Kepler-210b和Kepler-210c是離恆星Kepler-210很近的兩顆行星，這兩顆行星有掩星現象及transit timing variation (TTV)。本篇論文的目標是運用擬合TTV的技巧得到兩顆行星的軌道參數並討論是否有第三顆行星存在於該系統的可能性，我們使用TTVFAST動力模型擬合來自文獻上的498掩星資料，我們同時也用Differential Evolution Markov Chain with snooker update 來探索卡方檢驗下的最小值。從我們的結果可以知道行星b和行星c的質量分別是0.02M_J和0.95M_J，根據卡方檢驗的結果，我們也提出第三顆行星存在的可能性，並提供第三顆行星的軌道參數。在所有可能的的行星軌道結構中，第三顆行星坐落於行星b和行星c之外的軌道是最有可能且是個穩定的行星系統。

Kepler-210 b and Kepler-210 c are two close-orbiting transiting planets with confirmed transit timing variations (TTVs). The aim of this thesis is to constrain the orbital parameters of both planets and discuss the plausibility of an additional planet in the system by fitting the TTVs. We have used the dynamical model, TTVFast, to fit the total 498 transit data from the literature. A Differential Evolution Markov Chain with snooker update was performed to search the minima chi-square value. From our analysis, we obtain the mass of 0.02 $M_{\rm J}$ and 0.95 $M_{\rm J}$ for planet b and planet c respectively. We also claim the possible existence of planet d regarding the minima chi-square and provide the system orbital parameters. In the most favorable scenario, planet d is outside the two transiting planets, which satisfies our stability check.

1 Introduction 7
2 Target Details 11
3 Method and Setup 13
3.1 TTVFast and MC3 . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Parameters and Priors . .. . . . . . . . . . . . . . . . . . 17
3.2.1 Two-Planet Case . . . . . . . . . . . . . . . . . . . . . 18
3.2.2 Three-Planet Case . . . . . . . . . . . . . . . . . . . . 20
4 Results 22
4.1 Two-Planet Scenario . . . . . . . . . . . . . . . . . . . . 22
4.2 Three-Planet Scenario . . . . . . . . . . . . . . . . . . . 28
5 Discussions 37
5.1 Mass-Eccentricity Degeneracy . . . . . . . . . . . . . . . . 37
5.2 Stability . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.3 Habitable Zone . . . . . . . . . . . . . . . . . . . . . . . 41
6 The Conclusion and Future Work 43
6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 43
6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . 44
A DEMC with Snooker Update 45
B GELMAN & ROBIN Convergence 49

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