View source for 20000 Varuna

{{Short description|Kuiper belt object}}
{{About|the minor planet|other uses|Varuna (disambiguation)}}
{{Use dmy dates|date=September 2019}}
{{Infobox planet
 |minorplanet     = yes
 |background      = #C2E0FF
 |name            = 20000 Varuna
 |symbol          = [[File:Varuna symbol (bold).svg|24px]] (astrological)
 |image           = 20000-varuna_hst.jpg
 |image_scale     =
 |caption         = [[Hubble Space Telescope]] image of Varuna, taken in 2005
 |discovery_ref   = <ref name="jpldata"/>
 |discoverer      = [[Spacewatch]]<br/>{{small|([[Robert S. McMillan (astronomer)|Robert McMillan]])}}
 |discovered      = 28 November 2000
 |earliest_precovery_date = 24 November 1954
 |mpc_name        = (20000) Varuna
 |pronounced      = {{IPAc-en|ˈ|v|ær|ən|ə}} {{respell|VARR|ə-nə}}<ref name="pronounced"/><br/>[[Sanskrit]] वरुण {{IPA|sa|ˈʋɐɾuɳɐ|}}
 |alt_names       = {{mp|2000 WR|106}}
 |adjectives      = Varunian {{IPAc-en|v|ə|'|r|uː|n|i|ə|n}}<ref>Duchesne-Guillemin (1958) ''The Western response to Zoroaster''</ref>
 |named_after     = [[Varuna]]
 |mp_category     = [[trans-Neptunian object|TNO]]{{·}}[[Classical Kuiper belt object|classical]] (hot)<ref name="Mommert2013"/><br/>[[Scattered disc|Scat-Ext]]<ref name="Buie"/>
 |orbit_ref       = <ref name="jpldata"/>
 |epoch           = 2025-05-05 ([[Julian day|JD]] 2460800.5)
 |uncertainty     = 0
 |observation_arc = {{nowrap|70.28 yr (25,670 days)}}
 |neptune_moid    = {{convert|12.040|AU|Tm|abbr=on}}<ref name="MPC"/>
 |aphelion        = {{convert|45.448|AU|Tm|abbr=on|lk=on}}
 |perihelion      = {{convert|40.827|AU|Tm|abbr=on}}
 |semimajor       = {{convert|42.718|AU|Tm|abbr=on}}
 |eccentricity    = 0.0536
 |period          = 279.21 [[Julian year (astronomy)|yr]] (101,980 [[Julian year (astronomy)|d]])
 |time_periastron = 1934-11-30 (JD 2427771)
 |avg_speed       = 4.53 km/s
 |inclination     = 17.140°
 |asc_node        = 97.213°
 |arg_peri        = 272.579°
 |mean_anomaly    = 114.900[[Degree (angle)|°]]
 |mean_motion     = {{Deg2DMS|0.003478745|sup=ms}} / day
 | satellites     = 0 (1 suspected)
 |dimensions      = 
 |mean_diameter   = {{val|654|154|102|u=km}}<ref name="Lellouch2019"/><br/>{{val|668|+154|-86|u=km}}<ref name="TNOsCool9"/>
 |mass            = 
 |density         = {{val|0.992|0.086|0.015|u=g/cm3}} <ref name="LacerdaJewitt2007"/> 
 |albedo          = {{val|0.127|0.04|0.042}}<ref name="TNOsCool9"/>
 |spectral_type   = [[Trans-Neptunian object#Colors|IR]] (moderately red)<ref name="Mommert2013"/><br/>B−V={{val|0.88|0.02}}<ref name="Belskaya2015"/><ref name="lcdb"/><br/>V−R={{val|0.62|0.01}}<ref name="Belskaya2015"/><br/>V−I={{val|1.24|0.01}}<ref name="Belskaya2015"/>
 |magnitude       = 20.3 ([[Opposition (astronomy)|opposition]])<ref name="Horizons"/><ref name="AstDys"/>
 |abs_magnitude   = 3.79<ref name="jpldata"/>
 |rotation        = {{val|6.343572|0.000006|ul=h|fmt=none}}<ref name="Valenzuela2019"/>
}}

'''20000 Varuna'''{{efn|With stress on the first syllable}} (provisional designation '''{{mp|2000 WR|106}}''') is a large [[trans-Neptunian object]] in the [[Kuiper belt]]. It was discovered in November 2000 by American astronomer [[Robert S. McMillan (astronomer)|Robert McMillan]] during a [[Spacewatch]] survey at the [[Kitt Peak National Observatory]]. It is named after the [[Hindu deity]] [[Varuna]], one of the oldest deities mentioned in the [[Vedas|Vedic texts]].

Varuna's [[light curve]] is compatible with the body being a [[Jacobi ellipsoid]], suggesting that it has an elongated shape due to its rapid [[rotation]]. Varuna's surface is [[Trans-Neptunian object#Colors|moderately red]] in color due to the presence of complex [[organic compound]]s on its surface. Water [[ice]] is also present on its surface, and is thought to have been exposed by past [[impact event|collision]]s which may have also caused Varuna's rapid rotation. Although no [[natural satellite]]s have been found or directly imaged around Varuna, analysis of variations in its light curve in 2019 suggests the presence of a possible satellite orbiting closely around Varuna. Assumptions that the body is in [[hydrostatic equilibrium]] (and thus a [[dwarf planet]]) result in a calculated density too low for it to be a dwarf planet.

