Astronomy:1437 Diomedes

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Short description: Trojan asteroid
1437 Diomedes
001437-asteroid shape model (1437) Diomedes.png
Modelled shape of Diomedes from its light curve
Discovery[1]
Discovered byK. Reinmuth
Discovery siteHeidelberg Obs.
Discovery date3 August 1937
Designations
(1437) Diomedes
Pronunciation/ˌdəˈmdz/[7]
Named afterDiomedes[2]
(Greek mythology)
1937 PB · 1931 DN
1936 PQ · 1971 RD
Minor planet categoryJupiter trojan[1][3][4]
Greek[5][6] · background[6]
AdjectivesDiomedian
Orbital characteristics[3]
Epoch 23 March 2018 (JD 2458200.5)
Uncertainty parameter 0
Observation arc80.80 yr (29,514 d)
|{{{apsis}}}|helion}}5.4248 AU
|{{{apsis}}}|helion}}4.9720 AU
5.1984 AU
Eccentricity0.0435
Orbital period11.85 yr (4,329 d)
Mean anomaly234.43°
Mean motion0° 4m 59.52s / day
Inclination20.485°
Longitude of ascending node315.80°
130.93°
Jupiter MOID0.275 AU
TJupiter2.8720
Physical characteristics
Dimensions284 km × 126 km × 65 km[8][9]
Mean diameter117.79±1.18 km[10]
132.5 km[9]
164.31±4.1 km[11]
172.60±3.42 km[12]
173.0 km[8]
Rotation period16 h[13]
18 h[14]
21 h[15]
24.46 h[9]
24.49±0.01 h[16][17]
Geometric albedo0.028±0.001[12]
0.0313±0.002[11]
0.061±0.011[10]
Tholen = DP[3][4][8]
U–B = 0.250±040[8]
B–V = 0.700±014[8]
V–I = 0.810±0.025[4]
Absolute magnitude (H)8.18±0.28[18]
8.30[1][3][4][10][11][12]


1437 Diomedes /ˌdəˈmdz/ is a large Jupiter trojan from the Greek camp, approximately 150 kilometers (90 miles) in diameter. It was discovered on 3 August 1937, by astronomer Karl Reinmuth at the Heidelberg-Königstuhl State Observatory in southwest Germany.[1] The dark D/P-type asteroid belongs to the largest Jupiter trojans and has a notably elongated shape and a longer than average rotation period of 24.49 hours.[4] Diomedes was the first Jupiter trojan successfully observed during an occultation event of star.[9] It was named after the hero Diomedes from Greek mythology.[2]

Orbit and classification

Diomedes is a dark Jovian asteroid orbiting in the leading Greek camp at Jupiter's L4 Lagrangian point, 60° ahead of the Gas Giant's orbit in a 1:1 resonance (see Trojans in astronomy). It is also a non-family asteroid in the Jovian background population.[6] Jupiter trojans are thought to have been captured into their orbits during or shortly after the early stages of the formation of the Solar System. More than 4,500 Jupiter trojans in the Greek camp have already been discovered.[5]

It orbits the Sun at a distance of 5.0–5.4 AU once every 11 years and 10 months (4,329 days; semi-major axis of 5.2 AU). Its orbit has an eccentricity of 0.04 and an inclination of 20° with respect to the ecliptic.[3] The asteroid was first observed as 1931 DN at Lowell Observatory in February 1931. The body's observation arc begins at Heidelberg with its official discovery observation in August 1937.[1]

Physical characteristics

In the Tholen classification, Diomedes has an ambiguous spectral type, closest to the dark D-type asteroids and somewhat similar to the primitive P-type asteroids.[3] Its V–I color index of 0.810 is also lower than that measured for most D-type Jupiter trojans (0.95).[4]

Rotation period

Several rotational lightcurves of Diomedes have been obtained from photometric observations since the 1960s.[9][13][14][15][16] The so-far best-rated photometric observations by Robert Stephens at the Goat Mountain Astronomical Research Station (G79) and Santana Observatory (646) in November 2008, gave a longer-than average rotation period of 24.49±0.01 hours with a brightness variation of 0.34 magnitude ({{{1}}}).[17]

Diameter and albedo

In the 1970s, radiometric observations were published in the Tucson Revised Index of Asteroid Data (TRIAD) compilation gave a diameter of 173.0 kilometers with a radiometric albedo 0.021.[8]

