in size as larger objects (Eris, Haumea, Makemake and Gonggong) were discovered. The uncorrected 2004 Hubble estimates only marginally agree with the 2007 infrared measurements by the Spitzer Space Telescope that suggest a higher albedo (0.19) and consequently a smaller diameter (844.4+206.7
−189.6 km).[55] Adopting a Uranian satellite limb darkening profile suggests that the 2004 Hubble size estimate for Quaoar was approximately 40 percent too large, and that a more proper estimate would be about 900 km.[44] In 2010, Quaoar was estimated to be about 890 km in diameter, using a weighted average of Spitzer and corrected Hubble estimates.[44] In observations of the object's shadow as it occulted an unnamed 16th-magnitude star on 4 May 2011, Quaoar was estimated to be 1,170 km (730 mi) in diameter.[58] Measurements from the Herschel Space Observatory in 2013 suggested that Quaoar has a diameter of 1,070 km (660 mi).[56] In that same year, Quaoar occulted a 15.8-magnitude star, with multiple positive detections yielding a mean diameter of 1,110±5 km, consistent with the Herschel estimate.[8] Another occultation by Quaoar in June 2019 yielded a similar chord length of 1,121±1.2 km.[48]

Rotation and shape

Rotational light curves of Quaoar observed on March through June 2003 gave two possible rotation periods: 8.64 hours for a single-peaked light curve by a spheroidal body, or 17.68 hours for a double-peaked light curve by an elongated ellipsoidal body.[11][59] The discovery of Quaoar's two rings in 2023 showed that its true rotation period should most likely be 17.68 hours in order to explain the rings' locations in stable spin-orbit resonances.[10][7] This in turn implies Quaoar should be somewhat elongated to induce such a resonance.[10] Various occultation measurements of Quaoar's dimensions show that its diameter slightly varies at different epochs, further supporting the possibility of a triaxial ellipsoid shape for Quaoar.[7]

Composition and cryovolcanism

In 2004, signs of crystalline water ice were found on Quaoar, indicating that the temperature rose to at least 110 K (−163 °C) sometime in the last ten million years.[45] Speculation began as to what could have caused Quaoar to heat up from its natural temperature of 55 K (−218.2 °C). Some have theorized that a barrage of mini-meteors may have raised the temperature, but the most discussed theory speculates that cryovolcanism may be occurring, spurred by the decay of radioactive elements within Quaoar's core.[45] Crystalline water ice was also found on Haumea in 2006, but it is present in larger quantities and is thought to have originated from an impact.[60]

More precise observations of Quaoar's near infrared spectrum in 2007 indicated the presence of small quantities (5%) of solid methane and ethane. Given its boiling point of 112 K (−161 °C), methane is a volatile ice at average surface temperatures of Quaoar, unlike water ice or ethane. Both models and observations suggest that only a few larger bodies (Pluto, Eris and Makemake) can retain the volatile ices whereas the dominant population of small trans-Neptunian objects lost them. Quaoar, with only small amounts of methane, appears to be in an intermediary category.[30]

In 2022, near-infrared (0.7–5 μm) spectroscopic observations by the James Webb Space Telescope (JWST) revealed the presence of significant amounts of ethane ice (C2H6) on the surface of Quaoar. The JWST spectra also contain evidence of presence of small amounts of methane (CH4) and carbon dioxide (CO2) ices as well as complex organics. Other possible chemical compounds include hydrogen cyanide (HCN) and carbon monoxide (CO).[61]

Ring–moon system

Satellite

Quaoar has one known moon, Weywot (full designation (50000) Quaoar I Weywot), discovered in 2006 and named after the sky god Weywot, son of Quaoar.[19][62] It orbits Quaoar at distance of about 13,300 km and is thought to be approximately 170 km (110 mi) in diameter.[63]

Discovery of rings

Light curve graph of a star's brightness as seen by the Gemini North Observatory during the 9 August 2022 occultation by Quaoar and its two rings. The asymmetry of the outer Q1R ring's opacity is apparent from its differing brightness dips before and after the occultation by Quaoar at the center.

