View source for 588 Achilles

{{Short description|Jupiter trojan}}
{{Use dmy dates|date=June 2018}}
{{Infobox planet
 | minorplanet     = yes
 | name            = 588 Achilles
 | background      = #C2FFFF
 | image           = [[File:Modelled shape of 588 Achilles from its light curve.png|300px|Image: 300 pixels]]
 | image_scale      =
 | caption         = Modelled shape of ''Achilles'' from its [[light curve]]
 | discovery_ref   = <ref name="MPC-object" />
 | discovered      = 22 February 1906
 | discoverer      = [[Max Wolf|M. F. Wolf]]
 | discovery_site  = [[Heidelberg-Königstuhl State Observatory|Heidelberg Obs.]]
 | mpc_name        = (588) Achilles
 | alt_names       = 1906 TG
 | pronounced      = {{IPAc-en|ə|ˈ|k|ɪ|l|iː|z}}
 | adjective       = Achillean {{IPAc-en|ˌ|æ|k|ᵻ|ˈ|l|iː|ə|n|,_|ə|ˈ|k|ɪ|l|i|ə|n}}<ref>{{OED|Achillean, achillea}}</ref>
 | named_after     = {{nowrap|[[Achilles]] {{small|(Greek mythology)}}<ref name="springer" />}}
 | mp_category     = [[Jupiter trojan]]<ref name="MPC-object" /><ref name="jpldata" /><br />{{nowrap|[[Greek camp|Greek]]<ref name="MPC-Jupiter-Trojans" />{{·}}[[Background asteroid|background]]<ref name="AstDys-object" />}}
 | orbit_ref       = <ref name="jpldata" />
 | epoch           = 23 March 2018 ([[Julian day|JD]] 2458200.5)
 | uncertainty     = 0
 | observation_arc = 112.25 [[Julian year (astronomy)|yr]] (41,000 d)
 | aphelion        = 5.9714 [[Astronomical unit|AU]]
 | perihelion      = 4.4467 AU
 | semimajor       = 5.2091 AU
 | eccentricity    = 0.1463
 | period          = 11.89 yr (4,343 d)
 | mean_anomaly    = 205.11[[Degree (angle)|°]]
 | mean_motion     = {{Deg2DMS|0.0829|sup=ms}} / day
 | inclination     = 10.318°
 | asc_node        = 316.54°
 | arg_peri        = 133.50°
 | jupiter_moid    = 0.5704 AU
 | tisserand       = 2.9460
 | mean_diameter      = {{val|130.10|0.55|u=km}}<ref name="Grav-2012" /><br />{{val|133.22|3.33|u=km}}<ref name="AKARI" /><br />{{val|135.47|4.1|ul=km}}<ref name="SIMPS" />
 | rotation        = {{val|7.306|0.002|ul=h}}<ref name="Shevchenko-2009a" /><ref name="Shevchenko-2012a" />
 | albedo          = {{val|0.0328|0.002}}<ref name="SIMPS" /><br />{{val|0.035|0.002}}<ref name="AKARI" /><br />{{val|0.043|0.006}}<ref name="Grav-2012" />
 | spectral_type   = [[Tholen classification|Tholen]] {{=}} [[D-type asteroid|D]]U<ref name="jpldata" /><ref name="lcdb" /><br />[[Asteroid color indices|B–V]] {{=}} 0.755<ref name="jpldata" /><br />[[Asteroid color indices|U–B]] {{=}} 0.216<ref name="jpldata" /><br />[[Asteroid color indices|V–I]] {{=}} {{val|0.940|0.019}}<ref name="lcdb" />
 | abs_magnitude   = 8.47<ref name="Grav-2012" /><br />8.67<ref name="MPC-object" /><ref name="jpldata" /><ref name="AKARI" /><ref name="SIMPS" />
}}

'''588 Achilles''' is a large [[Jupiter trojan|Jupiter]] [[trojan asteroid]] of the [[Greek camp]]. Achilles was the first Jupiter trojan to be discovered, and was discovered by [[Max Wolf]] at the [[Heidelberg Observatory]] in 1906. Wolf named the minor planet after the legendary hero [[Achilles]] from Greek mythology.<ref name="MPC-object" /><ref name="springer" /> The dark [[D-type asteroid]] measures approximately {{convert|133|km|mi|abbr=off|sp=us}} in diameter which makes it one of the [[#Largest Jupiter trojans|10 largest Jupiter trojans]]. It has a [[rotation period]] of 7.3 hours and possibly a spherical shape.<ref name="lcdb" />