== History ==
=== Discovery ===
[[File:At Kitt Peak National Observatory.jpg|thumb|left|Varuna was discovered with the Spacewatch 0.9-meter telescope at the [[Kitt Peak National Observatory]]]]
Varuna was discovered by American astronomer [[Robert S. McMillan (astronomer)|Robert McMillan]] using the [[Spacewatch]] 0.9-meter telescope during a routine survey on 28 November 2000.<ref name="spacewatch"/> The Spacewatch survey was conducted by McMillan at the [[Kitt Peak National Observatory]] near Tucson, Arizona.<ref name="jpldata"/> At the time of discovery, Varuna was located at a moderately dense star field close to the northern [[galactic equator]].<ref name="NYT-2000"/> Although Varuna was not detected by McMillan's [[Real-time computing|real-time computer software]], he was able to identify Varuna moving slowly among the background stars by manually comparing multiple scans of the same region using the [[Blink comparator#modern replacements|blinking technique]]. After McMillan's observing shift, follow-up observations of Varuna were conducted by astronomer Jeffrey Larsen in order to confirm the object.<ref name="spacewatch"/><ref name="NYT-2000"/> By the end of Larsen's observing shift, both McMillan and Larsen had made a total of 12 observations that spanned three nights.<ref name="spacewatch"/>

The discovery of Varuna was formally announced in a [[Minor Planet Center#Publications|Minor Planet Electronic Circular]] on 1 December 2000.<ref name="MPEC"/> It was given the [[Provisional designation in astronomy|provisional designation]] {{mp|2000 WR|106}}, indicating that it was discovered during the second half of November 2000.<ref name="designation"/> Varuna was the 2667th object observed in the latter half of November, as indicated by the last letter and numbers in its provisional designation.<ref name="spaceguard"/> At the time, Varuna was thought to be one of the largest and brightest [[minor planet]]s in the Solar System due to its relatively high [[apparent magnitude]] of 20 for a distant object, which implied that it might be around one-fourth the size of [[Pluto]] and comparable in size to the dwarf planet {{dp|Ceres}}.<ref name="spacewatch"/><ref name="JewittSheppard2002"/><ref name="NYT-2000"/>

Subsequently, after the announcement of Varuna's discovery, [[precovery|precovery image]]s of Varuna were found by German astronomers Andre Knofel and Reiner Stoss at the [[Palomar Observatory]].<ref name="spacewatch"/><ref name="spaceguard"/> One particular precovery image, which was taken with the Palomar Observatory's Big Schmidt telescope in 1955, showed that Varuna was located three&nbsp;[[degree (angle)|degree]]s away from its extrapolated location based on the approximate circular orbit determined in December 2000.<ref name="spacewatch"/> The oldest known precovery image of Varuna was taken on 24 November 1954.<ref name="jpldata"/> These precovery images along with additional observations from Japan, Hawaii, and Arizona helped astronomers refine its orbit and determine Varuna's proper classification.<ref name="JewittSheppard2002"/><ref name="spacewatch"/><ref name="spaceguard"/>

In January 2001, Varuna was assigned the [[minor planet number]] 20000 by the Minor Planet Center as its orbit was well determined from precovery images and subsequent observations.<ref name="MPC41805"/><ref name="spacewatch"/><ref name="spaceguard"/> The minor planet number 20000 was particularly chosen to commemorate Varuna's large size, being the largest [[classical Kuiper belt object]] known at that time and was believed to be as large as Ceres.<ref name="MPC41805"/> The number 20000 was also chosen to commemorate the coincidental 200th anniversary of the discovery of Ceres, which occurred in the same month as the numbering of Varuna.<ref name="MPC41805"/>

=== Name ===
Varuna is named after the eponymous [[Deva (Hinduism)|Hindu deity]] [[Varuna]], following the [[International Astronomical Union]] naming convention for non-resonant Kuiper belt objects after creator deities.<ref name="spacewatch"/> The name was proposed by Indian choreographer [[Mrinalini Sarabhai]], and was approved by the IAU in March 2001.<ref name="MPC42368"/> Varuna is one of the oldest [[Vedas|Vedic]] deities of [[Hindu literature]], being mentioned in the earliest [[hymn]]s of the ''[[Rigveda]]''.<ref name="MPC42368"/><ref name="jpldata"/> In Hindu literature, Varuna created and presided over the waters of the heaven and of the ocean.<ref name="Oldenberg1988p104"/> Varuna is the king of gods and men and the universe, and has unlimited knowledge.<ref name="MPC42368"/><ref name="Srinivasan1997p48"/>

[[Planetary symbol]]s are no longer much used in astronomy, so Varuna never received a symbol in the astronomical literature. There is no standard symbol for Varuna used by astrologers either. Denis Moskowitz, a software engineer in Massachusetts who designed the symbols for most of the dwarf planets, proposed a symbol for Varuna ([[File:Varuna symbol (fixed width).svg|16px]]): it derives from the [[Devanagari]] letter ''va'' व and Varuna's snake-lasso. This symbol is occasionally mentioned on astrology websites, but is not broadly used.<ref name=miller>{{cite web|url=https://www.unicode.org/L2/L2021/21224-dwarf-planet-syms.pdf|title=Unicode request for dwarf-planet symbols|last=Miller|first=Kirk|date=26 October 2021|website=unicode.org}}</ref> Another sometimes seen is a variant of Neptune ([[file:Varuna Neptune symbol (fixed width).svg|16px]] with a globe and outward-facing tines), as Varuna is the Hindu equivalent of Neptune.