According to the space-based surveys carried out by the Infrared Astronomical Satellite IRAS, the Japanese Akari satellite and the NEOWISE mission of NASA's Wide-field Infrared Survey Explorer, Diomedes measures between 117.786 and 172.60 kilometers in diameter and its surface has an albedo between 0.028 and 0.061.[10][11][12] The Collaborative Asteroid Lightcurve Link adopts the results obtained by IRAS, that is, an albedo of 0.0313 and a diameter of 164.31 kilometers based on an absolute magnitude of 8.30.[4] The Collaborative Asteroid Lightcurve Link adopts the results obtained by IRAS, that is, an albedo of 0.0313 and a diameter of 164.31 kilometers based on an absolute magnitude of 8.30.[4]

Diomedes is the third largest Jupiter trojan according to IRAS and Akari, and the 9th largest based on NEOWISE data:

100+ largest Jupiter trojans
Largest Jupiter Trojans by survey(A)
(mean-diameter in kilometers; YoD: Year of Discovery)
Designation H WISE IRAS Akari Ln RP V–I YoD Ref
624 Hektor 7.2 225 233 230.99 L4 6.92 0.930 1907 list
617 Patroclus 8.19 140.362 140.92 140.85 L5 102.80 0.830 1906 list
911 Agamemnon 7.89 131.038 166.66 185.30 L4 6.59 0.980 1919 list
588 Achilles 8.67 130.099 135.47 133.22 L4 7.31 0.940 1906 list
3451 Mentor 8.4 126.288 116.30 117.91 L5 7.70 0.770 1984 list
3317 Paris 8.3 118.790 116.26 120.45 L5 7.09 0.950 1984 list
1867 Deiphobus 8.3 118.220 122.67 131.31 L5 58.66 0.930 1971 list
1172 Äneas 8.33 118.020 142.82 148.66 L5 8.71 0.950 1930 list
1437 Diomedes 8.3 117.786 164.31 172.60 L4 24.49 0.810 1937 list
1143 Odysseus 7.93 114.624 125.64 130.81 L4 10.11 0.860 1930 list
2241 Alcathous 8.64 113.682 114.63 118.87 L5 7.69 0.940 1979 list
659 Nestor 8.99 112.320 108.87 107.06 L4 15.98 0.790 1908 list
3793 Leonteus 8.7 112.046 86.26 87.58 L4 5.62 0.780 1985 list
3063 Makhaon 8.4 111.655 116.14 114.34 L4 8.64 0.830 1983 list
1583 Antilochus 8.6 108.842 101.62 111.69 L4 31.54 0.950 1950 list
884 Priamus 8.81 101.093 96.29 119.99 L5 6.86 0.900 1917 list
1208 Troilus 8.99 100.477 103.34 111.36 L5 56.17 0.740 1931 list
1173 Anchises 8.89 99.549 126.27 120.49 L5 11.60 0.780 1930 list
2207 Antenor 8.89 97.658 85.11 91.32 L5 7.97 0.950 1977 list
2363 Cebriones 9.11 95.976 81.84 84.61 L5 20.05 0.910 1977 list
4063 Euforbo 8.7 95.619 102.46 106.38 L4 8.85 0.950 1989 list
2357 Phereclos 8.94 94.625 94.90 98.45 L5 14.39 0.960 1981 list
4709 Ennomos 8.5 91.433 80.85 80.03 L5 12.28 0.690 1988 list
2797 Teucer 8.7 89.430 111.14 113.99 L4 10.15 0.920 1981 list
2920 Automedon 8.8 88.574 111.01 113.11 L4 10.21 0.950 1981 list
(15436) 1998 VU30 9.1 87.646 85.71 78.63 L4 8.97 0.870 1998 list
3596 Meriones 9.2 87.380 75.09 73.28 L4 12.96 0.830 1985 list
2893 Peiroos 9.23 86.884 87.46 86.76 L5 8.96 0.950 1975 list
4086 Podalirius 9.1 85.495 86.89 85.98 L4 10.43 0.870 1985 list
4060 Deipylos 9.3 84.043 79.21 86.79 L4 9.30 0.760 1987 list
