List of possible dwarf planets

The number of dwarf planets in the Solar System is unknown. Estimates have run as high as 200 in the Kuiper belt[1] and over 10,000 in the region beyond.[2] However, consideration of the surprisingly low densities of many dwarf-planet candidates suggests that the numbers may be much lower (e.g. at most 10 among bodies known so far).[3] The International Astronomical Union (IAU) notes five in particular: Ceres in the inner Solar System and four in the trans-Neptunian region: Pluto, Eris, Haumea, and Makemake, the last two of which were accepted as dwarf planets for naming purposes. Only Pluto is confirmed as a dwarf planet, and it has also been declared one by the IAU independently of whether it meets the IAU definition of a dwarf planet.

IAU naming procedures

In 2008, the IAU modified its naming procedures such that objects considered most likely to be dwarf planets receive differing treatment than others. Objects that have an absolute magnitude (H) less than +1, and hence a minimum diameter of 838 kilometres (521 mi) if the albedo is below 100%,[4] are overseen by two naming committees, one for minor planets and one for planets. Once named, the objects are declared to be dwarf planets. Makemake and Haumea are the only objects to have proceeded through the naming process as presumed dwarf planets; currently there are no other bodies that meet this criterion. All other bodies are named by the minor-planet naming committee alone, and the IAU has not stated how or if they will be accepted as dwarf planets.

Limiting values

Calculation of the diameter of Ixion depends on the albedo (the fraction of light that it reflects). Current estimates are that the albedo is 13–15%, a bit under the midpoint of the range shown here and corresponding to a diameter of 620 km.

Beside directly orbiting the Sun, the qualifying feature of a dwarf planet is that it have "sufficient mass for its self-gravity to overcome rigid-body forces so that it assumes a hydrostatic equilibrium (nearly round) shape".[5][6][7] Current observations are generally insufficient for a direct determination as to whether a body meets this definition. Often the only clues for trans-Neptunian objects is a crude estimate of their diameters and albedos. Icy satellites as large as 1500 km in diameter have proven to not be in equilibrium, whereas dark objects in the outer solar system often have low densities that imply they are not even solid bodies, much less gravitationally controlled dwarf planets.

Ceres, which has a significant amount of ice in its composition, is the only confirmed dwarf planet in the asteroid belt although Hygeia may possibly also be one.[8][9] 4 Vesta, the second-most-massive asteroid and one that is basaltic in composition, appears to have a fully differentiated interior and was therefore in equilibrium at some point in its history, but no longer is today.[10] The third-most massive object, 2 Pallas, has a somewhat irregular surface and is thought to have only a partially differentiated interior; it is also less icy than Ceres. Michael Brown has estimated that, because rocky objects such as Vesta are more rigid than icy objects, rocky objects below 900 kilometres (560 mi) in diameter may not be in hydrostatic equilibrium and thus not dwarf planets.[1][11]

Based on a comparison with the icy moons that have been visited by spacecraft, such as Mimas (round at 400 km in diameter) and Proteus (irregular at 410440 km in diameter), Brown estimated that an icy body relaxes into hydrostatic equilibrium at a diameter somewhere between 200 and 400 km.[1] However, after Brown and Tancredi made their calculations, better determination of their shapes showed that Mimas and the other mid-sized ellipsoidal moons of Saturn up to at least Iapetus (which is of the approximate size of Haumea and Makemake) are no longer in hydrostatic equilibrium; they are also icier than TNOs are likely to be. They have equilibrium shapes that froze in place some time ago, and do not match the shapes that equilibrium bodies would have at their current rotation rates.[12] Thus Ceres, at 950 km in diameter, is the smallest body for which gravitational measurements indicate current hydrostatic equilibrium.[13] Much larger objects, such as Earth's moon, are not near hydrostatic equilibrium today,[14][15][16] though the Moon is composed primarily of silicate rock (in contrast to most dwarf planet candidates, which are ice and rock). Saturn's moons may have been subject to a thermal history that would have produced equilibrium-like shapes in bodies too small for gravity alone to do so. Thus, at present it is unknown whether any trans-Neptunian objects smaller than Pluto and Eris are in hydrostatic equilibrium.[3]

The majority of mid-sized TNOs up to about 900–1000 km in diameter have significantly lower densities (~ 1.0–1.2 g/ml) than larger bodies such as Pluto (1.86 g/ml). Brown had speculated that this was due to their composition, that they were almost entirely icy. However, Grundy et al.[3] point out that there is no known mechanism or evolutionary pathway for mid-sized bodies to be icy while both larger and smaller objects are partially rocky. They demonstrated that at the prevailing temperatures of the Kuiper Belt, water ice is strong enough to support open interior spaces (interstices) in objects of this size; they concluded that mid-size TNOs have low densities for the same reason that smaller objects do—because they have not compacted under self-gravity into fully solid objects, and thus the typical TNO smaller than 900–1000 km in diameter is (pending some other formative mechanism) unlikely to be a dwarf planet.