== Orbit and classification ==
{| class="infobox"
|-
|
{| style="background: white; white-space: nowrap;" cellpadding=0 cellspacing=2
|-
| [[File:TheKuiperBelt Orbits Varuna.svg|frameless|center|upright=1.45|Ecliptic view]]
|-
| [[File:TheKuiperBelt_Orbits_Varuna_PolarView.svg|frameless|upright=0.7|Polar view]][[File:Cubewanos.png|frameless|upright=0.75|Polar view with other classical KBOs]]
|}
|-
| Polar and [[ecliptic]] view of the orbits of Varuna (blue), Pluto (red), and Neptune (white). The orbital inclinations of Varuna and Pluto as shown in the ecliptic view are similar. The image on the right shows the orbits of several other large Kuiper belt objects including Pluto.
|}

Varuna orbits the [[Sun]] at an average distance of {{convert|42.7|AU|e9km e9mi|lk=in|abbr=unit}}, taking 279 years to complete a full orbit.<ref name="MPC"/> Its orbit is nearly circular, with a low [[orbital eccentricity]] of 0.056. Due to its low orbital eccentricity, its distance from the Sun varies only slightly over the course of its orbit. Varuna's minimum distance possible ([[Minimum orbit intersection distance|MOID]]) from Neptune is 12.04&nbsp;AU.<ref name="MPC"/> Over the course of its orbit, Varuna's distance from the Sun ranges from 40.3&nbsp;AU at [[perihelion]] (closest distance) to 45.1&nbsp;AU at [[aphelion]] (farthest distance).<ref name="jpldata"/> Varuna's orbit is [[orbital inclination|inclined]] to the [[ecliptic]] by 17 [[degree (angle)|degree]]s, similar to Pluto's orbital inclination.<ref name="jpldata"/> Varuna had passed its perihelion in 1928 and is currently moving away from the Sun, approaching aphelion by 2071.<ref name="jpldata"/><ref name="Horizons"/>

With a nearly circular orbit at around 40 to 50&nbsp;AU, Varuna is classified as a [[classical Kuiper belt object]] (KBO), or sometimes a "cubewano".<ref name="MPEC2009-P26"/> Varuna's semi-major axis of 42.8&nbsp;AU is similar to that of other large classical KBOs such as Quaoar ([[semi-major axis|a]]=43.7&nbsp;AU)<ref name="ssd-quaoar"/> and [[Makemake]] (a=45.6&nbsp;AU),<ref name="ssd-makemake"/> although other orbital characteristics such as inclination widely differ.<ref name="jpldata"/> Varuna is a member of the "dynamically hot" class of classical KBOs,<ref name="Mommert2013"/> meaning that it has an orbital inclination greater than 4 degrees, the imposed maximum inclination for dynamically cold members of its population.<ref name="beyond"/> As a classical KBO, Varuna is not in [[orbital resonance]] with Neptune and is also free from any significant perturbation by Neptune.<ref name="MPC"/><ref name="Buie"/>

== Rotation ==
[[File:Varuna artistic2.png|thumb|upright=1|Art concept of Varuna, incorporating some of what is known including its shape and coloration from spectral analysis]]
Varuna has a rapid [[rotation period]] of approximately 6.34 hours, derived from a double-peaked solution for Varuna's rotational [[light curve]].<ref name="IAUC7583"/> Varuna's rotation was first measured January 2001 by astronomer Tony Farnham using the [[McDonald Observatory]]'s 2.1-meter telescope, as part of a study on the rotation and colors of distant objects. [[charge-coupled device|CCD]] [[Photometry (astronomy)|photometry]] of Varuna's light curve in 2001 revealed that it displays large brightness variations with an [[amplitude]] of about 0.5 [[magnitude (astronomy)|magnitude]]s.<ref name="Farnham2001"/> The measured rotational light curve of Varuna provided two ambiguous rotation periods of 3.17 and 6.34 hours, for a single-peaked and a double-peaked solution, respectively. Additional possible rotation periods of 2.79 and 3.66 hours were also obtained by Farnham, although these values could not be ruled out at the time.<ref name="Farnham2001"/><ref name="IAUC7583"/>

A single-peaked interpretation of Varuna's rotational light curve (3.17 h) would assume a spherical shape for Varuna, with [[albedo feature]]s on its surface that would account for its brightness variations. However, in order for this interpretation to be valid, Varuna must have a density much greater than {{val|1|ul=g/cm3}} (roughly the density of water), otherwise it would deform and break apart as the given rotation period exceeds the [[critical speed|critical rotation rate]] of ~3.3 hours for a body with a density of {{val|1|u=g/cm3}}.<ref name="Farnham2001"/> A double-peaked interpretation of Varuna's rotational light curve (6.34 h) would assume that Varuna's shape is an elongated [[ellipsoid]], with an estimated ''a''/''b'' [[aspect ratio]] of 1.5–1.6.<ref name="Farnham2001"/><ref name="IAUC7583"/> The rotational light curve of Varuna was later investigated by astronomers [[David C. Jewitt]] and [[Scott Sheppard]] during February and April 2001, and concluded that the double-peaked interpretation for Varuna's light curve is the most plausible solution due to the absence of rotational variation in Varuna's color in the [[visible spectrum]].<ref name="Lellouch2002"/><ref name="JewittSheppard2002"/>