1404 Ajax 9.3 83.990 81.69 96.34 L4 29.38 0.960 1936 list
4348 Poulydamas 9.5 82.032 70.08 87.51 L5 9.91 0.840 1988 list
5144 Achates 9.0 80.958 91.91 89.85 L5 5.96 0.920 1991 list
4833 Meges 8.9 80.165 87.33 89.39 L4 14.25 0.940 1989 list
2223 Sarpedon 9.41 77.480 94.63 108.21 L5 22.74 0.880 1977 list
(4489) 1988 AK 9.0 76.595 92.93 95.02 L4 12.58 0.950 1988 list
2260 Neoptolemus 9.31 76.435 71.65 81.28 L4 8.18 0.950 1975 list
5254 Ulysses 9.2 76.147 78.34 80.00 L4 28.72 0.970 1986 list
(3708) 1974 FV1 9.3 75.661 79.59 76.75 L5 6.55 0.980 1974 list
2674 Pandarus 9.1 74.267 98.10 101.72 L5 8.48 1.000 1982 list
3564 Talthybius 9.4 73.730 68.92 74.11 L4 40.59 0.900 1985 list
4834 Thoas 9.1 72.331 86.82 96.21 L4 18.19 0.950 1989 list
(7641) 1986 TT6 9.4 71.839 68.97 75.28 L4 27.77 0.980 1986 list
3540 Protesilaos 9.3 70.225 76.84 87.66 L4 8.95 0.940 1973 list
(11395) 1998 XN77 9.8 68.977 64.71 67.78 L4 17.38 1998 list
(4035) 1986 WD 9.6 68.733 68.23 66.99 L4 13.47 0.970 1986 list
5264 Telephus 9.4 68.472 73.26 81.38 L4 9.53 0.970 1991 list
1868 Thersites 9.5 68.163 70.08 78.89 L4 10.48 0.960 1960 list
(9799) 1996 RJ 9.6 68.033 64.87 72.42 L4 21.52 0.910 1996 list
4068 Menestheus 9.5 67.625 62.37 68.46 L4 14.40 0.950 1973 list
(23135) 2000 AN146 9.9 66.230 58.29 68.50 L4 8.69 0.860 2000 list
2456 Palamedes 9.3 65.916 91.66 99.60 L4 7.24 0.920 1966 list
3709 Polypoites 9.1 65.297 99.09 85.23 L4 10.04 1.000 1985 list
1749 Telamon 9.5 64.898 81.06 69.14 L4 16.98 0.970 1949 list
3548 Eurybates 9.6 63.885 72.14 68.40 L4 8.71 0.730 1973 list
4543 Phoinix 9.7 63.836 62.79 69.54 L4 38.87 1.200 1989 list
12444 Prothoon 9.8 63.835 64.31 62.41 L5 15.82 1996 list
4836 Medon 9.5 63.277 67.73 78.70 L4 9.82 0.920 1989 list
(16070) 1999 RB101 9.7 63.191 64.13 68.98 L5 20.24 0.960 1999 list
(15440) 1998 WX4 9.6 62.519 66.48 71.88 L4 21.43 0.970 1998 list
(4715) 1989 TS1 9.7 62.097 63.91 65.93 L5 8.81 0.850 1989 list
(34746) 2001 QE91 9.8 61.684 60.51 63.63 L5 19.63 0.950 2001 list
(38050) 1998 VR38 9.8 61.603 61.04 50.44 L4 18.85 0.990 1998 list
5130 Ilioneus 9.7 60.711 59.40 52.49 L5 14.77 0.960 1989 list
5027 Androgeos 9.6 59.786 57.86 n.a. L4 11.38 0.910 1988 list
(6090) 1989 DJ 9.4 59.568 74.53 81.92 L4 18.48 0.980 1989 list
(5648) 1990 VU1 9.7 59.295 63.91 n.a. L5 37.56 0.900 1990 list
7119 Hiera 9.7 59.150 76.40 77.29 L4 400 0.950 1989 list
4805 Asteropaios 10.0 57.647 53.16 43.44 L5 12.37 1990 list
16974 Iphthime 9.8 57.341 55.43 57.15 L4 78.9 0.960 1998 list
4867 Polites 9.8 57.251 58.29 64.29 L5 11.24 1.010 1989 list
2895 Memnon 10.0 56.706 55.67 n.a. L5 7.50 0.710 1981 list
4708 Polydoros 9.9 54.964 55.67 n.a. L5 7.52 0.960 1988 list
(21601) 1998 XO89 10.0 54.909 55.67 56.08 L4 12.65 0.970 1998 list
(12929) 1999 TZ1 9.9 54.077 61.04 55.34 L5 9.27 0.880 1999 list
17492 Hippasos 10.0 53.975 55.67 n.a. L5 17.75 1991 list