== Discovery ==

Achilles was discovered on 22 February 1906, by the German astronomer [[Max Wolf]] at the [[Heidelberg-Königstuhl State Observatory]] in southern Germany. It was the first discovery of a Jupiter trojan, although {{mpl|(12126) 1999 RM|11}} had been observed as {{mp|A904 RD}} two years previously. This body, however, remained unconfirmed as the observation period was not long enough to calculate an orbit. [[August Kopff]], a colleague of Wolf at Heidelberg, then discovered [[617 Patroclus]] eight months after Achilles, and, in early 1907, he discovered the largest of all Jupiter trojans, [[624&nbsp;Hektor]].<ref name="large-trojan"/>

== Orbit and classification ==
Achilles orbits the Sun at a distance of 4.4–6.0&nbsp;[[Astronomical unit|AU]] in the {{L4}} [[Lagrangian point]] of the [[Sun]]–[[Jupiter]] System once every 11 years and 11 months (4,343 days; [[semi-major axis]] of 5.21&nbsp;AU). Its orbit shows an [[orbital eccentricity|eccentricity]] of 0.15 and an [[orbital inclination|inclination]] of 10 degrees from the plane of the [[ecliptic]].<ref name="jpldata" />

Achilles is the first known example of the stable solution of the [[three-body problem]] worked out by French mathematician [[Joseph Lagrange]] in 1772, after whom the minor planet [[1006&nbsp;Lagrangea]] is named. After the discovery of other asteroids with similar orbital characteristics, which were also named after heroes from the Trojan War ''(see below)'', the term "Trojan asteroids" or "Jupiter trojans" became commonly used.<ref name="springer" /> In addition, a rule was established that the {{L4}} point was the "[[Greek camp]]", whereas the {{L5}} point was the "[[Trojan camp]]", though not before each camp had acquired a "spy" (Hektor in the Greek camp and Patroclus in the Trojan camp).

== Physical characteristics ==
<div style="float:left; font-size: 0.9em; margin-right: 20px; margin-top: 0;">
{{JPL SBDB Jupiter Trojans}}
</div>

=== Spectral type ===
In the [[Tholen classification|Tholen]] taxonomic scheme, Achilles is classified as a [[D-type asteroid]] with an unusual spectrum (DU).<ref name="jpldata" /> Its [[Asteroid color indices|V–I]] color index of 0.94 is typical for most larger Jupiter trojans ''(see table below)''.

=== Photometry ===

Achilles's [[rotation period]] of 7.3 hours is somewhat shorter than that of most other large Jupiter trojans but close to that of [[911&nbsp;Agamemnon]], [[3451&nbsp;Mentor]] and [[3317&nbsp;Paris]], which are similar in size ''(see table below)''. Its low brightness amplitude is indicative of a rather spherical shape.<ref name="lcdb" /> From July 2007 until September 2008, coordinated [[Photometry (astronomy)|photometric]] observations were carried out by astronomers at [[Simeiz Observatory|Simeiz]] (Crimea), [[Rozhen Observatory|Rozhen]] (Bulgaria), Maidanak (Uzbekistan) and [[IAU code#101|Kharkiv]] (Ukraine) observatories.<ref name="Shevchenko-2009a" /><ref name="Stephens-2010c" /> Analysis of the obtained [[lightcurve]]s determined a period of {{val|7.306|0.002}} hours with a brightness amplitude of 0.02–0.11 [[Magnitude (astronomy)|magnitude]] ({{small|[[LCDB quality code|U=3/3/3/3]]}}).<ref name="lcdb" /> Alternative period determinations by Cláudia Angeli (7.0&nbsp;h), [[Robert D. Stephens|Robert Stephens]] (7.312&nbsp;h), [[Stefano Mottola]] (7.32&nbsp;h) and [[Vincenzo Zappalà]] (12&nbsp;h) are mostly in good agreement ({{small|[[LCDB quality code|U=1/3-/3/1]]}}).<ref name="lcdb" /><ref name="Angeli-1999" /><ref name="Stephens-2010c" /><ref name="Mottola-2011" /><ref name="Zappala-1989" />

=== Diameter and albedo ===
According to the surveys carried out by the Infrared Astronomical Satellite, [[IRAS]], the Japanese [[Akari (satellite)|Akari satellite]], and the [[NEOWISE]] mission of NASA's [[Wide-field Infrared Survey Explorer]], the body's surface has a very low [[astronomical albedo|albedo]] in the range of 0.0328 to 0.043, making its [[absolute magnitude]] of approximately 8.57 correspond to a diameter of 130.1 to 135.5&nbsp;kilometers.<ref name="SIMPS" /><ref name="AKARI" /><ref name="Grav-2012" />