Examination of past photometric observations of Varuna's light curve has shown that its light curve amplitude had increased by roughly 0.13 magnitudes from 2001 to 2019.<ref name="Valenzuela2019"/> This increase in amplitude is due to the combined effects of Varuna's ellipsoidal shape, rotation, and varying [[Phase angle (astronomy)|phase angle]]. [[Geometric model]]s for Varuna's changing amplitude have provided several possible solutions for the orientation of Varuna's rotational poles in [[ecliptic coordinates]], with the best-fit solution adopting a [[Poles of astronomical bodies|spin axis]] [[right ascension]] and [[declination]] of 54° and −65°, respectively.<ref name="Valenzuela2019"/>{{efn|The given [[right ascension]] and [[declination]] values specify the position of an object in the [[geocentric]] [[equatorial coordinate system]]. The right ascension is the [[angular distance]] eastward of the [[celestial equator]] starting at the vernal (March) [[equinox]] while the declination is the angular distance perpendicular or vertical to the celestial equator.<ref name="coordinates"/>}} The best-fit pole orientation of Varuna implies that it is being viewed at a near-edge on configuration, in which Varuna's equator nearly faces directly toward Earth.<ref name="Valenzuela2019"/>{{efn|Varuna's north pole points in the direction of {{nowrap|RA <nowiki>=</nowiki> 54°}} and {{nowrap|Dec <nowiki>=</nowiki> −65°}}, meaning that pole's right ascension points nearly perpendicular to the vernal equinox (resulting in an edge-on view of Varuna's equator) and the negative declination indicating that Varuna's north pole points downwards, 65° south of the celestial equator.}}

Varuna's rapid rotation is believed to have resulted from disruptive [[impact event|collision]]s that have sped up its rotation during the [[formation of the Solar System]]. The present collision rate in the trans-Neptunian region is minimal, though collisions were more frequent during the formation of the Solar System.<ref name="JewittSheppard2002"/> However, Jewitt and Sheppard calculated that the rate of disruptive collisions among large trans-Neptunian objects (TNOs) during the Solar System's formation is extremely uncommon, contradictory to the current abundance of binary and rapidly rotating TNOs that are believed to have originated from such collisions.<ref name="JewittSheppard2002"/> To explain the abundance of binary and rapidly rotating TNOs, the rate of collisions among TNOs had likely increased as a result of Neptune's outward [[planetary migration|migration]] perturbing the orbits of TNOs, thus increasing the frequency of collisions which may have led to Varuna's rapid rotation.<ref name="JewittSheppard2002"/>

== Physical characteristics ==
=== Size and shape ===
{| class="wikitable floatleft" style="text-align: center; font-size: 0.9em; margin-right: 12px;"
|+ Size estimates for Varuna
!Year!!Diameter (km)!!Method!!Refs
|-
|2000
|{{val|900|129|145}}
|thermal
|<ref name="Jewitt2001"/>
|-
|2002
|{{val|1060|180|220}}
|thermal
|<ref name="Lellouch2002"/>
|-
|2002
|{{val|788|p=~}}
|best fit albedo
|<ref name="Doressoundiram2002"/>
|-
|2005
|{{val|936|238|324}}
|thermal
|<ref name="Grundy2005"/>
|-
|2005
|{{val|600|150}}
|thermal
|<ref name="Stansberry2005"/>
|-
|2005
|{{val|586|129|190}}
|thermal
|<ref name="Cruikshank2005"/>
|-
|2007
|{{val|502|64.0|69.5}}<br/>''or''&nbsp;412.3~718.2<br/>''or''&nbsp;≤744.1
|thermal<br/>{{small|(Spitzer 1-Band)}}
|<ref name="Stansberry2008"/>
|-
|2007
|>{{val|621|178.1|139.1}}
|thermal<br/>{{small|(Spitzer 2-Band)}}
|<ref name="Stansberry2008"/>
|-
|2007
|{{val|500|100}}
|thermal<br/>{{small|(adopted)}}
|<ref name="Stansberry2008"/>
|-
|2008
|{{val|714|178|128}}
|thermal
|<ref name="Brucker2009"/>
|-
|2010
|{{val|1003|9}}<br/>{{small|(long-axis minimum only)}}
|occultation
|<ref name="Bruno2010"/>
|-
|2013
|{{val|668|+154|-86}}
|thermal
|<ref name="TNOsCool9"/>
|-
|2013
|{{val|p=~|816}}
|best fit albedo
|<ref name="Mommert2013"/>
|-
|2013
|{{val|p=~|686}}
|occultation
|<ref name="Braga-Ribas2014"/>
|-
|2014
|{{val|p=~|670}} {{small|(minimum)}}
|occultation
|<ref name="Braga-Ribas2014"/>
|-
|2019
|{{val|654|154|102}}
|thermal
|<ref name="Lellouch2019"/>
|}

[[File:Varuna, Earth & Moon size comparison.png|thumb|upright=1|Varuna compared to the [[Earth]] and the [[Moon]]]]
As a result of its rapid rotation, the shape of Varuna is deformed into a triaxial ellipsoid. Given the rapid rotation, rare for objects so large, Varuna's shape is described as a [[Jacobi ellipsoid]], with an ''a''/''b'' aspect ratio of around 1.5–1.6 (in which Varuna's longest [[semi-axis]] ''a'' is 1.5–1.6 times longer than its ''b'' semi-axis).<ref name="JewittSheppard2002"/><ref name="IAUC7583"/> Examination of Varuna's light curve has found that the best-fit model for Varuna's shape is a triaxial ellipsoid with the semi-axes ''a'', ''b'', and ''c'' in ratios in the range of ''b''/''a'' = 0.63–0.80, and ''c''/''a'' = 0.45–0.52.<ref name="LacerdaJewitt2007"/>