5652 Amphimachus 10.1 53.921 53.16 52.48 L4 8.37 1.050 1992 list
2759 Idomeneus 9.9 53.676 61.01 52.55 L4 32.38 0.910 1980 list
(5258) 1989 AU1 10.2 53.275 50.77 n.a. L4 19.85 1.010 1989 list
(12126) 1999 RM11 10.1 53.202 n.a. n.a. L5 n.a. ? 1999 list
(15502) 1999 NV27 10.0 53.100 55.67 50.86 L5 15.13 0.875 1999 list
4754 Panthoos 10.0 53.025 53.15 56.96 L5 27.68 1977 list
4832 Palinurus 10.0 52.058 53.16 n.a. L5 5.32 1.000 1988 list
5126 Achaemenides 10.5 51.922 44.22 48.57 L4 53.02 1989 list
3240 Laocoon 10.2 51.695 50.77 n.a. L5 11.31 0.880 1978 list
4902 Thessandrus 9.8 51.263 61.04 71.79 L4 738 0.960 1989 list
11552 Boucolion 10.1 51.136 53.16 53.91 L5 32.44 1993 list
(20729) 1999 XS143 10.4 50.961 46.30 n.a. L4 5.72 1.000 1999 list
(6545) 1986 TR6 10.1 50.951 53.16 n.a. L4 16.26 0.910 1986 list
4792 Lykaon 10.1 50.870 53.16 n.a. L5 40.09 0.960 1988 list
21900 Orus 10.0 50.810 55.67 53.87 L4 13.45 0.950 1999 list
1873 Agenor 10.1 50.799 53.76 54.38 L5 20.60 1971 list
5028 Halaesus 10.2 50.770 50.77 n.a. L4 24.94 0.900 1988 list
2146 Stentor 9.9 50.755 58.29 n.a. L4 16.40 1976 list
4722 Agelaos 10.0 50.378 53.16 59.47 L5 18.44 0.910 1977 list
5284 Orsilocus 10.1 50.159 53.16 n.a. L4 10.31 0.970 1989 list
11509 Thersilochos 10.1 49.960 53.16 56.23 L5 17.37 1990 list
5285 Krethon 10.1 49.606 58.53 52.61 L4 12.04 1.090 1989 list
4791 Iphidamas 10.1 49.528 57.85 59.96 L5 9.70 1.030 1988 list
9023 Mnesthus 10.1 49.151 50.77 60.80 L5 30.66 1988 list
5283 Pyrrhus 9.7 48.356 64.58 69.93 L4 7.32 0.950 1989 list
4946 Askalaphus 10.2 48.209 52.71 66.10 L4 22.73 0.940 1988 list
(22149) 2000 WD49 10.2 48.190 50.77 50.37 L4 7.84 1.090 2000 list
(32496) 2000 WX182 10.2 48.017 50.77 51.63 L5 23.34 0.950 2000 list
5120 Bitias 10.2 47.987 50.77 n.a. L5 15.21 0.780 1988 list
12714 Alkimos 10.1 47.819 61.04 54.62 L4 28.48 1991 list
(7352) 1994 CO 9.9 47.731 55.67 47.07 L5 648 0.850 1994 list
1870 Glaukos 10.6 47.649 42.23 n.a. L5 5.99 1971 list
4138 Kalchas 10.1 46.462 53.16 61.04 L4 29.2 0.810 1973 list
(23958) 1998 VD30 10.2 46.001 50.77 47.91 L4 562 0.990 1998 list
4828 Misenus 10.4 45.954 46.30 43.22 L5 12.87 0.920 1988 list
4057 Demophon 10.1 45.683 53.16 n.a. L4 29.82 1.060 1985 list
4501 Eurypylos 10.4 45.524 46.30 n.a. L4 6.05 1989 list
4007 Euryalos 10.3 45.515 48.48 53.89 L4 6.39 1973 list
5259 Epeigeus 10.3 44.741 42.59 44.42 L4 18.42 1989 list
30705 Idaios 10.4 44.546 46.30 n.a. L5 15.74 1977 list
16560 Daitor 10.7 43.861 51.42 43.38 L5 1991 list
(15977) 1998 MA11 10.4 43.530 46.30 51.53 L5 250 0.906 1998 list
7543 Prylis 10.6 42.893 42.23 n.a. L4 17.80 1973 list
4827 Dares 10.5 42.770 44.22 n.a. L5 19.00 1988 list
1647 Menelaus 10.5 42.716 44.22 n.a. L4 17.74 0.866 1957 list
(A) Used sources: WISE/NEOWISE catalog (NEOWISE_DIAM_V1 PDS, Grav, 2012); IRAS data (SIMPS v.6 catalog); and Akari catalog (Usui, 2011); RP: rotation period and V–I (color index) taken from the LCDB