Achilles is the 6th largest Jupiter trojan according to IRAS and Akari, and the 4th largest based on NEOWISE data:
{{Largest Jupiter trojans}}

== Naming ==

This [[minor planet]]'s name was suggested by Austrian astronomer [[Johann Palisa]]. It was named after [[Achilles]], the legendary hero from [[Greek mythology]] and central figure in Homer's ''[[Iliad]]'' which tells the accounts of the [[Trojan War]] ''(also see [[5700&nbsp;Homerus]] and [[6604&nbsp;Ilias]])''. As an infant, Achilles was plunged in the River Styx by his mother Thetis ''(also see [[17&nbsp;Thetis]])'', thus rendering his body invulnerable excepting the heel by which he was held. He slew Hector (''see also [[624&nbsp;Hektor]]''), the greatest Trojan warrior. He was eventually killed by an arrow in the heel by Paris (''see [[3317&nbsp;Paris]]'').<ref name="springer" />

== References ==
{{reflist|refs=

<ref name="jpldata">{{cite web
  |type       = 2018-05-25 last obs.
  |title      = JPL Small-Body Database Browser: 588 Achilles (1906 TG)
  |url        = https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=2000588
  |publisher  = [[Jet Propulsion Laboratory]]
  |access-date = 15 June 2018}}</ref>

<ref name="springer">{{cite book
  |last       = Schmadel | first = Lutz D.
  |title = Dictionary of Minor Planet Names |publisher  = [[Springer Berlin Heidelberg]]
  |page       = 61
  |date       = 2007
  |isbn       = 978-3-540-00238-3
  |doi       = 10.1007/978-3-540-29925-7_589 |chapter       = (588) Achilles }}</ref>

<ref name="MPC-object">{{cite web
  |title      = 588 Achilles (1906 TG)
  |work       = Minor Planet Center
  |url        = https://www.minorplanetcenter.net/db_search/show_object?object_id=588
  |access-date = 15 June 2018}}</ref>

<ref name="MPC-Jupiter-Trojans">{{cite web
  |title      = List of Jupiter Trojans
  |work       = Minor Planet Center
  |date       = 20 June 2016
  |url        = https://www.minorplanetcenter.net/iau/lists/JupiterTrojans.html
  |access-date = 15 June 2016}}</ref>

<ref name="Grav-2012">{{cite journal
  |first1     = T. |last1 = Grav
  |first2     = A. K. |last2 = Mainzer
  |first3     = J. M. |last3 = Bauer
  |first4     = J. R. |last4 = Masiero
  |first5     = C. R. |last5 = Nugent
  |date       = November 2012
  |title      = WISE/NEOWISE Observations of the Jovian Trojan Population: Taxonomy
  |journal    = The Astrophysical Journal
  |volume     = 759
  |issue      = 1
  |page       = 10
  |bibcode    = 2012ApJ...759...49G
  |doi        = 10.1088/0004-637X/759/1/49
  |arxiv      = 1209.1549
  |s2cid = 119101711
 }} ([http://vizier.cfa.harvard.edu/viz-bin/VizieR-6?-source=J/ApJ/759/49/table1&MPC=00588 online catalog])</ref>

<ref name="AstDys-object">{{cite web
  |title      = Asteroid (588) Achilles – Proper elements
  |publisher  = AstDyS-2, Asteroids – Dynamic Site
  |url        = https://newton.spacedys.com/astdys/index.php?n=588&pc=1.1.6
  |access-date = 13 June 2018}}</ref>

<ref name="lcdb">{{cite web
  |title      = LCDB Data for (588) Achilles
  |publisher  = Asteroid Lightcurve Database (LCDB)
  |url        = http://www.minorplanet.info/PHP/generateOneAsteroidInfo.php?AstInfo=588%7CAchilles
  |access-date = 2 August 2016}}</ref>

<ref name="large-trojan">{{cite web
 |title       = JPL Small-Body Database Search Engine: orbital class (TJN) and diameter > 50 (km)
 |publisher   = JPL's Solar System Dynamics Group
 |url         = http://ssd.jpl.nasa.gov/sbdb_query.cgi?obj_group=all;obj_kind=all;obj_numbered=all;ast_orbit_class=TJN;OBJ_field=0;ORB_field=0;c1_group=OBJ;c1_item=Ap;c1_op=%3E;c1_value=50;table_format=HTML;max_rows=100;format_option=comp;c_fields=AcBhBgBjBiBnBsAiAp;.cgifields=format_option;.cgifields=ast_orbit_class;.cgifields=table_format;.cgifields=obj_kind;.cgifields=obj_group;.cgifields=obj_numbered;.cgifields=com_orbit_class&query=1&c_sort=ApD |access-date=2012-03-28}}</ref>