Besides accurately determining sizes and shapes, stellar occultation campaigns were planned on a long-term basis to search for rings and/or atmospheres around small bodies of the outer solar system. These campaigns agglomerated efforts of various teams in France, Spain and Brazil and were conducted under the umbrella of the European Research Council project Lucky Star.[10] The discovery of Quaoar's first known ring, Q1R, involved various instruments used during stellar occultations observed between 2018 and 2021: the robotic ATOM telescope of the High Energy Stereoscopic System (HESS) in Namibia, the 10.4-m Gran Telescopio Canarias (La Palma Island, Spain); the ESA CHEOPS space telescope, and several stations run by citizen astronomers in Australia where a report of a Neptune-like ring originated and a dense arc in Q1R was first observed.[10][64][65] Taken together, these observations reveal the presence of a partly dense, mostly tenuous and uniquely distant ring around Quaoar, a discovery announced in February 2023.[10][64]

In April 2023, astronomers of the Lucky Star project published the discovery of another ring of Quaoar, Q2R.[7] The Q2R ring was detected by the highly-sensitive 8.2-m Gemini North and the 4.0-m Canada-France-Hawaii Telescope in Mauna Kea, Hawaii, during an observing campaign to confirm Quaoar's Q1R ring in a stellar occultation on 9 August 2022.[7] Quaoar is the third minor planet known and confirmed to have a ring system, after 10199 Chariklo and 136108 Haumea.[10][lower-alpha 8]

Ring properties

Orbit diagrams of the Quaoar–Weywot system
Viewed from Earth
Viewed top-down over Quaoar's north pole

Quaoar possesses two narrow rings, provisionally named Q1R and Q2R by order of discovery, which are confined at radial distances where their orbital periods are integer ratios of Quaoar's rotational period. That is, the rings of Quaoar are in spin-orbit resonances.[7]

Ring–moon system data[7]
Rings
Ring
designation 		Radius
(km) 		Width
(km) 		Optical depth
(τ)
Q2R 2520±20 10 ≈0.004
Q1R 4057±6 5–300 0.004–0.7
Moon
Name Semi-major axis
(km) 		Diameter
(km) 		Period
(days)
Weywot 13289±189 170 12.4311±0.0015

The outer ring, Q1R, orbits Quaoar at a distance of 4,057 ± 6 km (2,521 ± 4 mi), over seven times the radius of Quaoar and more than double the theoretical maximum distance of the Roche limit.[7] The Q1R ring is not uniform and is strongly irregular around its circumference, being more opaque (and denser) where it is narrow and less opaque where it is broader.[10] The Q1R ring's radial width ranges from 5 to 300 km (3 to 200 mi) while its optical depth ranges from 0.004 to 0.7.[7] The irregular width of the Q1R ring resembles Saturn's frequently-perturbed F ring or Neptune's ring arcs, which may imply the presence of small, kilometer-sized moonlets embedded within the Q1R ring and gravitationally perturbing the material. The Q1R ring likely consists of icy particles that elastically collide with each other without accreting into a larger mass.[10]

Q1R is located in between the 6:1 mean-motion orbital resonance with Quaoar's moon Weywot at 4,021 ± 57 km (2,499 ± 35 mi) and Quaoar's 1:3 spin-orbit resonance at 4,197 ± 58 km (2,608 ± 36 mi). The Q1R ring's coincidental location at these resonances implies they play a key role in maintaining the ring without having it accrete into a single moon.[10] In particular, the confinement of rings to the 1:3 spin-orbit resonance may be common among ringed small Solar System bodies, as it has been previously seen in Chariklo and Haumea.[10]

The inner ring, Q2R, orbits Quaoar at a distance of 2,520 ± 20 km (1,566 ± 12 mi), about four and a half times Quaoar's radius and also outside Quaoar's Roche limit.[7] The Q2R ring's location coincides with Quaoar's 5:7 spin-orbit resonance at 2,525 ± 58 km (1,569 ± 36 mi). Compared to Q1R, the Q2R ring appears relatively uniform with a radial width of 10 km (6.2 mi). With an optical depth of 0.004, the Q2R ring is very tenuous and its opacity is comparable to the least dense part of the Q1R ring.[7]