Note: missing data was completed with figures from the JPL SBDB (query) and from the LCDB (query form) for the WISE/NEOWISE and SIMPS catalogs, respectively. These figures are given in italics. Also, listing is incomplete above #100.

Occultation and shape

Diomedes was the first Jupiter trojan that was successfully observed during an asteroid occultation, when it occulted the star HIP 014402A over Japan on 7 November 1997. The silhouette was elongated with a major and minor occultation axis of 284 × 126 kilometers (poor fit).[8][9] The ellipsoid dimensions of 284 × 126 × 65 kilometers – corresponding to a mean-diameter of 132.5 kilometers, equivalent to the volume of a sphere – were estimated using follow-up photometry at Ondřejov Observatory and Mitaka Observatory (388) that determined the body's rotational phase at the exact time of the occultation event.[9]

Naming

This minor planet was named from Greek mythology after the hero Diomedes, King of Argos and known for his participation in the Trojan War, regarded as the best warriors of the Achaeans, just behind Achilles and alongside Ajax. The official naming citation was mentioned in The Names of the Minor Planets by Paul Herget in 1955 (H 129).[2]

References

  1. 1.0 1.1 1.2 1.3 1.4 "1437 Diomedes (1937 PB)". Minor Planet Center. https://www.minorplanetcenter.net/db_search/show_object?object_id=1437. 
  2. 2.0 2.1 2.2 Schmadel, Lutz D. (2007). "(1437) Diomedes". Dictionary of Minor Planet Names. Springer Berlin Heidelberg. p. 115. doi:10.1007/978-3-540-29925-7_1438. ISBN 978-3-540-00238-3. 
  3. 3.0 3.1 3.2 3.3 3.4 3.5 "JPL Small-Body Database Browser: 1437 Diomedes (1937 PB)". Jet Propulsion Laboratory. https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=2001437. 
  4. 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 "LCDB Data for (1437) Diomedes". Asteroid Lightcurve Database (LCDB). http://www.minorplanet.info/PHP/generateOneAsteroidInfo.php?AstInfo=1437%7CDiomedes. 
  5. 5.0 5.1 "List of Jupiter Trojans". Minor Planet Center. 7 October 2017. https://www.minorplanetcenter.net/iau/lists/JupiterTrojans.html. 
  6. 6.0 6.1 6.2 "Asteroid (1437) Diomedes – Proper elements". AstDyS-2, Asteroids – Dynamic Site. https://newton.spacedys.com/astdys/index.php?n=1437&pc=1.1.6. 
  7. "Diomedes". Merriam-Webster Dictionary. https://www.merriam-webster.com/dictionary/Diomedes. 
  8. 8.0 8.1 8.2 8.3 8.4 8.5 8.6 "Asteroid 1437 Diomedes". Small Bodies Data Ferret. https://sbntools.psi.edu/ferret/SimpleSearch/results.action?targetName=1437+Diomedes. 
  9. 9.0 9.1 9.2 9.3 9.4 9.5 9.6 Sato, Isao; Sarounová, Lenka; Fukushima, Hideo (May 2000). "Size and Shape of Trojan Asteroid Diomedes from Its Occultation and Photometry". Icarus 145 (1): 25–32. doi:10.1006/icar.1999.6316. Bibcode2000Icar..145...25S. http://adsabs.harvard.edu/cgi-bin/bib_query?bibcode=2000Icar..145...25S. Retrieved 26 October 2017. 
