ÅÊ NEAR (Near-Earth Asteroid Rendezvous) Hayabusa

54 5 Å ² Vol.54 No.5 2013 9 ACTA ASTRONOMICA SINICA Sep., 2013 ËÃ Ý Ï Õ Ç 1,2 ¾ ½ 1,2 ¼ 1,2 º»¹ 1,2 (1 ÆÆ 210008) (2 Ð ¼² 210008) ÝÙºÝÐ Å µ» Ð ºÝÐ À Ò Ì Å ½ ¼¾»Ð Ö»ÖÈÙ Ä Üº Ö Â ± J2000.0 Ú Đ» (118.02, 22.03 ). Ä ¼É¾ ÐÓ Ì Ê ±Å ¹ Õ Oren-Nayar Æ Ç Å À Ò Õ ĐÙ º Ü Đ Û Ù À Ò Å 300 km 500 km 1 000 km ± Ø Ú Ú Ð Í Ì»³Ì»Đ Å Ì «Ð ÉĐÖ Á «Û± ³ Ä Ê«P185; ¾Ú «A 1 ÅÆ º ³ Ê» Đ ¾Ö º Û ÅÊ NEAR (Near-Earth Asteroid Rendezvous) Hayabusa º Û Â Â [1 4]. 2012 12 13 16:30 ²Á ¹Ü Ô Ä«Ñ Ë ÎÍ (4179 )(» http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=1989ac), 1 à ÚØ º²Ë [5 6]. ر à ßØ ± à ßØ Å ¾ Ê Ò Ð «ß ÜØÂÃ¹Ü Ï º Ò Ý ¹Ü Ñ Ë ¼»½É ¼ Î ßÉ [7], Ó Ø Õ ºÕÇØ ÏÃ Û ¹ Õ ¾Á «2.2 J2000.0 Ù Ö ( «ÀÁ Í J2000.0 Í Ù 2013-01-16 Ï 2013-04-01 Ñ Đ (11273068, 11203087) ÈÐ µ Ð (KJZD-EW-Z001) ÆÆ «Ë zhaoyuhui@pmo.ac.cn

448 Æ 54 ÖÆ ICRF (International Celestial Reference Frame) Ò ÅÙ Ö Ø Å ³ «Ò Ò [8 13], «³ Ò Ì) «º ÒÏûȽ Ò Ë Ï [14 15] Ï [16 18],1, ßÉ Ë ³Ô«Oren-Nayar Å Ï Æ ¾ Ñ Ô Ø ¹ «Û ³ Ú Ø Ñ ¾ 300 km 500 km 1 000 km Ù Ù «Ì Ë º²Ë º 2 2.1 Ò Ù ¹Ü Ñà 2012 12 13 16:30 ²Á Ë «Å «Â Ñ Å Ò ¼ ½ [7], É ¼ Î Ø Ó Õ ºÕÇØ Ë 1 É ½ Ï ¹Ü Ó 30 d Ô¼ Ö ¾ Ë ¹Ü «Ä ëŠΠ± Ö 0.16 orbit of Chang e 2 Toutatis 0.14 0.12 0.10 y/au 0.08 0.06 0.04 0.02 Direction of sunlight 0.00 0.02 Direction of orbit 0.15 0.10 0.05 0.00 0.05 x/au Fig.1 Í 1»Þ Æ Ô 30 d ¾ The orbit of Chang e 2 from 30 d before flyby to 30 d after flyby Ë 1 ¹ Ö«¾º x Ð Ò ¾ ¹Ü Ñ ØË Ô Õ ß¹Ü ºÕÇØÅÎ 0 ¾º ¹Ü Õ Î Õ 180 ¾ ¹Ü Ã Ñ ÄË«Ñ Å ¼ ÖÊà 90, Ñ Å 1 Takahashi Y, Schecres D J, Busch M W. in preparation, 2013

