海王星外雙星系統與第三天體之重力交互作用｜國立中央大學博碩士論文系統

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研究生：	謝宗富 Zong-Fu Sie
論文名稱：	海王星外雙星系統與第三天體之重力交互作用 Gravitational Interaction of TNBs with the third body
指導教授：	葉永烜 Wing-Huen Ip
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 天文研究所 Graduate Institute of Astronomy
畢業學年度：	100
語文別：	中文
論文頁數：	72
中文關鍵詞：	海王星外雙星系統、海王星外天體、古柏帶、雙星、古柏帶天體、微行星、碰撞截面積、三體問題、數值模擬
外文關鍵詞：	numerical simulation, three-body probelm, binary, Kuiper belt, trans-Neptunian binary, trans-Neptunian object, TNO, TNB, KBO, planetesimal, collisional cross section
相關次數：	點閱：21 下載：0
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目前在太陽系中許多存在小天體的區域皆存在著雙星系統。而這些雙星系統
其各種性質更能夠提供建構該區域演化過程的限制條件。其中位於古柏帶的海王
星外雙星系統中，特別是屬於傳統型冷群海王星外天體的雙星系統，其成員間相
近的質量比、分布極廣的離心率、較高的大軌道比率及相近的順向與逆向軌道比，
無法僅用現有的形成理論來解釋它們的存在。而目前針對它們的演化至今討論不
多。在此我們探討於海王星外雙星系統形成之後其與海王星外天體彼此之間重力
交互作用過程，並以海王星外雙星系統為例測試雙微行星的碰撞截面積，來解釋
我們的結果。我們的結果顯示即便於高速( )的環境下雙微行星的碰
撞截面積仍舊比單獨兩顆微行星碰撞截面積來得高，並且碰撞截面積與雙星的軌
道半長軸具有正相關的關係。另外我們也發現高離心率( )、半長軸較大
( )的海王星外雙星系統的存活率偏低，即使存活其軌道參數也易受海王
星外天體的重力影響；低離心率( )、半長軸較小( )的海王星雙
星系統則反之。根據我們的結果，我們認為低離心率、半長軸較小的海王星外雙
星系統其演化過程可能以潮汐圓化過程為主導，而海王星外天體的遭遇事件可能
主導高離心率、半長軸較大的海王星外雙星系統其演化過程。最後，我們建議未
來探討海王星外雙星系統的各項特徵時，應該針對潮汐作用過程和遭遇事件發生
的頻率進行較細部的研究。

Many binary asteroids distribute at different regions in the solar system. Their
properties provide the restrictive condition to construct evolution model in different
regions. The trans-Neptunian binary (TNB), especially, being classified the dynamical
cold Kuiper belt object, cannot explain their existence by various formation theories
because their near-equal mass ratio, wide distributed eccentricity, higher large orbit
ratio, and near-equal prograde to retrograde orbit ratio. But their evolution is rare
discussed. We study gravitational interaction between TNBs and trans-Neptunian
objects (TNOs) after TNBs formed. We also test the collisional cross section of binary
planetesimals (BPs) to explain our results. Our results show the binary-single
collisional cross section is larger than the single-single collision even if the relative
velocity is high ( ), and the binary-single collisional cross section
depend on the semi-major axis of binary. We also find out that TNBs with the high
eccentric ( ) and larger semi-major axis ( ) are not easy to survival.
Their orbits are changed easily even if they survive after the TNOs close encounter,
vice versa. Follow our results, we think the low eccentric and small orbital TNBs are
dominated by tidal evolution and the evolution of higher eccentric and large orbital
TNBs are dominated by the close encounter with TNOs. In future, about studying the
properties of TNBs, we suggest that tidal evolution and frequency of the close
encounter events should be considered in detail.

中文摘要......................................................................................................................... i
英文摘要........................................................................................................................ ii
目錄............................................................................................................................... iii
圖目錄............................................................................................................................ v
表目錄.......................................................................................................................... vii
一、緒論 ..................................................................................................................... 1
1 太陽系內的小行星與海王星外天體 ............................................................ 1
2 海王星外天體的分類 .................................................................................... 3
2.1 傳統型海王星外天體 ......................................................................... 3
2.2 共振型海王星外天體 ......................................................................... 4
2.3 散射型海王星外天體 ......................................................................... 4
3 太陽系的雙星系統 ........................................................................................ 5
3.1 希爾半徑(Hill Radius) .......................................................................... 5
3.2 雙小行星系統的比較 ......................................................................... 6
3.2.1 近地小行星雙星系統 .............................................................. 6
3.2.2 主帶小行星雙星系統 .............................................................. 6
3.2.3 海王星外雙星系統 .................................................................. 7
3.3 雙星系統的形成理論 ......................................................................... 9
4 海王星外雙星系統的形成理論 .................................................................. 10
4.1 捕獲說(mutual capture) .................................................................... 10
4.2 撞擊說(impact collision) .................................................................... 10
4.3 混成說(hybrid) ................................................................................... 11
4.4 自轉分裂說(rotational fission) .......................................................... 12
4.5 重力塌縮說(gravitational collapse) ................................................... 12
5 海王星外雙星系統的演化 .......................................................................... 13
二、重力交互作用過程之模擬 ......................................................................... 14
1 定義與符號 .................................................................................................. 14
2 數值模擬方法 .............................................................................................. 15
2.1 遭遇事件 ........................................................................................... 15
2.2 動力學模型 ....................................................................................... 15
2.3 數值積分方法 ................................................................................... 16
3 初始條件 ...................................................................................................... 18
3.1 雙星系統的物理性質與軌道性質 ................................................... 18
2.2 外來天體的物理性質 ....................................................................... 18
3.3 外來天體的撞擊參數 ....................................................................... 20
3.4 外來天體的相對速度 ....................................................................... 21
4 遭遇事件的可能結果 .................................................................................. 22
4.1 軌道參數 ........................................................................................... 22
4.2 判定軌道類型 ................................................................................... 23
5 雙星系統的碰撞截面積 .............................................................................. 30
5.1 理論預測 ........................................................................................... 30
5.2 數值模擬與初始條件 ....................................................................... 32
5.3 截面積的計算與誤差估計 ............................................................... 32
三、結果與討論 ..................................................................................................... 33
1 碰撞軌道的海王星外雙星系統 .................................................................. 33
1.1 碰撞軌道的比率 ............................................................................... 33
1.2 雙微行星的碰撞截面積 ................................................................... 34
2 不同初始條件下海王星外雙星系統的生存率 .......................................... 37
2.1 不同相對速度下的生存率 ............................................................... 37
2.2 不同軌道參數的生存率 ................................................................... 38
3 海王星外雙星天體的軌道變化 .................................................................. 40
3.1 軌道離心率的變化 ........................................................................... 42
3.2 軌道半長軸的變化 ........................................................................... 46
3.3 軌道傾角的變化 ............................................................................... 50
四、總結 ................................................................................................................... 52
參考資料...................................................................................................................... 53
附表.............................................................................................................................. 56

                                

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