Exploration

Quaoar from New Horizons viewed at a distance of 14 AU

It has been calculated that a flyby mission to Quaoar using a Jupiter gravity assist would take 13.6 years, for launch dates of 25 December 2026, 22 November 2027, 22 December 2028, 22 January 2030 and 20 December 2040. Quaoar would be 41 to 43 AU from the Sun when the spacecraft arrived.[66] In July 2016, the Long Range Reconnaissance Imager (LORRI) aboard the New Horizons spacecraft took a sequence of four images of Quaoar from a distance of about 14 AU.[67] Interstellar Probe, a concept by Pontus Brandt and his colleagues at Johns Hopkins Applied Physics Laboratory would potentially fly by Quaoar in the 2030s before continuing to the interstellar medium, and the first of China National Space Administration's proposed Shensuo probe designed to explore the heliosphere has it considered as a potential flyby target.[68][69][70] Quaoar has been chosen as a flyby target for missions like these particularly for its escaping methane atmosphere and possible cryovolcanism, as well as its close proximity to the heliospheric nose.[68]

Notes

  1. ↑ Polar dimension calculated by multiplying the measured equatorial diameter 1,138+48
    −34     km     with the oblateness 0.0897 obtained from the occultation in 2013.[8]
  2. ↑ Calculated given a mean radius of 555±2.5 km[8]
  3. ↑ Calculated given a mass of (1.20±0.05)×1021 kg[10] and a radius of 555±2.5 km[8]
  4. ↑ Morgado et al. (2023) give the outer ring's north pole direction in terms of equatorial coordinates (α, δ) = (258.47°, +54.14°), where α is right ascension and δ is declination.[10](p3) Transforming these equatorial coordinates to ecliptic coordinates gives λ ≈ 240.17° and β ≈ +76.38°.[12] The ecliptic latitude, β, is the angular offset from the ecliptic plane, whereas inclination i with respect to the ecliptic is the angular offset from the ecliptic north pole at β = +90° ; i with respect to the ecliptic would be the complement of β, which is expressed by the difference i = 90° – β. Thus, the axial tilt of Quaoar's outer ring is 13.62° with respect to the ecliptic. If the outer ring is coplanar to Quaoar's equator (having the same north pole orientation), then Quaoar would have the same axial tilt with respect to the ecliptic.
  5. ↑ Pereira et al. (2023) give the outer ring's north pole direction in terms of equatorial coordinates (α, δ) = ( 17h 19m 16s, +53° 27′), where α is right ascension and δ is declination.[7](p4) Converting these equatorial coordinates from sexagesimal to decimal degrees gives (α, δ) = (259.82°, +53.45°). Then, transforming these equatorial coordinates to ecliptic coordinates gives λ ≈ 64.26° (ecliptic longitude) and β ≈ +75.98° (ecliptic latitude).[12] Subtracting this value of β from +90° gives the inclination of Quaoar's outer ring with respect to the ecliptic: i = 90° – β ≈ 14.02°. If the outer ring is coplanar to Quaoar's equator (having the same north pole orientation), then Quaoar would have the same axial tilt with respect to the ecliptic.
  6. ↑ In the convention for minor planet provisional designations, the first letter represents the half-month of the year of discovery while the second letter and numbers indicate the order of discovery within that half-month. In the case for 2002 LM60, the first letter 'L' corresponds to the first half-month of June 2002 while the preceding letter 'M' indicates that it is the 12th object discovered on the 61st cycle of discoveries (with 60 cycles completed). Each completed cycle consists of 25 letters representing discoveries, hence 12 + (60 completed cycles × 25 letters) = 1,512.[31]
  7. ↑ Charon's mass is (1.586±0.015)×1021 kg[57] while Quaoar's mass is (1.4±0.1)×1021 kg.[56] Both values are approximately similar, though Charon is slightly more massive. In a similar case, Charon's diameter is 1,212±1 km while Quaoar's diameter is 1,110±5 km, being slightly smaller than Charon.
  8. ↑ 2060 Chiron is also thought to have rings, but the evidence is tentative.