Due to Varuna's ellipsoidal shape, multiple observations have provided different estimates for its diameter, ranging from {{convert|500|–|1000|km|mi|abbr=on}}.<ref name="johnston"/> Most diameter estimates for Varuna were determined by measuring its [[thermal emission]], although size estimates have been constrained to smaller values as a result of higher albedos determined by space-based thermal measurements.<ref name="johnston"/> Observations of stellar [[occultation]]s by Varuna have also provided varying size estimates.<ref name="Braga-Ribas2014"/> An occultation by Varuna in February 2010 yielded a [[Chord (astronomy)|chord]] length of {{convert|1003|km|mi|abbr=on}}, inferred to be across its longest axis.<ref name="Bruno2010"/> Later occultations in 2013<ref name="Sendai2013"/> and 2014 yielded [[mean diameter]]s of {{convert|686|km|mi|abbr=on}} and {{convert|670|km|mi|abbr=on}} respectively.<ref name="Braga-Ribas2014"/>

Since the discovery of Varuna, {{dp|Haumea}}, another larger rapidly rotating (3.9 h) object over twice the size of Varuna,{{efn|Haumea's dimensions are {{val|2322|x|1704|x|1026|u=km}}, with {{val|2322|u=km}} being the longest semi-axis.<ref name="Ortiz2017"/> In comparison, Varuna's longest semi-axis is 1003 km, less than half than that of Haumea.<ref name="Bruno2010"/> In fact, Haumea's polar semi-axis of {{val|1026|u=km}} is also over twice as long as Varuna's, which has a polar semi-axis around {{val|400|–|500|u=km}} based on apparent oblateness values from occultations in 2010 and 2013.<ref name="Braga-Ribas2014"/>}} has been discovered and is also thought to have an elongated shape,<ref name="Rabinowitz2006"/> albeit slightly less pronounced (estimated ratios of ''b''/''a'' = 0.76~0.88, and ''c''/''a'' = 0.50~0.55, possibly due to a higher estimated density approximately {{val|1.757|–|1.965|u=g/cm3}}).<ref name="LacerdaJewitt2007"/><ref name="Ortiz2017"/>

==== Unlikely to be a dwarf planet ====

Astronomer [[Gonzalo Tancredi]] considered Varuna [[List of dwarf-planet candidates#Probable per Tancredi|likely to be a dwarf planet]] and a Jacobi ellipsoid in shape.<ref name="Tancredi2008"/><ref name="Tancredi2010"/> Based on a best-fit Jacobi ellipsoid model for Varuna, Lacerda and Jewitt estimate that Varuna has a quite low density, of {{val|0.992|u=g/cm3}}, just under Tancredi's minimum density criterion. Despite this, they assumed Varuna was in hydrostatic equilibrium for their calculations.<ref name="LacerdaJewitt2007"/> Astronomer William Grundy and colleagues propose that dark, low-density TNOs around the size range of approximately {{convert|400|–|1000|km|mi|abbr=on}} are likely to be uncompressed, partially porous bodies. While the larger objects in this range, such as Varuna, may have fully collapsed into solid material in their interiors, their mantles likely remain uncompressed. That is, they would not be in hydrostatic equilibrium and not dwarf planets.<ref name="Grundy2019"/>

==== Thermal measurements ====

Ground observations of Varuna's thermal emission from 2000 to 2005 yielded large diameter estimates ranging from {{convert|900|km|mi|abbr=on}} to {{convert|1060|km|mi|abbr=on}}, making it comparable to the size of Ceres.<ref name="johnston"/> Contrary to the ground-based estimates, space-based thermal observations from the Spitzer Space Telescope provided a smaller diameter range of {{convert|450|–|750|km|mi|abbr=on}}.<ref name="Grundy2005"/><ref name="Stansberry2008"/> The discrepancy between ground-based and space-based size estimates are due to the limited observable wavelengths for ground-based observations, as a result of [[absorption (electromagnetic radiation)|absorption]] of [[Earth's atmosphere]].<ref name="JewittKBOs"/> Distant trans-Neptunian objects such as Varuna intrinsically emit thermal radiation at longer wavelengths due to their low temperatures.<ref name="JewittKBOs"/> However, at long wavelengths, thermal radiation cannot pass through Earth's atmosphere and ground-based observations could only measure weak thermal emissions from Varuna at [[near-infrared]] and [[Submillimetre astronomy|submillimeter]] [[wavelength]]s, hindering the accuracy of ground-based thermal measurements.<ref name="JewittKBOs"/><ref name="Lellouch2002"/>

Space-based observations provided more accurate thermal measurements as they are able to measure thermal emissions at a broad range of wavelengths that are normally interfered by Earth's atmosphere.<ref name="Grundy2005"/><ref name="JewittKBOs"/> Preliminary thermal measurements with Spitzer in 2005 provided a higher albedo constraint of 0.12 to 0.3, corresponding to a smaller diameter constraint of {{convert|450|–|750|km|mi|abbr=on}}.<ref name="Stansberry2005"/><ref name="Cruikshank2005"/> Further Spitzer thermal measurements at multiple wavelength ranges (bands) in 2007 yielded mean diameter estimates around {{val|p=~|502|u=km}} and {{val|p=~|621|u=km}} for a single-band and two-band solution for the data, respectively. From these results, the adopted mean diameter was {{convert|500|km|mi|abbr=on}}.<ref name="Stansberry2008"/> Follow-up multi-band thermal observations from the Herschel Space Observatory in 2013 yielded a mean diameter of {{val|668|154|86|u=km}}, consistent with previous constraints on Varuna's diameter.<ref name="TNOsCool9"/>