5 Ôɼ»Þ Æ Í Ã Ì 449 Ú Ò Ñ ½ à 90 Ô ÚÖ Â ÇØĐ ¼ Ö ³ Û Ì Ê ÂÛ ¹Ü Ñ¹Ý ¾Á 2.2 Î²Æ ÃË ¹Ü Ñ ¼ ½Ç Ò¼Ò Â Ñ Ø ³ «Ò Ñ Ø Ò ÉÀÒ Ç Ø Ö Ñ³ Ì Ì Ø Ã Ò Ó Ç Æ¼ Ò Ú ¾ Å ¾ Å Æ ³ δ = 7, Ò¹Ü ¾ d, ¼ Á B Ê [19 21] Ä ¹Û Õ Â Û ³ Å ¾Æ ¾À ÜØ Æ³Ê Ë 2 ¹Ü ÑØË Ë Õ Ë ³ È l = d/ tan 3.5. (1) ØÃ³Ê ¾ ÅÕ ¾ 1 Ë Í 2»Þ Æ Í Fig. 2 The sketch of the imaging of Chang e 2 after flyby Ä 1 «ÅÓ ÆÒ¼Ò Ò ½ÒØ Ø 30 km, ¾ 30 km, ¹ ³ Ë Å ¾ 500 km. ¼ Ó ÆÒ Ú¹Ü Ñ¼ ¹Ã Û Ø Õ Õ ¹Ü Ñ Ø Õ J2000.0 Í Æ Ö«ÆÆ Æ (115.82, 1.07 ), ÅÙ Ö«ÆÕ Õ (118.02, 22.03 ). «ÅÙ Ö«ÆÕ Õ (118.07, 22.03 ). 1 Ó Â Å Table 1 The relation between the closest distance of imaging and flyby distance d/km 10 15 20 30 50 l/km 163 245 327 490 817

450 Æ 54 3 Ñ 3.1 ²ÆÐ ¹Ü Ñ ØË Ë Õ ³Ô«ÅÓ Äµ Ö Å ÅÙ Ö«¼ R r, ØÃ»È Ä ¾ ĵ Ö«[13 14,16 17,22 23], É (2) Å ÛÝÐ Å ÅÙ Ö«[8 14], Äß ÅÙ Ö«r = R z (γ)r x (β)r z (α)r, (2) «α β γ ¹ R x R z x z ± Þ [13 14]. Å ³ Ò ²É Å Æ ÖÆ Äµ Ö Ô Å Ö [15 18], (2) «3 ¹ Õ α = 27.31, β = 69.50, γ = 4.13. 3.2 Oren-Nayar ÀØÐ ¹Ü ÑØË Ïà ÊØ ¾º ØÃ Å Ê Ä Ê Õ±µ Lambert ÅÞÒ Æ À ßØà Ž Å Ê Oren Nayar Ïà Lambert ÄØÅ Ï Ø Õ ¹ ± Oren-Nayar Å Ï Oren-Nayar Å Ï Ó Å½ Ä Ê Ä V ² É ² À Ê Ê² Ê À À ½ ß Ä Ê Å½Õ Ð ½ Oren-Nayar Å Ï Õ ± [24 25] : L r (θ i, ϕ i ; θ r, ϕ r ) = ρ π E 0 cosθ i (A + Bmax[0, cos(ϕ r ϕ i )] sinutanv), (3) Ыρ Ä ÕÀ E 0 º ÕÕ Ë 3 (θ i, ϕ i ) (θ r, ϕ r ) ± Å Ê Ö«º ³ ÅÑ A = 1 0.5 σ 2 σ 2 +0.33, B = 0.45 σ 2 σ 2 +0.09, σ ±Ð ½ Ò Å Ê Å½ Õ Î σ = 0 Ä Lambert Ä ±µ Lambert Å Ò u = max(θ i, θ r ), v = min(θ i, θ r ). Hudson Ê ÕÀ 0.23, ÊÅ½Õ 0.529 9 [15], ¹ (3) Ø Ñ ºÕ ÄßÌÝÕ Ê Ø ÕÇÕË