References

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 "50000 Quaoar (2002 LM60)". Minor Planet Center. International Astronomical Union. https://www.minorplanetcenter.net/db_search/show_object?object_id=50000. 
  2. ↑ 2.0 2.1 Schmadel, Lutz D. (2006). "(50000) Quaoar". Dictionary of Minor Planet Names – (50000) Quaoar, Addendum to Fifth Edition: 2003–2005. Springer Berlin Heidelberg. p. 1197. doi:10.1007/978-3-540-29925-7. ISBN 978-3-540-00238-3. https://books.google.com/books?id=aeAg1X7afOoC&q=%2850000%29+Quaoar&pg=PA1339. Retrieved 7 December 2019. 
  3. ↑ 3.0 3.1 3.2 3.3 3.4 3.5 "JPL Small-Body Database Browser: 50000 Quaoar (2002 LM60)". Jet Propulsion Laboratory. 24 September 2019. https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=2050000. 
  4. ↑ 4.0 4.1 4.2 4.3 4.4 Buie, M. W.. "Orbit Fit and Astrometric record for 50000". Southwest Research Institute. http://www.boulder.swri.edu/~buie/kbo/astrom/50000.html. 
  5. ↑ 5.0 5.1 Marsden, Brian G. (17 July 2008). "MPEC 2008-O05 : Distant Minor Planets (2008 Aug. 2.0 TT)". Minor Planet Electronic Circular. Minor Planet Center. https://minorplanetcenter.net/mpec/K08/K08O05.html. 
  6. ↑ 6.0 6.1 JPL Horizons Observer Location: @sun (Perihelion occurs when deldot changes from negative to positive. Uncertainty in time of perihelion is 3-sigma.)
  7. ↑ 7.00 7.01 7.02 7.03 7.04 7.05 7.06 7.07 7.08 7.09 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18 7.19  , Wikidata Q117802048
  8. ↑ 8.00 8.01 8.02 8.03 8.04 8.05 8.06 8.07 8.08 8.09 8.10 8.11 8.12 8.13 8.14 Braga-Ribas, F.Expression error: Unrecognized word "etal". (August 2013). "The Size, Shape, Albedo, Density, and Atmospheric Limit of Transneptunian Object (50000) Quaoar from Multi-chord Stellar Occultations". The Astrophysical Journal 773 (1): 13. doi:10.1088/0004-637X/773/1/26. Bibcode: 2013ApJ...773...26B. https://orbi.uliege.be/handle/2268/156970. Retrieved 29 April 2021. 
  9. ↑ "Ellipsoid surface area: 3.82769×10^6 km2". https://www.wolframalpha.com/input/?i=ellipsoid+surface+area+semi-axis+lengths+569+569+518. 
  10. ↑ 10.00 10.01 10.02 10.03 10.04 10.05 10.06 10.07 10.08 10.09 10.10 10.11 10.12 10.13 10.14 10.15  , Wikidata Q116754015
  11. ↑ 11.0 11.1 Ortiz, J. L.; Gutiérrez, P. J.; Casanova, V.; Teixeira, V. R. (October 2003). "Rotational brightness variations in Trans-Neptunian Object 50000 Quaoar". Astronomy & Astrophysics 409 (2): L13–L16. doi:10.1051/0004-6361:20031253. Bibcode: 2003A&A...409L..13O. https://www.aanda.org/articles/aa/pdf/2003/38/aafg143.pdf. Retrieved 3 December 2019. 
  12. ↑ 12.0 12.1 "Coordinate Transformation & Galactic Extinction Calculator". NASA/IPAC Extragalactic Database. California Institute of Technology. https://ned.ipac.caltech.edu/forms/calculator.html. Retrieved 11 February 2023.  Equatorial → Ecliptic, J2000 for equinox and epoch. NOTE: When inputting equatorial coordinates, specify the units in the format "54.14d" instead of "54.14".
