木星特洛伊小行星位於太陽與木星的L4與L5的拉隔朗日點上。國際天文 年會中的小行星中心已登錄5223個木星特洛伊小行星,而我所使用的泛星計 畫資料庫中有觀測到2922個。由於木星特洛伊的形成位置與木星同軌道,所 以知道木星特洛伊小行星的表面成分與內部結構可以幫助我們了解木星與 木星的衛星的內部結構(Marzari et al. 2002)。但我們了解小行星的內部結構與 成分得先求得小行星的質量與密度,而目前求得小行星的質量與密度的方 法唯有藉由雙星系統。Mann et al. (2007)論文中估計木星特洛伊小行星群中約 有6% - 10%的雙星。我們要透過觀測找到光變量大的小行星,而光變量大 意味該小行星很有可能是雙星。
泛星計畫的資料庫幫助我們選出光變量大的特洛伊小行星作為觀測目 標。但由於泛星計畫觀測同一個小行星時,每半年約僅有五筆資料。所以 我們申請了台灣鹿林一米望遠鏡與亞利桑那州Tenagra望遠鏡作後續的觀測。 我們共觀測了60個特洛伊小行星,當中編號11663約有0.4的光變量、編號 32467約有0.5、編號22008約有0.7、編號20961約有1.1。
假設這4個目標都是由兩個直徑相等的小天體組成的雙星,且是吸積組 成的瓦礫堆結構(rubble pile)則推導出的密度:11663為0.23 g/cm3、32467為0.86 g/cm3、22008為1.52 g/cm3、20961為1.82 g/cm3和2.45g/cm3。
假設這四個目標為單體模型,Holsapple (2001)提供一個常用於土木學 的模型,該模型可由小行星的形狀和自轉速度判斷小行星的內部結構,結 果顯示大部分特洛伊小行星的摩擦角都約在100以下。而編號20961在150左右, 20961在模型中的位置與目前已知的特洛伊雙星624、17365、29314位置非常 靠近,很有可能具有雙星結構。
這次觀測總共發現了四個可能的特洛伊雙星目標,且20961是目前光變 量最大的特洛伊小行星。

Jovian Trojans are located at Lagrangian points L4 and L5 between the Sun and Jupiter. According to MPC (Minor Planet Center) there are 5223 detected Jupiter Trojans, and we have identified 2922 of them from the Pan-STARRS (ps1-3pi) data set. Trojan asteroids’ surfaces and internal structure are important in understanding the origin and evolution of Jupiter and Jupiter’s satellites, because the precursors of Trojans were planetesimals orbiting close to the growing planet (Marzari et al. 2002). Mann et al. (2007) estimated 6% to 10% Jovian Trojans should be binaries with large amplitudes of magnitude variations. Modeling a binary system is the only way to know an asteroid’s density and mass and to speculate about its internal structure and composition.
By this study, Pan-STARRs data set has been used to find candidates of binary or elongate-shaped Trojan asteroids. The targets were detected around 5 times only in half year by Pan-STARRs, so follow-up observations are need. We used the Lulin telescope and Tenagra telescope to do follow-up observation. Totally, we observed 60 Trojan asteroids. Fortunately, we found that asteroid No.11663 has a amplitude of Δm≈0.4 magnitude variation No.32467Δm ≈0.5、No.22008 has Δm≈0.7 and No.20961 has Δm≈1.1 magnitudes.
Because of large magnitude variable target is likely to binary asteroids. So we assumed that these four targets were composed by two spheres of equal size. By this model, we derived the density of the accumulation structure (rubble pile): No.11663 for 0.23 g/cm3, No.32467 for 0.86 g/cm3, No.22008 for 1.52 g/cm3, No.20961 for 1.82 g/cm3 and 2.45 g/cm3.
In the case of ellipsoidal objects, Holsapple (2001) presented a model commonly used in soil mechanics. The model can determine the internal structure of an asteroid in term of the ratio of the short and long axes and the rotation of period. His study showed that friction angles of most of the Trojan asteroids are lower than 10 degrees. In our work, asteroid No.20961 is found to be around 15 degrees pretty similar to known high magnitude variable Trojans like No.624, No.17365 and No.29314. Their internal structure might be similar.

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