==== Occultations ====

Previous attempted observations of stellar occultations by Varuna in 2005 and 2008 were unsuccessful due to uncertainties in Varuna's [[proper motion]] along with undesirable conditions for observing.<ref name="Occultation2005"/><ref name="Occultation2008"/> In 2010, an occultation by Varuna was successfully observed by a team of astronomers led by Bruno Sicardy on the night of 19 February.<ref name="Bruno2010"/> The occultation was observed from various regions in southern Africa and north-eastern Brazil.<ref name="Bruno2010"/> Although observations of the occultation from [[South Africa]] and [[Namibia]] had negative results, observations from Brazil, particularly at [[São Luís, Maranhão|São Luís]] in [[Maranhão]], successfully detected a {{nowrap|52.5-second}} occultation by Varuna of an 11.1 magnitude star. The occultation yielded a chord length of {{val|1003|9|u=km}}, quite large compared to mean diameter estimates from thermal measurements.<ref name="Bruno2010"/> Because the occultation occurred near Varuna's maximum brightness, the occultation was observing the maximum apparent surface area for an ellipsoidal shape; the longest axis of Varuna's shape was observed during the occultation.<ref name="Bruno2010"/> São Luís was also located very close to the predicted centerline of Varuna's shadow path,<ref name="MIT_PAL"/> meaning the chord length was close to the longest measurable during the event, closely constraining the possible maximum equatorial diameter.

Results from the same event from [[Camalaú]], [[Paraíba]], approximately {{convert|450|km|mi|abbr=on}} south (and on what was predicted to be the very southern extent of the shadow path),<ref name="MIT_PAL"/> showed a 28-second occultation, corresponding to an approximately {{convert|535|km|mi|abbr=on}} chord, much longer than might otherwise have been expected.<ref name="Occultation2010"/> However, [[Quixadá]], {{convert|255|km|mi|abbr=on}} south of São Luís–between it and Camalaú–paradoxically had a negative result.<ref name="Bruno2010"/> To account for the negative Quixadá results, the apparent [[oblateness]] (flattening) of Varuna was imposed at a minimum value of approximately 0.56 (aspect ratio ''c''/''a'' ≤ 0.44),<ref name="Braga-Ribas2014"/> corresponding to a minimum polar dimension of approximately {{convert|441.3|km|mi|abbr=on}}, based on the given chord length of {{val|1003|9|u=km}}.{{efn|Polar dimension calculated by multiplying the chord {{val|1003|9|u=km}} with the ''c''/''a'' ratio of 0.44, calculated from 1 – 0.56, the maximum oblateness imposed by Braga-Ribas ''et al.'' in 2014.<ref name="Braga-Ribas2014"/>}} The resulting lower bound on Varuna's polar dimension is approximately equal to Lacerda and Jewitt's lower bound ''c''/''a'' aspect ratio of 0.45, which they previously calculated in 2007.<ref name="LacerdaJewitt2007"/> A preliminary conference presentation, given before the Camalaú results were fully analyzed, concluded that the São Luís and Quixadá results together suggested a significantly elongated shape is required for Varuna.<ref name="Bruno2010"/>

Later occultations in 2013 and 2014 yielded mean diameters of {{convert|686|km|mi|abbr=on}} and {{convert|670|km|mi|abbr=on}}, respectively.<ref name="Braga-Ribas2014"/> The mean diameter of {{convert|678|km|mi|abbr=on}}, calculated from both chords from the occultations,{{efn|The mean diameter of {{val|p=≈|678|u=km}} is calculated as the average diameter of the 2013 and 2014 occultation chords of {{val|p=~|686|u=km}} and {{val|p=≈|670|u=km}}, respectively.<ref name="Braga-Ribas2014"/>|name=mean|group=lower-alpha}} appears seemingly consistent with the Spitzer and Herschel thermal measurement of {{convert|668|km|mi|abbr=on}}.<ref name="johnston"/> While the apparent oblateness of Varuna could not be determined from the single chord obtained from the 2014 occultation, the 2013 occultation yielded two chords, corresponding to an apparent oblateness of approximately 0.29.<ref name="occultation-2013"/><ref name="Braga-Ribas2014"/> The imposed oblateness for the 2013 chord length of {{val|686|u=km}} as Varuna's diameter corresponds to a polar dimension of approximately {{convert|487|km|mi|abbr=on}},{{efn|Polar dimension calculated by multiplying the 2013 chord {{val|686|u=km}} with the ''c''/''a'' ratio of 0.71, calculated from 1 – 0.29, the apparent oblateness imposed by Braga-Ribas ''et al.'' in 2014.<ref name="Braga-Ribas2014"/>}} somewhat consistent with the calculated 2010 minimum polar dimension of {{val|441.3|u=km}}.

=== Spectra and surface ===
[[File:TheTransneptunians Size Albedo Color.svg|thumb|upright=1.5|Comparison of sizes, albedo, and colors of various large trans-Neptunian objects. The gray arcs represent uncertainties of the object's size.]]
Varuna's [[absorption spectrum|spectrum]] was first analyzed in early 2001 with the Near Infrared Camera Spectrometer (NICS) at the [[Galileo National Telescope]] in [[Spain]]. Spectral observations of Varuna at near-infrared wavelengths revealed that the surface of Varuna is moderately red and displays a red [[spectral slope]] between the wavelength range of 0.9 and 1.8&nbsp;[[μm]]. Varuna's spectrum also exhibits strong [[absorption bands]] at wavelengths of 1.5 and 2&nbsp;μm, indicating the presence of [[ice|water ice]] on its surface.<ref name="Licandro2001"/><ref name="Lellouch2002"/>