<ref name="SIMPS">{{cite journal
  |first1     = E. F. |last1 = Tedesco
  |first2     = P. V. |last2 = Noah
  |first3     = M. |last3 = Noah
  |first4     = S. D. |last4 = Price
  |date       = October 2004
  |title      = IRAS Minor Planet Survey V6.0
  |url        = https://sbnarchive.psi.edu/pds3/iras/IRAS_A_FPA_3_RDR_IMPS_V6_0/data/diamalb.tab
  |journal    = NASA Planetary Data System – IRAS-A-FPA-3-RDR-IMPS-V6.0
  |volume = 12
 |pages = IRAS-A-FPA-3-RDR-IMPS-V6.0
  |bibcode    = 2004PDSS...12.....T
  |access-date = 15 June 2018}}</ref>

<ref name="AKARI">{{cite journal
  |display-authors = 6
  |first1     = Fumihiko |last1 = Usui
  |first2     = Daisuke |last2 = Kuroda
  |first3     = Thomas G. |last3 = Müller
  |first4     = Sunao |last4 = Hasegawa
  |first5     = Masateru |last5 = Ishiguro
  |first6     = Takafumi |last6 = Ootsubo
  |first7     = Daisuke |last7 = Ishihara
  |first8     = Hirokazu |last8 = Kataza
  |first9     = Satoshi |last9 = Takita
  |first10    = Shinki |last10 = Oyabu
  |first11    = Munetaka |last11 = Ueno
  |first12    = Hideo |last12 = Matsuhara
  |first13    = Takashi |last13 = Onaka
  |date       = October 2011
  |title      = Asteroid Catalog Using Akari: AKARI/IRC Mid-Infrared Asteroid Survey
  |journal    = Publications of the Astronomical Society of Japan
  |volume     = 63
  |issue      = 5
  |pages      = 1117–1138
  |bibcode    = 2011PASJ...63.1117U
  |doi        = 10.1093/pasj/63.5.1117
  |doi-access= free
  }} ([http://vizier.cfa.harvard.edu/viz-bin/VizieR-5?-source=J/PASJ/63/1117/acua_v1&Num=588 online], [https://core.ac.uk/download/pdf/43545172.pdf AcuA catalog p. 153])</ref>

<ref name="Zappala-1989">{{cite journal
  |first1     = V. |last1 = Zappala
  |first2     = M. |last2 = di Martino
  |first3     = A. |last3 = Cellino
  |first4     = G. |last4 = de Sanctis
  |first5     = P. |last5 = Farinella
  |date       = December 1989
  |title      = Rotational properties of outer belt asteroids
  |url        = http://adsabs.harvard.edu/cgi-bin/bib_query?bibcode=1989Icar...82..354Z
  |journal    = Icarus
  |volume = 82
  |issue = 2
  |pages      = 354–368.ResearchsupportedbyCNRandMPI
  |issn       = 0019-1035
  |bibcode    = 1989Icar...82..354Z
  |doi        = 10.1016/0019-1035(89)90043-2
  |access-date= 1 January 2016}}</ref>

<ref name="Angeli-1999">{{cite journal
  |first1     = C. A. |last1 = Angeli
  |first2     = D. |last2 = Lazzaro
  |first3     = M. A. |last3 = Florczak
  |first4     = A. S. |last4 = Betzler
  |first5     = J. M. |last5 = Carvano
  |date       = May 1999
  |title      = A contribution to the study of asteroids with longrotational period
  |url        = http://adsabs.harvard.edu/cgi-bin/bib_query?bibcode=1999P&SS...47..699A
  |journal    = Planetary and Space Science
  |volume     = 47
  |issue      = 5
  |pages      = 699–714
  |bibcode    = 1999P&SS...47..699A
  |doi        = 10.1016/S0032-0633(98)00122-6
  |access-date= 1 January 2016}}</ref>

<ref name="Shevchenko-2009a">{{cite journal
  |display-authors = 6
  |first1     = V. G. |last1 = Shevchenko
  |first2     = Yu. N. |last2 = Krugly
  |first3     = I. N. |last3 = Belskaya
  |first4     = V. G. |last4 = Chiorny
  |first5     = N. M. |last5 = Gaftonyuk
  |first6     = I. G. |last6 = Slyusarev
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  |first9     = V. |last9 = Ivanova
  |first10    = G. |last10 = Borisov
  |first11    = M. A. |last11 = Ibrahimov
  |first12    = A. L. |last12 = Marshalkina
  |first13    = I. E. |last13 = Molotov
  |date       = March 2009
  |title      = Do Trojan Asteroids Have the Brightness Opposition Effect?
  |url        = https://www.lpi.usra.edu/meetings/lpsc2009/pdf/1391.pdf
  |journal    = 40th Lunar and Planetary Science Conference
  |pages     = 1391 |bibcode    = 2009LPI....40.1391S
  |access-date = 15 June 2018}}</ref>