Tancredi's assessment

In 2010, Gonzalo Tancredi presented a report to the IAU evaluating a list of 46 candidates for dwarf planet status based on light-curve-amplitude analysis and a calculation that the object was more than 450 kilometres (280 mi) in diameter. Some diameters were measured, some were best-fit estimates, and others used an assumed albedo of 0.10 to calculate the diameter. Of these, he identified 15 as dwarf planets by his criteria (including the 4 accepted by the IAU), with another 9 being considered possible. To be cautious, he advised the IAU to "officially" accept as dwarf planets the top three not yet accepted: Sedna, Orcus, and Quaoar.[17] Although the IAU had anticipated Tancredi's recommendations, a decade later the IAU had never responded.

Brown's assessment

Artistic comparison of Pluto, Eris, Haumea, Makemake, Gonggong, Quaoar, Sedna, Orcus, Salacia, 2002 MS4, and Earth along with the Moon.
Brown's categories Min. Number of objects
nearly certainly >900 km 10
highly likely 600–900 km 17 (27 total)
likely 500–600 km 41 (68 total)
probably 400–500 km 62 (130 total)
possibly 200–400 km 611 (741 total)
Source: Mike Brown,[18] as of 2020 October 22

Mike Brown considers 130 trans-Neptunian bodies to be "probably" dwarf planets, ranked them by estimated size.[18] He does not consider asteroids, stating "in the asteroid belt Ceres, with a diameter of 900 km, is the only object large enough to be round."[18]

The terms for varying degrees of likelihood he split these into:

  • Near certainty: diameter estimated/measured to be over 900 kilometres (560 mi). Sufficient confidence to say these must be in hydrostatic equilibrium, even if predominantly rocky. 10 objects as of 2020.
  • Highly likely: diameter estimated/measured to be over 600 kilometres (370 mi). The size would have to be "grossly in error" or they would have to be primarily rocky to not be dwarf planets. 17 objects as of 2020.
  • Likely: diameter estimated/measured to be over 500 kilometres (310 mi). Uncertainties in measurement mean that some of these will be significantly smaller and thus doubtful. 41 objects as of 2020.
  • Probably: diameter estimated/measured to be over 400 kilometres (250 mi). Expected to be dwarf planets, if they are icy, and that figure is correct. 62 objects as of 2020.
  • Possibly: diameter estimated/measured to be over 200 kilometres (120 mi). Icy moons transition from a round to irregular shape in the 200–400 km range, suggesting that the same figure holds true for KBOs. Thus, some of these objects could be dwarf planets. 611 objects as of 2020.
  • Probably not: diameter estimated/measured to be under 200 km. No icy moon under 200 km is round, and the same may be true of KBOs. The estimated size of these objects would have to be in error for them to be dwarf planets.

Beside the five accepted by the IAU, the 'nearly certain' category includes Gonggong, Quaoar, Sedna, Orcus, 2002 MS4 and Salacia.

Grundy et al.’s assessment

Grundy et al. propose that dark, low-density TNOs in the size range of approximately 400–1000 km are transitional between smaller, porous (and thus low-density) bodies and larger, denser, brighter and geologically differentiated planetary bodies (such as dwarf planets). Bodies in this size range should have begun to collapse the interstitial spaces left over from their formation, but not fully, leaving some residual porosity.[3]

