Astronomy:1647 Menelaus

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1647 Menelaus
Discovery[1]
Discovered byS. B. Nicholson
Discovery sitePalomar Obs.
Discovery date23 June 1957
Designations
(1647) Menelaus
Pronunciation/mɛnəˈleɪəs/[6]
Named afterMenelaus[2]
(Greek mythology)
1957 MK
Minor planet categoryJupiter trojan[1][3]
Greek[4] · background[5]
AdjectivesMenelaian
Orbital characteristics[3]
Epoch 23 March 2018 (JD 2458200.5)
Uncertainty parameter 0
Observation arc65.57 yr (23,949 d)
|{{{apsis}}}|helion}}5.3255 AU
|{{{apsis}}}|helion}}5.1006 AU
5.2130 AU
Eccentricity0.0216
Orbital period11.90 yr (4,347 d)
Mean anomaly101.16°
Mean motion0° 4m 58.08s / day
Inclination5.6507°
Longitude of ascending node240.32°
298.95°
Jupiter MOID0.1563 AU
TJupiter2.9900
Physical characteristics
Mean diameter42.72±0.517 km[7]
Rotation period17.74±0.01 h[8]
Geometric albedo0.056±0.009[7]
C (assumed)[9]
V–R = 0.428±0.043[10]
V–I = 0.866±0.043[10]
Absolute magnitude (H)10.5[1][3][9]


1647 Menelaus /mɛnəˈleɪəs/ is a mid-sized Jupiter trojan from the Greek camp, approximately 42 kilometers (26 miles) in diameter. It was discovered on 23 June 1957 by American astronomer Seth Nicholson at the Palomar Observatory in California, and later named after the Spartan King Menelaus from Greek mythology.[1][2] The dark asteroid has a rotation period of 17.7 hours.[9] It is the principal body of the proposed Menelaus cluster, which encompasses several, mostly tentative Jovian asteroid families.

Orbit and classification

Menelaus is a dark Jovian asteroid in a 1:1 orbital resonance with Jupiter. It is located in the leading Greek camp at the Gas Giant's L4 Lagrangian point, 60° ahead on its orbit (see Trojans in astronomy). Since the discovery of the first Jupiter trojan, 588 Achilles, by astronomer Max Wolf in 1906, more than 7000 Jovian asteroids have already been discovered.[4]

It orbits the Sun at a distance of 5.1–5.3 AU once every 11 years and 11 months (4,347 days; semi-major axis of 5.21 AU). Its orbit has an eccentricity of 0.02 and an inclination of 6° with respect to the ecliptic.[3] Menelaus was first imaged at Palomar in November 1951. This precovery extends the body's observation arc by more than 5 years prior to its official discovery observation.[1]

Menelaus cluster

In 1993, Andrea Milani suggested that Menelaus might be the parent body of an asteroid family based on a modified HCM-analysis.[11]:78 The finding was also mentioned by David Jewitt in 2004,[12]:12 who noted that the Menelaus family is the largest proposed dynamical family to exist among the Jupiter trojans, despite having only 8 members.[lower-alpha 1]

In 2008, Fernando Roig and Ricardo Gil-Hutton described this particular aggregation of Jupiter trojans as the "Menelaus clan", which, similar to the Flora family in the inner asteroid belt, is composed of several families (or subfamilies).[13]:9 In this publication, the Menelaus clan encompasses a dozen clusters, if the separation criteria used in the HCM analysis are sufficiently relaxed. The principal bodies of these proposed family-like clusters include: 1647 Menelaus, 3548 Eurybates, 1749 Telamon, 12973 Melanthios, 13062 Podarkes, 5436 Eumelos, 2148 Epeios, 4007 Euryalos, 4138 Kalchas, 3063 Makhaon and others.[13]:10

With the exception of the Eurybates family, which was studies in more detail by Jakub Rozehnal and Miroslav Brož in 2011 (also see 3548 Eurybates § Eurybates family), all other proposed families with their principal bodies in the Menelaus clan, including Menelaus itself,[5] are tentative and not listed neither on the Asteroids—Dynamic Site (Milani and Knežević), nor included in the robust HCM-analysis by Nesvorný (also see Asteroid family § All families).[14]:23 Instead, these bodies are considered non-family asteroids of the Jovian background population.