<ref name="Stephens-2010c">{{cite journal
  |author     = Stephens, Robert D.
  |date       = April 2010
  |title      = Trojan Asteroids Observed from GMARS and Santana Observatories: 2009 October - December
  |url        = http://adsabs.harvard.edu/cgi-bin/bib_query?bibcode=2010MPBu...37...47S
  |journal    = The Minor Planet Bulletin
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  |issue      = 2
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  |issn       = 1052-8091
  |bibcode    = 2010MPBu...37...47S
  |access-date= 1 January 2016}}</ref>

<ref name="Mottola-2011">{{cite journal
  |display-authors = 6
  |first1     = Stefano |last1 = Mottola
  |first2     = Mario |last2 = Di Martino
  |first3     = Anders |last3 = Erikson
  |first4     = Maria |last4 = Gonano-Beurer
  |first5     = Albino |last5 = Carbognani
  |first6     = Uri |last6 = Carsenty
  |first7     = Gerhard |last7 = Hahn
  |first8     = Hans-Josef |last8 = Schober
  |first9     = Felix |last9 = Lahulla
  |first10    = Marco |last10 = Delbò
  |first11    = Claes-Ingvar |last11 = Lagerkvist
  |date       = May 2011
  |title      = Rotational Properties of Jupiter Trojans. I. Light Curves of 80 Objects
  |journal    = The Astronomical Journal
  |volume     = 141
  |issue      = 5
  |page       = 32
  |bibcode    = 2011AJ....141..170M
  |doi        = 10.1088/0004-6256/141/5/170
  |doi-access= free
  }}</ref>

<ref name="Shevchenko-2012a">{{cite journal
  |display-authors = 6
  |first1     = V. G. |last1 = Shevchenko
  |first2     = I. N. |last2 = Belskaya
  |first3     = I. G. |last3 = Slyusarev
  |first4     = Yu. N. |last4 = Krugly
  |first5     = V. G. |last5 = Chiorny
  |first6     = N. M. |last6 = Gaftonyuk
  |first7     = Z. |last7 = Donchev
  |first8     = V. |last8 = Ivanova
  |first9     = M. A. |last9 = Ibrahimov
  |first10    = Sh. A. |last10 = Ehgamberdiev
  |first11    = I. E. |last11 = Molotov
  |date       = January 2012
  |title      = Opposition effect of Trojan asteroids
  |url        = http://adsabs.harvard.edu/cgi-bin/bib_query?bibcode=2012Icar..217..202S
  |journal    = Icarus
  |volume     = 217
  |issue      = 1
  |pages      = 202–208
  |bibcode    = 2012Icar..217..202S
  |doi        = 10.1016/j.icarus.2011.11.001
  |access-date= 1 January 2016}}</ref>

}} <!-- end of reflist -->

== External links ==
* [http://www.minorplanet.info/PHP/lcdbsummaryquery.php Asteroid Lightcurve Database (LCDB)], query form ([http://www.minorplanet.info/lightcurvedatabase.html info] {{Webarchive|url=https://web.archive.org/web/20171216050541/http://www.minorplanet.info/lightcurvedatabase.html |date=16 December 2017 }})
* [https://books.google.com/books?id=aeAg1X7afOoC&pg Dictionary of Minor Planet Names], Google books
* [https://www.minorplanetcenter.net/iau/lists/NumberedMPs000001.html Discovery Circumstances: Numbered Minor Planets (1)-(5000)] – Minor Planet Center
* [https://sbntools.psi.edu/ferret/SimpleSearch/results.action?targetName=588 Asteroid 588 Achilles] {{Webarchive|url=https://web.archive.org/web/20230310121234/https://sbntools.psi.edu/ferret/SimpleSearch/results.action?targetName=588 |date=10 March 2023 }}, at the Small Bodies Data Ferret
* {{AstDys|588}}
* {{JPL small body}}

{{Minor planets navigator|587 Hypsipyle|number=588|589 Croatia}}
{{Authority control}}

{{DEFAULTSORT:Achilles}}
[[Category:Jupiter trojans (Greek camp)|000588]]
[[Category:Discoveries by Max Wolf]]
[[Category:Named minor planets]]
[[Category:DU-type asteroids (Tholen)|000588]]
[[Category:Astronomical objects discovered in 1906|19060222]]