5 Ôɼ»Þ Æ Í Ã Ì 451 4 È Í 3 Ç Ë Ø Fig. 3 Local coordinate system of the diffuse reflection surface 4.1 Å Þ Ã¹Ü Ñ± ¼ ØË Â Ë Ý Ã ÑÆ Ø Ñ ³ Ø Ñ Ò¼ É ¼ Î ÒÕ ÅÙ Ö«Ø ÅÓ Ñ Ø r = (x, y, z), (4) Û Å Ù Ö«¹Ü ³ Õ λ ϕ: x = cosλcosϕ y = sin λcosϕ. (4) z = sinϕ ¹Ü Ñ Ë 2012 12 13 16:30 ²Á ß 2012 12 11 ¼ à 300 km 500 km 1 000 km Ø Õ Ø¹Ü Ñ Ë Ò¼ Î Øà 7 7 ³ 1024 pixel 1024 pixel CCD º² ¹Ü ¾Ë 300 km 500 km 1 000 km À Ì km/pixel, Ð 93 pixel 53 pixel 55 pixel 32 pixel 28 pixel 16 pixel, Õ ¾ 2, Ыձ ÅÙ Ö«2  ͵ Ê ß Ü «Û Table 2 Imaging parameters of Toutatis by Chang e 2 after flyby Distance/km Imaging time (Beijing time) Pixel Imaging azimuth/( ) 300 2012-12-13T16:31:35 93 53 (297.58, -19.32) 504 2012-12-13T16:31:54 56 32 (297.77, -20.41) 908 2012-12-13T16:32:49 28 16 (297.92, -21.20)

N e ( 54 #53T_% GK~Z. N ~tg6ma ='7nh BJ q= S H"^g2'; 1 'd'; 4.2 p9 l D2?G6m 3 s_~ta 9^ Oren-Nayar M W e: d'p _?.qs+ S 4 &5 3 S " F 3 q $ _? W LS "9 F 3 K q~z_'~ K 'R.qOt6bG' 6% GKJpG6m~t a = K 2 F_S 81 o ~Z. S 4 I5 3 S " F~C_? 6 S =l 8< q 2in{r 452 U 4 Æ FA Y (') PA 8U (J) Fig. 4 4.3 Imaging model (left) and imaging effect picture (right) after flyby d1` p9 \N o G6md Toutatis 3 km H[ -Eod ~Z. h~ Z';=&T_ ' %' _ ~Z';/1 +6X_ '_DÆ Z^ 114.5 121.5, D` Z^ 19.5 26.5, GJ"9WK q t ' vg6 mts?f4 _? 6 u 2 90 km H_ u 6GS 5 &S F

5 Ôɼ»Þ Æ Í Ã Ì 453 Ë«² ÆÐ Ð Ë«Ã Ñ «Ï Ø Đ «ÌÝ º²Ë Ë Ë 5 ÁË Ïû½À ÅÙ ÖÏ Ê Ï Ê Õ ¾ 90 km. Ã Ë ÈÀ ³ «ÖÈÀ Ù Â Æ²Ë Ù ØÕ Í± Ë 4 5 Ù º²Ë ³ ³Ô«ºÕ ±Ï Fig. 5 Í 5 µ ÜÚÍ ÅÛ (³) È Ñ ÎÞÍ (Â) Ú Comparison of imaging simulation of Toutatis in the starry background (left) and the image obtained in the mission (right) 5 ÜØ¹Ü Ï º Ø Õ ºÕÇØ ÏÃÂÛ ¹ Õ ¾Á J2000.0 Ù Ö«º (118.02, 22.03 ). Ò ßÀ Ï ßÉ ³Ô«Oren-Nayar Å Ï Æ ¾ Ñ Ô Ø ¹ «Û ³ Ú Ø Ñ ¾ 300 km 500 km 1 000 km Ù Ù «Ì Ë º²Ë º Ä Ù Æº²Ë Đº»È½ É º Ü Ò Ï Æ Ìº²Ë À ³Ê É Øº²Ë Đß «¹ ³Ô«±Ï Ç Ò Õ ØÝ µ«ð [1] Kubota T, Hashimoto T, Kawaguchi J, et al. IEEE, 2006: 2793 [2] Kawaguchi J, Fujiwara A, Uesugi T. AcAcu, 2008, 62: 639 [3] Williams B G. JHATD, 2002, 23: 34