Naming

This minor planet was named after the Greek mythological figure, Menelaus, husband of Helen of Troy, brother of Agamemnon, and king and leader of the Spartan contingent of the Greek army during the Trojan War. The discoverer followed the convention to name bodies located in the camp to the east of Jupiter after famous Greek heroes.

The Dictionary of Minor Planet Names also mentions that the lunar crater Menelaus was named after the Greek hero.[2] However, based on the official International Astronomical Union–WGPSN nomenclature, it is named after Greek geometer and astronomer Menelaus of Alexandria (70–140).[15] The official naming citation was published by the Minor Planet Center in June 1960 (M.P.C. 2019).[16]

Physical characteristics

Menelaus is an assumed C-type, while most larger Jupiter trojans are D-type asteroids. It has a V–I color index of 0.866.[9][10]

Rotation period

The Palomar Transient Factory in California obtained a rotational lightcurve of Menelaus from photometric observation in the R-band in October 2010. It gave a rotation period of 17.7390 hours with a brightness variation of 0.32 magnitude in the R-band ({{{1}}}).[9][17] In February 2014, a refined period of 17.74±0.01 hours with an amplitude of 0.15 magnitude was determined by American astronomer Robert D. Stephens at the Center for Solar System Studies ({{{1}}}).[8][lower-alpha 2]

Diameter and albedo

According to the survey carried out by NASA's Wide-field Infrared Survey Explorer with its subsequent NEOWISE mission, Menelaus measures 42.72 kilometers in diameter and its surface has an albedo of 0.056.[7] The Collaborative Asteroid Lightcurve Link assumes a standard albedo for carbonaceous asteroids of 0.057 and calculates a diameter of 44.22 kilometers using an absolute magnitude of 10.5.[9]

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.

Notes

  1. ↑ Members of the Menelaus cluster identified by Milani in 1993 are 1749 Telamon, 3548 Eurybates, (6053) 1993 BW3, 6076 Plavec, (6002) 1988 RO, 6051 Anaximenes and 6006 Anaximandros, some of which are main-belt or Amor asteroids (Milani 1993, p. 94). Besides the Menelaus family, Milani found four other potential families in the Greek camp, clustered around the Jovian asteroids 1437 Diomedes, 2456 Palamedes, 2797 Teucer and (4035) 1986 WD, as well as the asteroid pair 1583 Antilochus—3801 Thrasymedes.
  2. ↑ Lightcurve plots of (1647) Menelaus from Jan–Feb 2014 by Robert Stephens at the Center for Solar System Studies (U81). Quality code is 3- (lightcurve rating at CS3). Summary figures at the LCDB and CS3.

