臺灣博碩士論文加值系統

小行星族群的形成主要是因為，母體經過不知名的猛烈撞擊後，造成母體表面甚至內部碎裂，有大量的碎片帶著可觀的速度脫離母體的重力束縛。而這些當初逃脫母體表面的射出速度可能與其碎片大小有關。因此我們利用現在小行星的反照率與其速度位置的觀測資料再加上一些理論的模型假設，去探討隱藏在現在小行星族群分佈的原始射出速度與碎片直徑大小的關係。我們提出了三個模型，分別是Takagi
模型，Nakamura 一次撞擊模型與Nakamura 二次撞擊模型。在灶神族群中，我們發現，Takagi 模型的結果與觀測資料的結果較符合，這意味著，對於高撞擊速度的撞擊事件，可能不存在明顯的碎片的射出速度與直徑的關係式，或者是絕大部分成員的產生，可能源自於碰撞頻繁時期的低撞擊速度的撞擊事件。

Asteroid families are thought to be formed through collisional events that a catastrophic impact kicks on the parent body and produces many fragments ejected away. The ejection-velocities of these fragments might be related with their sizes. Through the observed and theoretically produced velocities of asteroids, we study the original ejection-velocities of fragments, and investigate the implied vleocity-size relation of asteroid families. Three models were proposed, Takagi model, Nakamura one-impact model and Nakamura two-impact model separately. In Vesta family, we found that maybe it didn't exist the velocity-size relation or most members were produced from low impact-velocity events of the collisional era.

中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
第一章、簡介. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 最初的碎片速度分佈. . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 撞擊與碎片的射出速度. . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第二章、模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 速度與直徑的關係式. . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 模擬的程序. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 灶神族群. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 小行星的直徑觀測資料的處理. . . . . . . . . . . . . . . . . . 10
2.2.3 初始條件與軌道計算. . . . . . . . . . . . . . . . . . . . . . . 10
2.2.4 小行星資料圖. . . . . . . . . . . . . . . . . . . . . . . . . . . 12
第三章、Takagi 模型與模擬結果. . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1 結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
第四章、Nakamura 模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.1 Nakamura 一次撞擊模型的模擬結果. . . . . . . . . . . . . . . . . . 24
4.1.1 初始分佈圖. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.1.2 模擬結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1.3 討論與結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2 Nakamura 二次撞擊模型的模擬結果. . . . . . . . . . . . . . . . . . 33
4.2.1 討論與結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3 Cellino 模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
第五章、總結與未來展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.2 未來工作. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
附錄甲：軌道軟體Mercury6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
附錄乙：亂數分佈問題. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
乙.1 高斯分佈的亂數方法. . . . . . . . . . . . . . . . . . . . . . . . . . . 46
乙.2 均勻的立體角分佈. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

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