  10. 10.0 10.1 10.2 10.3 Grav, T.; Mainzer, A. K.; Bauer, J. M.; Masiero, J. R.; Nugent, C. R. (November 2012). "WISE/NEOWISE Observations of the Jovian Trojan Population: Taxonomy". The Astrophysical Journal 759 (1): 10. doi:10.1088/0004-637X/759/1/49. Bibcode2012ApJ...759...49G.  (online catalog)
  11. 11.0 11.1 11.2 11.3 Tedesco, E. F.; Noah, P. V.; Noah, M.; Price, S. D. (October 2004). "IRAS Minor Planet Survey V6.0". NASA Planetary Data System – IRAS-A-FPA-3-RDR-IMPS-V6.0: IRAS-A-FPA-3-RDR-IMPS-V6.0. Bibcode2004PDSS...12.....T. https://sbnarchive.psi.edu/pds3/iras/IRAS_A_FPA_3_RDR_IMPS_V6_0/data/diamalb.tab. Retrieved 15 June 2018. 
  12. 12.0 12.1 12.2 12.3 Usui, Fumihiko; Kuroda, Daisuke; Müller, Thomas G.; Hasegawa, Sunao; Ishiguro, Masateru; Ootsubo, Takafumi et al. (October 2011). "Asteroid Catalog Using Akari: AKARI/IRC Mid-Infrared Asteroid Survey". Publications of the Astronomical Society of Japan 63 (5): 1117–1138. doi:10.1093/pasj/63.5.1117. Bibcode2011PASJ...63.1117U.  (online, AcuA catalog p. 153)
  13. 13.0 13.1 Binzel, Richard P.; Sauter, Linda M. (February 1992). "Trojan, Hilda, and Cybele asteroids – New lightcurve observations and analysis". Icarus 95 (2): 222–238. doi:10.1016/0019-1035(92)90039-A. ISSN 0019-1035. Bibcode1992Icar...95..222B. http://adsabs.harvard.edu/cgi-bin/bib_query?bibcode=1992Icar...95..222B. Retrieved 26 October 2017. 
  14. 14.0 14.1 Taylor, Ronald C. (December 1970). "Photometric Observations and Reductions of Lightcurves of Asteroids". Physical Studies of Minor Planets 267: 117–131. Bibcode1971NASSP.267..117T. http://adsabs.harvard.edu/cgi-bin/bib_query?bibcode=1971NASSP.267..117T. Retrieved 26 October 2017. 
  15. 15.0 15.1 Dunlap, J. L.; Gehrels, T. (August 1969). "Minor Planets. III. Lightcurves of a Trojan Asteroid". Astronomical Journal 74: 796. doi:10.1086/110860. Bibcode1969AJ.....74..796D. http://adsabs.harvard.edu/cgi-bin/bib_query?bibcode=1969AJ.....74..796D. Retrieved 26 October 2017. 
  16. 16.0 16.1 Mottola, Stefano; Di Martino, Mario; Erikson, Anders; Gonano-Beurer, Maria; Carbognani, Albino; Carsenty, Uri et al. (May 2011). "Rotational Properties of Jupiter Trojans. I. Light Curves of 80 Objects". The Astronomical Journal 141 (5): 32. doi:10.1088/0004-6256/141/5/170. Bibcode2011AJ....141..170M. 
  17. 17.0 17.1 Stephens, Robert D. (April 2009). "Asteroids Observed from GMARS and Santana Observatories". The Minor Planet Bulletin 36 (2): 59–62. ISSN 1052-8091. Bibcode2009MPBu...36...59S. http://adsabs.harvard.edu/cgi-bin/bib_query?bibcode=2009MPBu...36...59S. Retrieved 26 October 2017. 
  18. Veres, Peter; Jedicke, Robert; Fitzsimmons, Alan; Denneau, Larry; Granvik, Mikael; Bolin, Bryce et al. (November 2015). "Absolute magnitudes and slope parameters for 250,000 asteroids observed by Pan-STARRS PS1 – Preliminary results". Icarus 261: 34–47. doi:10.1016/j.icarus.2015.08.007. Bibcode2015Icar..261...34V. 

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