References

  1. ↑ 1.0 1.1 1.2 1.3 1.4 "1647 Menelaus (1957 MK)". Minor Planet Center. https://www.minorplanetcenter.net/db_search/show_object?object_id=1647. 
  2. ↑ 2.0 2.1 2.2 Schmadel, Lutz D. (2007). "(1647) Menelaus". Dictionary of Minor Planet Names. Springer Berlin Heidelberg. p. 131. doi:10.1007/978-3-540-29925-7_1648. ISBN 978-3-540-00238-3. 
  3. ↑ 3.0 3.1 3.2 3.3 "JPL Small-Body Database Browser: 1647 Menelaus (1957 MK)". Jet Propulsion Laboratory. https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=2001647. 
  4. ↑ 4.0 4.1 "List of Jupiter Trojans". Minor Planet Center. 1 June 2018. https://www.minorplanetcenter.net/iau/lists/JupiterTrojans.html. 
  5. ↑ 5.0 5.1 "Asteroid (1647) Menelaus – Proper Elements". AstDyS-2, Asteroids – Dynamic Site. https://newton.spacedys.com/astdys/index.php?n=1647&pc=1.1.6. 
  6. ↑ Noah Webster (1884) A Practical Dictionary of the English Language
  7. ↑ 7.0 7.1 7.2 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. Bibcode: 2012ApJ...759...49G. http://adsabs.harvard.edu/cgi-bin/bib_query?bibcode=2012ApJ...759...49G. Retrieved 22 June 2018.  (Grav (2012) Grav (2011))
  8. ↑ 8.0 8.1 Stephens, Robert D.; Coley, Daniel R.; Warner, Brian D.; French, Linda, M. (October 2016). "Lightcurves of Jovian Trojan Asteroids from the Center for Solar System Studies: L4 Greek Camp and Spies". The Minor Planet Bulletin 43 (4): 323–331. ISSN 1052-8091. Bibcode: 2016MPBu...43..323S. http://adsabs.harvard.edu/cgi-bin/bib_query?bibcode=2016MPBu...43..323S. Retrieved 22 June 2018. 
  9. ↑ 9.0 9.1 9.2 9.3 9.4 9.5 "LCDB Data for (1647) Menelaus". Asteroid Lightcurve Database (LCDB). http://www.minorplanet.info/PHP/generateOneAsteroidInfo.php?AstInfo=1647%7CMenelaus. 
  10. ↑ 10.0 10.1 10.2 Hainaut, O. R.; Boehnhardt, H.; Protopapa, S. (October 2012). "Colours of minor bodies in the outer solar system. II. A statistical analysis revisited". Astronomy and Astrophysics 546: 20. doi:10.1051/0004-6361/201219566. Bibcode: 2012A&A...546A.115H. 
  11. ↑ Milani, Andrea (October 1993). "The Trojan asteroid belt: Proper elements, stability, chaos and families". Celestial Mechanics and Dynamical Astronomy 57 (1–2): 59–94. doi:10.1007/BF00692462. ISSN 0923-2958. Bibcode: 1993CeMDA..57...59M. http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1993CeMDA..57...59M&data_type=PDF_HIGH. Retrieved 13 April 2017. 
  12. ↑ Jewitt, David C.; Sheppard, Scott; Porco, Carolyn C. (2004). "Jupiter's Outer Satellites and Trojans – 12.4.2 Families". in Bagenal, Fran. Jupiter: The planet, Satellites and Magnetosphere. Cambridge University Press. p. 12. http://www.dtm.ciw.edu/users/sheppard/pub/Sheppard04JupChapter.pdf. Retrieved 13 April 2017. 
  13. ↑ 13.0 13.1 Roig, F.; Ribeiro, A. O.; Gil-Hutton, R. (June 2008). "Taxonomy of asteroid families among the Jupiter Trojans: comparison between spectroscopic data and the Sloan Digital Sky Survey colors". Astronomy and Astrophysics 483 (3): 911–931. doi:10.1051/0004-6361:20079177. Bibcode: 2008A&A...483..911R. 
  14. ↑ Nesvorný, D.; Broz, M.; Carruba, V. (December 2014). "Identification and Dynamical Properties of Asteroid Families". Asteroids IV. pp. 297–321. doi:10.2458/azu_uapress_9780816532131-ch016. ISBN 9780816532131. Bibcode: 2015aste.book..297N. 
  15. ↑ "Gazetteer of Planetary Nomenclature – Planetary Names: Crater, craters: Menelaus on Moon". International Astronomical Union (IAU) Working Group for Planetary System Nomenclature (WGPSN). http://planetarynames.wr.usgs.gov/Feature/3840. 
  16. ↑ Schmadel, Lutz D. (2009). "Appendix – Publication Dates of the MPCs". Dictionary of Minor Planet Names – Addendum to Fifth Edition (2006–2008). Springer Berlin Heidelberg. p. 221. doi:10.1007/978-3-642-01965-4. ISBN 978-3-642-01964-7. Bibcode: 2009dmpn.book.....S. https://cds.cern.ch/record/1339661. 
  17. ↑ Waszczak, Adam; Chang, Chan-Kao; Ofek, Eran O.; Laher, Russ; Masci, Frank; Levitan, David et al. (September 2015). "Asteroid Light Curves from the Palomar Transient Factory Survey: Rotation Periods and Phase Functions from Sparse Photometry". The Astronomical Journal 150 (3): 35. doi:10.1088/0004-6256/150/3/75. Bibcode: 2015AJ....150...75W. 

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