454 Æ 54 [4] Dunham D W, McAdams J V, Farquhar R W. JHATD, 2002, 23: 18 [5] Mueller B E A, Samarasinha N H, Belton M J S. Icar, 2002, 158: 305 [6] Lupishko D F, Vasilyev S V, Efimov J S, et al. Icar, 1995, 113: 200 [7] ÁºÆ ÞÈ Ôɼ 2013, 43: 506 [8] Archinal B A, A Hearn M F, Bowell E, et al. CeMDA, 2011, 109: 101 [9] Seidelmann P K, Archinal B A, A Hearn M F, et al. CeMDA, 2007, 98: 155 [10] Murray C D. Solar System Dynamics. New York: Cambridge University Press, 2000: 225-227 [11] McCarthy D D, Petit G. IERS conventions (2003). Frankfurt: International Earth Rotation and Reference Systems Service Central Bureau, 2004: 21-69 [12] Moyer T D. CeMeC, 1981, 23: 33 [13] Ôɼ Ó Æ 2010, 51: 412 [14] Liu L, Zhao Y H, Zhang W, et al. ChA&A, 2011, 35: 188 [15] Hudson R S, Ostro S J, Scheeres D J. Icar, 2003, 161: 346 [16] Hudson R S, Ostro S J. Icar, 1998, 135: 451 [17] Kryszczynska A, Kwiatkowski T, Breiter S, et al. A&A, 1999, 345: 643 [18] Ostro S J, Hudson R S, Rosema K D, et al. Icar, 1999, 137: 122 [19] Battin R H. An Introduction to the Mathematics and Methods of Astrodynamics. Reston: Aiaa, 1999: 237-363 [20] Æ Á ¾ Ë Æ Ø 2009: 24-43 [21] Ôɼ µá ¾ ¾ Ë Æ Ø 2012: 159-168 [22] Hudson R S, Ostro S J. Sci, 1995, 270: 84 [23] Cicalò S, Scheeres D J. CeMDA, 2010, 106: 301 [24] Oren M, Nayar S K. SIGGRAPH 94 Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques. New York, 1994: 239 [25] Oren M, Nayar S K. International Journal of Computer Vision, 1995, 14: 227 A Research on Imaging Strategy and Imaging Simulation of Toutatis in the Chang e 2 Flyby Mission ZHAO Yu-hui 1,2 WANG Su 1,2 HU Shou-cun 1,2 JI Jiang-hui 1,2 (1 Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008) (2 Key Laboratory of Planet Sciences, Chinese Academy of Sciences, Nanjing 210008) ABSTRACT For the flyby mission of Toutatis by the Chang e 2 detector, the light conditions for imaging are calculated in this paper based on the orbital parameters of both the detector and the asteroid and the viewing angle. On the basis of the result, it s suggested to take the picture during the out-bound track, and the proposed orientation for the optical axis in the mean equator and equinox of J2000.0 coordinate system is represented to be (118.02, 22.03 ). Based on the shape model determined by radar data, the Oren-Nayar reflection model is used for imaging simulation according to the position relation among the sun, the asteroid, and the detector. The simulations are done at the distances of 300 km, 500 km, and 1000 km respectively from the asteroid after flyby, and the results are certificated by the optical images obtained in the mission. Key words planets and satellites: detection, space vehicles, methods: numerical