Many TNOs in the size range of about 400–1000 km have oddly low densities, in the range of about 1.0–1.2 g/cm3, that are substantially less than dwarf planets such as Pluto, Eris and Ceres, which have densities closer to 2. Brown has suggested that large low-density bodies must be composed almost entirely of water ice, since he presumed that bodies of this size would necessarily be solid. However, this leaves unexplained why TNOs both larger than 1000 km and smaller than 400 km, and indeed comets, are composed of a substantial fraction of rock, leaving only this size range to be primarily icy. Experiments with water ice at the relevant pressures and temperatures suggest that substantial porosity could remain in this size range, and it is possible that adding rock to the mix would further increase resistance to collapsing into a solid body. Bodies with internal porosity remaining from their formation could be at best only partially differentiated, in their deep interiors. (If a body had begun to collapse into a solid body, there should be evidence in the form of fault systems from when its surface contracted.) The higher albedos of larger bodies is also evidence of full differentiation, as such bodies were presumably resurfaced with ice from their interiors. Grundy et al.[3] propose therefore that mid-size (< 1000 km), low-density (< 1.4 g/ml) and low-albedo (< ~0.2) bodies such as Salacia, Varda, Gǃkúnǁʼhòmdímà and (55637) 2002 UX25 are not differentiated planetary bodies like Orcus, Quaoar and Charon. The boundary between the two populations would appear to be in the range of about 900–1000 km.[3]

If Grundy et al.[3] are correct, then among known bodies in the outer Solar System only Pluto–Charon, Eris, Haumea, Gonggong, Makemake, Quaoar, Orcus, Sedna and perhaps Salacia (which if it were spherical and had the same albedo as its moon would have a density of between 1.4 and 1.6 g/cm3, calculated a few months after Grundy et al's initial assessment, though still an albedo of only 0.04)[19] are likely to have compacted into fully solid bodies, and thus to possibly have become dwarf planets at some point in their past or to still be dwarf planets at present.

Likeliest dwarf planets

The assessments of the IAU, Tancredi et al., Brown and Grundy et al. for the dozen largest potential dwarf planets are as follows. For the IAU, the acceptance criteria were for naming purposes. Several of these objects had not yet been discovered when Tancredi et al. did their analysis. Brown's sole criterion is diameter; he accepts a great many more as highly likely to be dwarf planets (see below). Grundy et al. did not determine which bodies were dwarf planets, but rather which could not be. A red marks objects too dark or not dense enough to be solid bodies, a question mark the smaller bodies consistent with being differentiated (the question of current equilibrium was not addressed).

Iapetus, Earth's moon and Phoebe are included for comparison, as none of these objects are in equilibrium today. Triton (which formed as a TNO and is likely still in equilibrium) and Charon are included as well.

Designation Measured mean
diameter (km)
Density
(g/cm3)
Albedo Per IAU Per Tancredi
et al.[17]
Per Brown[18] Per Grundy
et al.[3][19]
Category
The Moon 34753.3440.136(no longer in equilibrium)[20][21](moon of Earth)
N I Triton 2707±22.060.76(likely in equilibrium)[22](moon of Neptune)
134340 Pluto 2376±31.854±0.0060.49 to 0.662:3 resonant
136199 Eris 2326±122.43±0.050.96SDO
136108 Haumea  1560 2.0180.51
(naming rules)
cubewano
S VIII Iapetus 1469±61.09±0.010.05 to 0.5(no longer in equilibrium)[23](moon of Saturn)
136472 Makemake 1430+38
−22
1.9±0.20.81
(naming rules)
cubewano
225088 Gonggong 1230±501.74±0.160.14NA3:10 resonant
P I Charon 1212±11.70±0.020.2 to 0.5(possibly in equilibrium)[24](moon of Pluto)
50000 Quaoar 1110±52.0±0.50.11cubewano
90377 Sedna 995±80?0.32detached
1 Ceres 946±22.16±0.010.09 (close to equilibrium)[25] asteroid
90482 Orcus 910+50
−40
1.53±0.140.232:3 resonant
120347 Salacia 846±211.5±0.120.04cubewano
(307261) 2002 MS4 778±11?0.10NAcubewano
(55565) 2002 AW197 768±39?0.11cubewano
174567 Varda 749±181.27±0.060.104:7 resonant
(532037) 2013 FY27 742+78
−83
?0.17NASDO
(208996) 2003 AZ84 707±240.87±0.01?0.102:3 resonant
S IX Phoebe 213±21.64±0.030.06(no longer in equilibrium)[26](moon of Saturn)

Largest candidates

The following trans-Neptunian objects have estimated diameters at least 400 kilometres (250 mi) and so are considered "probable" dwarf planets by Brown's assessment. Not all bodies estimated to be this size are included. The list is complicated by bodies such as 47171 Lempo that were at first assumed to be large single objects but later discovered to be binary or triple systems of smaller bodies.[27] The dwarf planet Ceres is added for comparison. Explanations and sources for the measured masses and diameters can be found in the corresponding articles linked in column "Designation" of the table.