  13. ↑ 13.0 13.1 13.2 13.3 13.4 13.5 Fraser, Wesley C.; Trujillo, Chad; Stephens, Andrew W.; Gimeno, German; Brown, Michael E.; Gwyn, Stephen; Kavelaars, J. J. (September 2013). "Limits on Quaoar's Atmosphere". The Astrophysical Journal Letters 774 (2): 4. doi:10.1088/2041-8205/774/2/L18. Bibcode: 2013ApJ...774L..18F. 
  14. ↑ 14.0 14.1 Tegler, Stephen C. (1 February 2007). "Kuiper Belt Object Magnitudes and Surface Colors". Northern Arizona University. http://www.physics.nau.edu/~tegler/research/survey.htm. 
  15. ↑ 15.0 15.1 Belskaya, Irina N.; Barucci, Maria A.; Fulchignoni, Marcello; Lazzarin, M. (April 2015). "Updated taxonomy of trans-neptunian objects and centaurs: Influence of albedo". Icarus 250: 482–491. doi:10.1016/j.icarus.2014.12.004. Bibcode: 2015Icar..250..482B. 
  16. ↑ "LCDB Data for (50000) Quaoar". Asteroid Lightcurve Database. http://www.minorplanet.info/PHP/generateOneAsteroidInfo.php?AstInfo=50000%7CQuaoar. 
  17. ↑ 17.0 17.1 Grundy, Will (5 November 2019). "Quaoar and Weywot (50000 2002 LM60)". Lowell Observatory. http://www2.lowell.edu/users/grundy/tnbs/50000_2002_LM60_Quaoar.html. 
  18. ↑ 18.0 18.1 18.2 18.3 18.4 18.5 Brown, Michael E.; Trujillo, Chadwick A. (April 2004). "Direct Measurement of the Size of the Large Kuiper Belt Object (50000) Quaoar". The Astronomical Journal 127 (4): 2413–2417. doi:10.1086/382513. Bibcode: 2004AJ....127.2413B. http://web.gps.caltech.edu/~mbrown/papers/ps/qu.pdf. Retrieved 27 February 2018. 
  19. ↑ 19.0 19.1 Green, Daniel W. E., ed (22 February 2007). "Satellites of 2003 AZ_84, (50000), (55637), and (90482)". International Astronomical Union Circular (International Astronomical Union) (8812). ISSN 0081-0304. Bibcode: 2007IAUC.8812....1B. http://www.cbat.eps.harvard.edu/iauc/08800/08812.html#Item1. 
  20. ↑ 20.0 20.1 Trujillo, Chad. "Quaoar Precoveries". http://www.gps.caltech.edu/~chad/quaoar/precovery.html. 
  21. ↑ 21.0 21.1 Trujillo, C. A.; Brown, M. E. (June 2003). "The Caltech Wide Area Sky Survey". Earth, Moon, and Planets 92 (1): L13–L16. doi:10.1023/B:MOON.0000031929.19729.a1. Bibcode: 2003EM&P...92...99T. http://web.gps.caltech.edu/~mbrown/papers/ps/wide.pdf. Retrieved 9 January 2020. 
  22. ↑ 22.0 22.1 22.2 22.3 22.4 22.5 Trujillo, Chad. "Frequently Asked Questions About Quaoar". Northern Arizona University. http://www.chadtrujillo.com/quaoar/. 
  23. ↑ 23.0 23.1 23.2 23.3 Marsden, Brian G. (7 October 2002). "MPEC 2002-T34 : 2002 LM60". Minor Planet Electronic Circular. Minor Planet Center. https://www.minorplanetcenter.net/mpec/K02/K02T34.html. 
  24. ↑ "A Cold New World". NASA Science. NASA. 7 October 2002. https://science.nasa.gov/science-news/science-at-nasa/2002/07oct_newworld. 
  25. ↑ 25.0 25.1 Nadin, Elisabeth (7 October 2002). "Caltech scientists find largest object in solar system since Pluto's discovery". Caltech Matters. California Institute of Technology. https://www.caltech.edu/about/news/caltech-scientists-find-largest-object-solar-system-plutos-discovery-618. 
  26. ↑ Wilford, John Noble (8 October 2002). "Telescopes Find a Miniplanet At the Solar System's Edge". The New York Times. https://www.nytimes.com/2002/10/08/science/telescopes-find-a-miniplanet-at-the-solar-system-s-edge.html?searchResultPosition=3. 