The red color of Varuna's surface results from the [[photolysis]] of [[organic compounds]] being irradiated by sunlight and [[cosmic rays]]. The irradiation of organic compounds such as [[methane]] on Varuna's surface produces [[tholin]]s, which are known to reduce its surface reflectivity ([[albedo]]) and are expected to cause its spectrum to appear featureless. Compared to {{dp|Huya}}, which was observed along with Varuna in 2001, it appears less red and displays more apparent water ice absorption bands, suggesting that Varuna's surface is relatively fresh and had maintained some of its original material in its surface. The fresh appearance of Varuna's surface may have resulted from collisions that have exposed fresh water ice beneath Varuna's layer of tholins above its surface.<ref name="Licandro2001"/>

Another study of Varuna's spectra at near-infrared wavelengths in 2008 yielded a featureless spectrum with a blue spectral slope, contrary to earlier results in 2001.<ref name="Barkume2008"/><ref name="Lorenzi2014"/> The spectra obtained in 2008 showed no clear indication of water ice, contradictory to the 2001 results. The discrepancy between the two results was interpreted as an indication of surface variation on Varuna, though this possibility was later ruled out by a 2014 study of Varuna's spectra. The 2014 results closely matched the previous spectra obtained in 2001, implying that the featureless spectra obtained in 2008 is likely erroneous.<ref name="Lorenzi2014"/>

Models for Varuna's spectrum suggest that its surface is most likely formed of a mixture of amorphous [[silicate]]s (25%), complex organic compounds (35%), [[amorphous carbon]] (15%) and water ice (25%), with a possibility of up to 10% methane ice. For an object with a size similar to Varuna, the presence of [[Volatile (astrogeology)|volatile]] methane could not be primordial as Varuna is not massive enough to retain volatiles on its surface. An event that had occurred subsequently after Varuna's formation–such as an energetic impact–would likely account for the presence of methane on Varuna's surface.<ref name="Lorenzi2014"/> Additional near-infrared observations of Varuna's spectra were conducted at the [[NASA Infrared Telescope Facility]] in 2017 and have identified absorption features between 2.2 and 2.5&nbsp;μm that might be associated with [[ethane]] and [[ethylene]], based on preliminary analysis.<ref name="Holler2017"/> For mid-sized bodies such as Varuna, volatiles such as ethane and ethylene are more likely to be retained than lighter volatiles such as methane according to volatile retention theories formulated by astronomers Schaller and Brown in 2007.<ref name="Holler2017"/><ref name="Schaller2007"/>

==== Brightness ====

Varuna's [[apparent magnitude]], its brightness as seen from Earth, varies from 19.5 to 20 magnitudes.<ref name="JewittSheppard2002"/> At [[opposition (astronomy)|opposition]], its apparent magnitude can reach up 20.3 magnitudes.<ref name="Horizons"/><ref name="AstDys"/> Combined thermal measurements from the Spitzer Space Telescope and the Herschel Space Observatory in 2013 obtained a visual [[absolute magnitude]] (''H<sub>V</sub>'') of 3.76, comparable to that of the similarly-sized Kuiper belt object {{dp|Ixion}} (''[[absolute magnitude|H<sub>V</sub>]]''=3.83).<ref name="TNOsCool9"/> Varuna is among the twenty brightest trans-Neptunian objects known, despite the Minor Planet Center assuming an absolute magnitude of 3.6.<ref name="MPC-TNOs"/><ref name="MPC"/>

The surface of Varuna is dark, with a measured [[geometric albedo]] of 0.127 based on thermal observations in 2013.<ref name="TNOsCool9"/> Varuna's geometric albedo is similar to that of the possible dwarf planet {{dp|Quaoar}}, which has a geometric albedo of 0.109.<ref name="Braga-Ribas-2013"/><ref name="TNOsCool9"/> Varuna was initially thought to have a much lower geometric albedo, as early ground observations of Varuna's thermal emissions from 2000 to 2005 estimated albedo values ranging from 0.04 to 0.07,<ref name="johnston"/> around eight times darker than [[Pluto]]'s albedo.<ref name="IAUC7554"/> Later thermal measurements of Varuna with space-based telescopes refuted these previous albedo measurements: Spitzer measured a higher geometric albedo of 0.116<ref name="Stansberry2008"/> while further thermal measurements from Spitzer and Herschel in 2013 estimated a geometric albedo of 0.127.<ref name="TNOsCool9"/>

Photometric observations of Varuna in 2004 and 2005 were carried out to observe changes in Varuna's light curve caused by [[opposition surge]]s when the [[phase angle (astronomy)|phase angle]] of Varuna approaches zero degrees at opposition. The photometry results showed that Varuna's light curve amplitude had decreased to 0.2 magnitudes at opposition, less than its overall amplitude of 0.42 magnitudes. The photometry results also showed an increase in asymmetry of Varuna's light curve near opposition, indicating variations of [[scattering]] properties over its surface. The opposition surge of Varuna differs from those of dark [[asteroid]]s, which gradually becomes more pronounced near opposition in contrast to Varuna's narrow opposition surge, in which its light curve amplitude sharply changes within a phase angle of 0.5 degrees. The opposition surges of other Solar System bodies with moderate albedos behave similarly to Varuna, indirectly suggesting that Varuna might have a higher albedo in contrast to ground-based albedo estimates.<ref name="Belskaya2006"/> This implication of a higher albedo for Varuna was confirmed in subsequent thermal measurements from Spitzer and Herschel.<ref name="TNOsCool9"/>