The Best diameter column uses a measured diameter if one exists, otherwise it uses Brown's assumed-albedo diameter. If Brown does not list the body, the size is calculated from an assumed-albedo of 9% per Johnston.[28]

Designation Best[lower-alpha 1]
diameter
km
Measured per
measured
Per Brown[18] Diameter
per assumed albedo
Result
per Tancredi[17]
Category
Mass[lower-alpha 2]
(1018 kg)
H

[29][30]

Diameter
(km)
Geometric
albedo[lower-alpha 3]
(%)
H
Diameter[lower-alpha 4]
(km)
Geometric
albedo

(%)
Small
albedo=100%
(km)
Large
albedo=4%
(km)
134340 Pluto237713030−0.762377±3.263−0.723296418869430accepted (measured)2:3 resonant
136199 Eris232616466−1.12326±1290−1.1233099220611028accepted (measured)SDO
136108 Haumea155940060.21559580.412528012126060acceptedcubewano
136472 Makemake14293100−0.21429+38
−20
1040.114268114577286acceptedcubewano
225088 Gonggong123017502.341230±5014212901963631803:10 resonant
50000 Quaoar110314002.741103+47
−33
112.71092133631813accepted (and recommended)cubewano
1 Ceres9399393.36939±292831414asteroid belt
90482 Orcus9106412.31910+50
−40
252.3983234592293accepted (and recommended)2:3 resonant
90377 Sedna9061.83906+314
−258
331.81041325722861accepted (and recommended)detached
120347 Salacia8464924.25846±2154.29214188939possiblecubewano
(307261) 2002 MS47873.6787±1310496052531266cubewano
(55565) 2002 AW1977683.3768+39
−38
143.6754122911454acceptedcubewano
174567 Varda7492453.81749±18103.7689132521260possiblecubewano
(532037) 2013 FY277423.15742+78
−83
183.5721143121558SDO
28978 Ixionca. 7303.83732143.8674122281139accepted2:3 resonant
(208996) 2003 AZ847073.74707±24113.9747112371187accepted2:3 resonant
(90568) 2004 GV96804.25680±3484.27038188939acceptedcubewano
(145452) 2005 RN436793.89679+55
−73
113.9697112221108possiblecubewano
(55637) 2002 UX256591253.87659±38113.9704112241118cubewano
2018 VG18ca. 6603.63.9656122531266SDO
20000 Varuna6543.76654+154
−102
123.975692351176acceptedcubewano
(145451) 2005 RM43ca. 6404.46444.85248175876possibleSDO
229762 Gǃkúnǁʼhòmdímà6401363.7640±30153.7612172421209SDO
2014 UZ2246353.4635+65
−72
133.7688112781388SDO
(523794) 2015 RR245ca. 6303.84.1626102311155SDO
(523692) 2014 EZ51ca. 6303.84.1626102311155detached
2010 RF43ca. 6103.94.2611102211103SDO
19521 Chaos6004.8600+140
−130
656125146729cubewano
2015 KH162ca. 5904.14.4587102011006detached
(303775) 2005 QU1825843.8584+155
−144
133.8415332311155cubewano
2010 JO179ca. 57044.557492111053SDO
2010 KZ39ca. 57044.557492111053detached
(523759) 2014 WK509ca. 5704.44.55749175876detached
2012 VP113ca. 57044.557492111053detached
(78799) 2002 XW935655.5565+71
−73
45.45844106528SDO
(523671) 2013 FZ27ca. 5604.44.656191758761:2 resonant
(523639) 2010 RE64ca. 5604.44.65619175876SDO
(543354) 2014 AN55ca. 5604.14.656192011006SDO
2004 XR190ca. 5604.34.65619183917detached
2002 XV935495.42549+22
−23
45.456441105482:3 resonant
2010 FX86ca. 5504.74.65499153763cubewano
(528381) 2008 ST291ca. 5504.44.65499175876detached
(84922) 2003 VS25484.1548+30
−45
154.1537152011006not accepted2:3 resonant
2006 QH181ca. 5404.34.75368183917SDO
2014 YA50ca. 5404.64.75368160799cubewano
2017 OF69ca. 5304.61607992:3 resonant
2015 BP519ca. 5204.54.85248167837SDO
(482824) 2013 XC26ca. 5204.44.85248175876cubewano
(470443) 2007 XV50ca. 5204.44.85248175876cubewano
(84522) 2002 TC3025143.9514±15144.25911222111032:5 resonant
(470308) 2007 JH43ca. 5104.54.951381678372:3 resonant
(278361) 2007 JJ43ca. 5104.54.95138167837cubewano
(523681) 2014 BV64ca. 5104.74.95138153763cubewano
2014 HA200ca. 5104.74.95138153763SDO
2014 FC72ca. 5104.74.95138153763detached