  27. ↑ 27.0 27.1 27.2 27.3 "Hubble Spots an Icy World Far Beyond Pluto". HubbleSite. Space Telescope Science Institute. 7 October 2002. http://hubblesite.org/newscenter/archive/releases/2002/17/text/. 
  28. ↑ 28.00 28.01 28.02 28.03 28.04 28.05 28.06 28.07 28.08 28.09 28.10 28.11 28.12 28.13 Brown, Michael E. (7 December 2010). "Chapter Five: An Icy Nail". How I Killed Pluto and Why It Had It Coming. Spiegel & Grau. pp. 63–85. ISBN 978-0-385-53108-5. 
  29. ↑ Brown, Michael E. (18 June 2002). "Direct Measurement of the Size of the Largest Kuiper Belt Object". Mikulski Archive for Space Telescopes (Space Telescope Science Institute): 9678. Bibcode: 2002hst..prop.9678B. https://www.stsci.edu/hst/phase2-public/9678.prop. Retrieved 8 January 2020. 
  30. ↑ 30.0 30.1 Schaller, E. L.; Brown, M. E. (November 2007). "Detection of Methane on Kuiper Belt Object (50000) Quaoar". The Astrophysical Journal 670 (1): L49–L51. doi:10.1086/524140. Bibcode: 2007ApJ...670L..49S. 
  31. ↑ 31.0 31.1 31.2 31.3 "How Are Minor Planets Named?". Minor Planet Center. International Astronomical Union. https://minorplanetcenter.net/iau/info/HowNamed.html. 
  32. ↑ 32.0 32.1 32.2 Street, Nick (August 2008). "Heavenly Bodies and the People of the Earth". Search Magazine (Heldref Publications). http://www.searchmagazine.org/Archives/Back%20Issues/2008%20July-August/full-heavenly-bodies.html. Retrieved 8 January 2020. 
  33. ↑ NASA/JHUAPL/SwRI (2016) Quaoar
  34. ↑ Marsden, Brian G. (28 September 2004). "MPEC 2004-S73 : Editorial Notice". Minor Planet Electronic Circular. Minor Planet Center. https://minorplanetcenter.net/mpec/K04/K04S73.html. 
  35. ↑ 35.0 35.1 "M.P.C. 47066". Minor Planet Center. International Astronomical Union. 20 November 2002. https://minorplanetcenter.net/iau/ECS/MPCArchive/2002/MPC_20021120.pdf. 
  36. ↑ "M.P.C. 41805". Minor Planet Center. International Astronomical Union. 9 January 2001. http://www.minorplanetcenter.org/iau/ECS/MPCArchive/2001/MPC_20010109.pdf. 
  37. ↑ Miller, Kirk (26 October 2021). "Unicode request for dwarf-planet symbols". https://www.unicode.org/L2/L2021/21224-dwarf-planet-syms.pdf. 
  38. ↑ "Proposed New Characters: The Pipeline". https://www.unicode.org/alloc/Pipeline.html. 
  39. ↑ Anderson, Deborah (4 May 2022). "Out of this World: New Astronomy Symbols Approved for the Unicode Standard". The Unicode Consortium. http://blog.unicode.org/2022/05/out-of-this-world-new-astronomy-symbols.html. 
  40. ↑ "Horizon Online Ephemeris System for 50000 Quaoar (2002 LM60)". Jet Propulsion Laboratory. http://ssd.jpl.nasa.gov/horizons.cgi?find_body=1&body_group=sb&sstr=50000. 
  41. ↑ 41.0 41.1 Delsanti, Audrey; Jewitt, David (2006). "The Solar System Beyond The Planets". in Blonde, P.; Mason, J.. Solar System Update. Springer. pp. 267–293. doi:10.1007/3-540-37683-6_11. ISBN 3-540-26056-0. Bibcode: 2006ssu..book..267D. http://www2.ess.ucla.edu/~jewitt/papers/2006/DJ06.pdf. 
