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研究生： 陳徵
Cheng Chen
論文名稱： 利用橢圓限制性三體運動模擬土星F環與牧羊犬衛星普羅米修斯的重力與碰撞交互作用
A Simulation Of The Gravitational And Collisional Interaction Of Saturn's F Ring With The Shepherding Moon, Prometheus, By Elliptic Restricted Three-Body Calculation
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
論文出版年： 2016
畢業學年度： 104
語文別： 英文
論文頁數： 56
中文關鍵詞： 普羅米修斯 、土星 、F環 、三體
外文關鍵詞： Prometheus, Saturn, F ring, three body
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    • 由於離心率的緣故，土星的F環和其中一個牧羊犬衛星，普羅米修斯會在每個軌道周期相互接近。在普羅米修斯接近F環的過程中，會在F環盤面上產生出糾結且分段的構造，且由於重力散射，F環中的粒子也會撞擊到普羅米修斯的表面。我們利用限制性橢圓三體運動來研究F環的粒子受到普羅米修斯的影響的運動，來了解重力擾動與在洛希極限附近的質量損失(增加)。

    Because of their eccentricities, the narrow F ring of Saturn and one of the shepherding moons, Prometheus, can intercept each other's orbit. This process would lead to the formation of kinky and segmented structures along the F ring when Prometheus penetrate into the F ring. Besides gravitational scattering, collisional impact at the surface of Prometheus by the F ring particle could also occur. The numerical method in the elliptic restricted three-body problem is used to simulate the orbital motion of the F ring particles under the influence of Prometheus with a view to understand the related dynamical perturbation and mass loss (or accretion) effect in the vicinity of the Roche limit.

    摘要 i Abstract vi Acknowledgement vii List of Figures ix List of Tables xii Introduction 1 1.1 Saturnian system 1 1.2 Prometheus and Pandora 3 1.3 The F-ring and the interaction between the F ring and Prometheus 8 Numerical simulation of the gravitational interaction 10 2.1 Restricted three-body problem and elliptic restricted three-body problem 10 2.1.1 Definitions and symbols 11 2.1.2 Equations of motion 12 2.1.3 Normalized terms of the equation of motion of the elliptic restricted three-body problem 14 2.2 Initial conditions of numerical simulation 16 Image analysis 24 3.1 Introduction of SPICE 24 3.2 Image selection 25 3.3 The coordination and transformation 28 Discussion 30 4.1 Comparison between simulation result and images 30 4.2 2D collision map of Prometheus 35 4.3 The distribution of craters on the surface of Prometheus 37 Conclusion 41 Bibliography 43

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