2015 BZ518ca. 5104.74.95138153763cubewano
2014 WP509ca. 5104.54.95138167837cubewano
(120348) 2004 TY3645124.52512+37
−40
104.75368166829not accepted2:3 resonant
(145480) 2005 TB1905074.4507+127
−116
144.446915175876detached
(523645) 2010 VK201ca. 500555017133665cubewano
2013 AT183ca. 5004.655017160799SDO
(523742) 2014 TZ85ca. 5004.8550171467294:7 resonant
2014 FC69ca. 5004.655017160799detached
(499514) 2010 OO127ca. 5004.655017160799cubewano
(202421) 2005 UQ5134983.6498+63
−75
263.8643112531266cubewano
(315530) 2008 AP129ca. 4904.75.14907153763cubewano
(470599) 2008 OG19ca. 4904.75.14907153763SDO
(523635) 2010 DN93ca. 4904.85.14907146729detached
2003 QX113ca. 4905.15.14907127635SDO
2003 UA414ca. 49055.14907133665SDO
(472271) 2014 UM33ca. 4904.75.14907153763cubewano
(523693) 2014 FT71ca. 49055.149071336654:7 resonant
2014 HZ199ca. 48055.24797133665cubewano
2014 BZ57ca. 48055.24797133665cubewano
(523752) 2014 VU37ca. 4805.15.24797127635cubewano
(495603) 2015 AM281ca. 4804.85.24797146729detached
(455502) 2003 UZ4134724.38472+122
−25
154.75368964812:3 resonant
2015 AJ281ca. 47055.346871336654:7 resonant
(523757) 2014 WH509ca. 4705.25.34687121606cubewano
2014 JP80ca. 47055.346871336652:3 resonant
2014 JR80ca. 4705.15.346871276352:3 resonant
(523750) 2014 US224ca. 47055.34687133665cubewano
2013 FS28ca. 4704.95.34687139696SDO
2010 RF188ca. 4705.25.34687121606SDO
2011 WJ157ca. 47055.34687133665SDO
(120132) 2003 FY1284604.6460±21125.14678160799SDO
2010 ER65ca. 4605.25.44576121606detached
(445473) 2010 VZ98ca. 4604.85.44576146729SDO
2010 RF64ca. 4605.75.4457696481cubewano
(523640) 2010 RO64ca. 4605.25.44576121606cubewano
2010 TJca. 4605.75.4457696481SDO
2014 OJ394ca. 4605.15.44576127635detached
2014 QW441ca. 4605.25.44576121606cubewano
2014 AM55ca. 4605.25.44576121606cubewano
(523772) 2014 XR40ca. 4605.25.44576121606cubewano
(523653) 2011 OA60ca. 4605.15.44576127635cubewano
(26181) 1996 GQ214564.9456+89
−105
65.34687139696SDO
(84719) 2002 VR1284495.58449+42
−43
55.645951025092:3 resonant
(471137) 2010 ET65ca. 4505.15.54476127635SDO
(471165) 2010 HE79ca. 4505.15.544761276352:3 resonant
2010 EL139ca. 4505.65.544761015042:3 resonant
(523773) 2014 XS40ca. 4505.45.54476111553cubewano
2014 XY40ca. 4505.15.54476127635cubewano
2015 AH281ca. 4505.15.54476127635cubewano
2014 CO23ca. 4505.35.54476116579cubewano
(523690) 2014 DN143ca. 4505.35.54476116579cubewano
(523738) 2014 SH349ca. 4505.45.54476111553cubewano
2014 FY71ca. 4505.45.544761115534:7 resonant
(471288) 2011 GM27ca. 4505.15.54476127635cubewano
(532093) 2013 HV156ca. 4505.25.544761216061:2 resonant
2013 SF106ca. 4405.0133665SDO
471143 Dziewanna4333.8433+63
−64
303.8475252311155SDO
(471165) 2002 JR146ca. 4205.11276352:3 resonant
(444030) 2004 NT334234.8423+87
−80
125.149071467294:7 resonant
(182934) 2002 GJ324166.16416+81
−73
36.12351278390SDO
(469372) 2001 QF2984085.43408+40
−45
75.442171095452:3 resonant
(175113) 2004 PF1154064.54406+98
−85
124.5482121648212:3 resonant
38628 Huya4065.04406±161054668130652accepted2:3 resonant
2012 VB116ca. 4005.2121606cubewano
(307616) 2003 QW904015401+63
−48
85.44576133665cubewano
(469615) 2004 PT1074006.33400+45
−51
36302872360cubewano
  1. The measured diameter, else Brown's estimated diameter, else the diameter calculated from H using an assumed albedo of 9%.
  2. This is the total system mass (including moons), except for Pluto and Ceres.
  3. The geometric albedo is calculated from the measured absolute magnitude and measured diameter via the formula:
  4. Diameters with the text in red indicate that Brown's bot derived them from heuristically expected albedo.