  42. ↑ Levison, Harold F.; Morbidelli, Alessandro; Van Laerhoven, Christa; Gomes, Rodney S.; Tsiganis, Kleomenis (July 2008). "Origin of the Structure of the Kuiper Belt during a Dynamical Instability in the Orbits of Uranus and Neptune". Icarus 196 (1): 258–273. doi:10.1016/j.icarus.2007.11.035. Bibcode: 2008Icar..196..258L. 
  43. ↑ Lellouch, E.Expression error: Unrecognized word "etal". (September 2013). ""TNOs are Cool": A survey of the trans-Neptunian region. IX. Thermal properties of Kuiper belt objects and Centaurs from combined Herschel and Spitzer observations". Astronomy & Astrophysics 557 (A60): 19. doi:10.1051/0004-6361/201322047. Bibcode: 2013A&A...557A..60L. http://www.aanda.org/articles/aa/pdf/2013/09/aa22047-13.pdf. Retrieved 23 October 2019. 
  44. ↑ 44.0 44.1 44.2 44.3 Fraser, Wesley C.; Brown, Michael E. (May 2010). "Quaoar: A Rock in the Kuiper Belt". The Astrophysical Journal 714 (2): 1547–1550. doi:10.1088/0004-637X/714/2/1547. Bibcode: 2010ApJ...714.1547F. 
  45. ↑ 45.0 45.1 45.2 Jewitt, David C.; Luu, Jane (December 2004). "Crystalline water ice on the Kuiper belt object (50000) Quaoar". Nature 432 (7018): 731–733. doi:10.1038/nature03111. PMID 15592406. Bibcode: 2004Natur.432..731J. http://www2.ess.ucla.edu/~jewitt/papers/2004/JL2004.pdf. Retrieved 14 April 2013. 
  46. ↑ Brown, Michael E. (2008). "The Largest Kuiper Belt Objects". The Solar System Beyond Neptune. University of Arizona Press. pp. 335–344. ISBN 978-0-8165-2755-7. Bibcode: 2008ssbn.book..335B. http://web.gps.caltech.edu/~mbrown/out/kbbook/Chapters/Brown_Planetoids.pdf. Retrieved 15 March 2019. 
  47. ↑ Hussmann, Hauke; Sohl, Frank; Spohn, Tilman (November 2006). "Subsurface oceans and deep interiors of medium-sized outer planet satellites and large trans-neptunian objects". Icarus 185 (1): 258–273. doi:10.1016/j.icarus.2006.06.005. Bibcode: 2006Icar..185..258H. 
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  49. ↑ Brown, Michael E.. "The Dwarf Planets". California Institute of Technology. http://web.gps.caltech.edu/~mbrown/dwarfplanets/. 
  50. ↑ "The IAU draft definition of "planet" and "plutons"" (Press release). International Astronomical Union. August 2006. Archived from the original on 15 July 2009. Retrieved 27 February 2018.
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  52. ↑ Tancredi, G.; Favre, S. (July 2008). "Which are the dwarfs in the solar system?". Asteroids, Comets, Meteors. Lunar and Planetary Institute. 8261. Bibcode: 2008LPICo1405.8261T. http://www.lpi.usra.edu/meetings/acm2008/pdf/8261.pdf. Retrieved 25 August 2011. 
  53. ↑ "Report of Division F “Planetary Systems and Astrobiology”: Annual Report 2022-23". International Astronomical Union. 2022–2023. https://www.iau.org/static/science/scientific_bodies/divisions/f/division-f-annual-report-2022-2023.pdf. 
  54. ↑ Musser, George (13 October 2009). "What do we really know about the Kuiper Belt? Fifth dispatch from the annual planets meeting". Scientific American. http://blogs.scientificamerican.com/observations/what-do-we-really-know-about-the-kuiper-belt-fifth-dispatch-from-the-annual-planets-meeting/. 