=== Internal structure ===
Varuna is estimated to have a [[bulk density]] of {{val|0.992|u=g/cm3}}, marginally less than that of water ({{val|1|u=g/cm3}}).<ref name="LacerdaJewitt2007"/> Varuna's low bulk density is likely due to a [[porosity|porous]] internal structure composed of a nearly proportional ratio of water ice and rock.<ref name="JewittSheppard2002"/> To explain its porous internal structure and composition, Lacerda and Jewitt suggested that Varuna may have a [[Granular material|granular]] internal structure. Varuna's granular internal structure is thought to have resulted from fractures caused by past collisions likely responsible for its rapid rotation.<ref name="JewittSheppard2002"/> Other objects including [[Saturn]]'s moons [[Tethys (moon)|Tethys]] and [[Iapetus (moon)|Iapetus]] are also known to have a similarly low density, with a porous internal structure and a composition that is predominantly water ice and rock.<ref name="JewittSheppard2002"/> William Grundy and colleagues proposed that dark, low-density TNOs around the size range of approximately {{convert|400|–|1000|km|mi|abbr=on}} are transitional between smaller, porous (and thus low-density) bodies and larger, denser, brighter and geologically differentiated planetary bodies (such as dwarf planets).<ref name="Grundy2019"/> The internal structures of low-density TNOs, such as Varuna, had only partially differentiated, as their likely rocky interiors had not reached sufficient temperatures to melt and collapse into pore spaces since formation. As a result, most mid-sized TNOs had remained internally porous, thus resulting in low densities.<ref name="Grundy2019"/> In this case, Varuna may not be in hydrostatic equilibrium.<ref name="Grundy2019"/>

== Possible satellite ==

[[Photometry (astronomy)|Photometric]] observations of Varuna's light curve, led by Valenzuela and colleagues in 2019, indicate that a possible satellite might be orbiting Varuna at a close distance.<ref name="Valenzuela2019"/> By using the [[Fourier analysis]] method of combining four separate light curves obtained in 2019, they derived a lower quality light curve amplitude with a greater amount of [[residual (statistics)|residual]]s. Their result indicated that Varuna's light curve experiences subtle changes over time. They plotted the residuals of the combined light curve in a [[Lomb periodogram]] and derived an orbital period of 11.9819 hours for the possible satellite.<ref name="Valenzuela2019"/> The satellite varies in brightness by 0.04 magnitudes as it orbits Varuna. Under the assumption that Varuna's density is {{val|1.1|u=g/cm3}} and the satellite is [[tidal locking|tidally locked]], the team estimates that it orbits Varuna at a distance of {{convert|1300-2000|km|mi|abbr=on}}, just beyond the estimated [[Roche limit]] of Varuna (~{{val|1000|u=km}}).<ref name="Valenzuela2019"/> Due to the satellite's close proximity to Varuna, it is not yet possible to resolve it with space-based telescopes such as the [[Hubble Space Telescope]] as the [[angular distance]] between Varuna and the satellite is smaller than the resolution of current space-based telescopes.<ref name="Valenzuela2019"/> Although direct observations of Varuna's satellite are unfeasible with current telescopes, Varuna's equator is being directly viewed at an edge-on configuration, implying that [[eclipse|mutual event]]s between the satellite and Varuna could possibly occur in the future.<ref name="Valenzuela2019"/>

== Exploration ==
[[Planetary science|Planetary scientist]] [[Amanda Zangari]] calculated that a flyby mission to Varuna could take just over 12 years using a Jupiter [[gravity assist]], based on a launch date of 2035 or 2038. Alternative trajectories using gravity assists from Jupiter, Saturn, or Uranus have been also considered.<ref name="Zangari2018"/> A trajectory using gravity assists from Jupiter and Uranus could take just over 13 years, based on a launch date of 2034 or 2037, whereas a trajectory using gravity assists from Saturn and Uranus could take under 18 years, based on an earlier launch date of 2025 or 2029. Varuna would be approximately 45 AU from the Sun when the spacecraft arrives before 2050, regardless of the trajectories used.<ref name="Zangari2018"/>

== Notes ==
{{notelist|2|group=lower-alpha}}

== References ==
{{Reflist|25em|refs=

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<ref name="MPC">{{cite web
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<ref name="IAU0603">{{cite press release
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<ref name="lcdb">{{cite web
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<ref name="occultation-2013">{{cite web
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<!-- http://occultations.ct.utfpr.edu.br/results/ -->

}} <!-- end of refs -->

== External links ==
* {{cite web
 | title=Size and Albedo of Kuiper Belt Object (20000) Varuna
 | url=http://www2.ess.ucla.edu/~jewitt/varuna.html
 | work=David Jewitt's Home Page
 | access-date=23 January 2010}}
* [http://www.astroamateur.de/kleinplaneten/2000wr106/ (20000) Varuna – Large TNO precovered on several old plates] Precovery images of Varuna. Retrieved 22 September 2019.
* [http://www.iota-es.de/JOA/JOA2017_2.pdf Beyond Jupiter: The World of Distant Minor Planets – (20000) Varuna]
* {{JPL small body|id=2020000}}

{{Minor planets navigator |19999 Depardieu |number=20000 |(20001) 1991 CM|20002 Tillysmith}}
{{Dwarf planets}}
{{Small Solar System bodies}}
{{Trans-Neptunian objects}}
{{Authority control}}

{{DEFAULTSORT:020000}}
[[Category:Classical Kuiper belt objects]]
[[Category:Discoveries by the Spacewatch project]]
[[Category:Named minor planets|Varuna]]
[[Category:Objects observed by stellar occultation]]
[[Category:Astronomical objects discovered in 2000|20001128]]
[[Category:Possible dwarf planets]]