See also

References

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  2. Stern, Alan (24 August 2012). "The Kuiper Belt at 20: Paradigm Changes in Our Knowledge of the Solar System". Applied Physics Laboratory. Today we know of more than a dozen dwarf planets in the solar system [and] it is estimated that the ultimate number of dwarf planets we will discover in the Kuiper Belt and beyond may well exceed 10,000.
  3. Grundy, W.M.; Noll, K.S.; Buie, M.W.; Benecchi, S.D.; Ragozzine, D.; Roe, H.G. (December 2019). "The mutual orbit, mass, and density of transneptunian binary Gǃkúnǁʼhòmdímà ((229762) 2007 UK126)" (PDF). Icarus. 334: 30–38. doi:10.1016/j.icarus.2018.12.037. Archived from the original (PDF) on 7 April 2019.
  4. Bruton, Dan. "Conversion of Absolute Magnitude to Diameter for Minor Planets". Department of Physics & Astronomy (Stephen F. Austin State University). Archived from the original on 23 March 2010. Retrieved 13 June 2008.
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  7. "Plutoid chosen as name for Solar System objects like Pluto" (Press release). 11 June 2008. Archived from the original on 2 July 2011. Retrieved 15 June 2008.
  8. "ESO science paper 1918a" (PDF).
  9. Hanuš, J.; Vernazza, P.; Viikinkoski, M.; Ferrais, M.; Rambaux, N.; Podlewska-Gaca, E.; Drouard, A.; Jorda, L.; Jehin, E.; Carry, B.; Marsset, M.; Marchis, F.; Warner, B.; Behrend, R.; Asenjo, V.; Berger, N.; Bronikowska, M.; Brothers, T.; Charbonnel, S.; Colazo, C.; Coliac, J-F.; Duffard, R.; Jones, A.; Leroy, A.; Marciniak, A.; Melia, R.; Molina, D.; Nadolny, J.; Person, M.; et al. (2020). "arXiv paper 1911.13049". Astronomy & Astrophysics. A65: 633. arXiv:1911.13049. doi:10.1051/0004-6361/201936639. S2CID 208512707.
  10. Savage, Don; Jones, Tammy; Villard, Ray (19 April 1995). "Asteroid or mini-planet? Hubble maps the ancient surface of Vesta". HubbleSite (Press release). News Release STScI-1995-20. Retrieved 17 October 2006.
  11. https://www.sciencenews.org/article/hygiea-may-be-solar-system-smallest-dwarf-planet
  12. "Iapetus' peerless equatorial ridge". www.planetary.org. Retrieved 2 April 2018.
  13. "DPS 2015: First reconnaissance of Ceres by Dawn". www.planetary.org. Retrieved 2 April 2018.
  14. Garrick; Bethell; et al. (2014). "The tidal-rotational shape of the Moon and evidence for polar wander". Nature. 512 (7513): 181–184. Bibcode:2014Natur.512..181G. doi:10.1038/nature13639. PMID 25079322. S2CID 4452886.
  15. Balogh, A.; Ksanfomality, Leonid; Steiger, Rudolf von (23 February 2008). Hydrostatic equilibrium of Mercury. ISBN 9780387775395 via Google Books.
  16. "[no title cited]". doi:10.1002/2015GL065101. Cite journal requires |journal= (help)
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