  55. ↑ 55.0 55.1 55.2 Stansberry, John; Grundy, Will; Brown, Mike; Cruikshank, Dale; Spencer, John; Trilling, David; Margot, Jean-Luc (2008). "Physical Properties of Kuiper Belt and Centaur Objects: Constraints from the Spitzer Space Telescope". The Solar System Beyond Neptune. University of Arizona Press. pp. 161–179. ISBN 978-0-8165-2755-7. Bibcode: 2008ssbn.book..161S. https://www.lpi.usra.edu/books/ssbn2008/7017.pdf. Retrieved 4 December 2019. 
  56. ↑ 56.0 56.1 56.2 Fornasier, S.Expression error: Unrecognized word "etal". (July 2013). "TNOs are Cool: A survey of the trans-Neptunian region. VIII. Combined Herschel PACS and SPIRE observations of nine bright targets at 70–500 μm". Astronomy & Astrophysics 555 (A15): 22. doi:10.1051/0004-6361/201321329. Bibcode: 2013A&A...555A..15F. 
  57. ↑ Stern, S. A.Expression error: Unrecognized word "etal". (September 2018). "The Pluto System After New Horizons". Annual Review of Astronomy and Astrophysics 56: 357–392. doi:10.1146/annurev-astro-081817-051935. Bibcode: 2018ARA&A..56..357S. 
  58. ↑ 58.0 58.1 Braga-Ribas, F.; Sicardy, B.; Ortiz, J. L.; Jehin, E.; Camargo, J. I. B.; Assafin, M. (October 2011). "Stellar Occultations by TNOs: the January 08, 2011 by (208996) 2003 AZ84 and the May 04, 2011 by (50000) Quaoar". EPSC-DPS Joint Meeting 2011. 6. European Planetary Science Congress. http://meetingorganizer.copernicus.org/EPSC-DPS2011/EPSC-DPS2011-1060-1.pdf. Retrieved 17 January 2012. 
  59. ↑ Fraser, Wesley C.; Batygin, Konstantin; Brown, Michael E.; Bouchez, Antonin (January 2013). "The mass, orbit, and tidal evolution of the Quaoar–Weywot system". Icarus 222 (1): 357–363. doi:10.1016/j.icarus.2012.11.004. Bibcode: 2013Icar..222..357F. 
  60. ↑ Truijillo, Chadwick A.; Brown, Michael E.; Barkume, Kristina M.; Schaller, Emily L.; Rabinowitz, David L. (February 2007). "The Surface of 2003EL61 in the Near Infrared". The Astrophysical Journal 655 (2): 1172–1178. doi:10.1086/509861. Bibcode: 2007ApJ...655.1172T. 
  61. ↑ Emery, J. P.; Wong, I.; Brunetto, R.; Cook, J. C.; Pinilla-Alonso, N.; Stansberry, J. A.; Holler, B. J.; Grundy, W. M. et al. (2023). "A Tale of 3 Dwarf Planets: Ices and Organics on Sedna, Gonggong, and Quaoar from JWST Spectroscopy". Arxiv. doi:10.48550/arXiv.2309.15230. 
  62. ↑ "Heavenly Bodies and the People of the Earth" , Nick Street, Search Magazine, July/August 2008
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  67. ↑ "New Horizons Spies a Kuiper Belt Companion". Johns Hopkins University Applied Physics Laboratory. 31 August 2016. http://pluto.jhuapl.edu/Multimedia/Science-Photos/image.php?gallery_id=2&image_id=459. 
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  70. ↑ Jones, Andrew (16 April 2021). "China to launch a pair of spacecraft towards the edge of the solar system". SpaceNews (SpaceNews). https://spacenews.com/china-to-launch-a-pair-of-spacecraft-towards-the-edge-of-the-solar-system/. 

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