由於系外行星 Qatar-1b 和HAT-P-23b 的凌星時間的變化之研究，尚未有明顯的結論。對於Qatar-1b系統，我們觀測並提供 10 條新的凌星光度曲線且研究分析凌星時間的變化。我們在假警報率 (false-alarm probability)為35%所對應的頻率之正弦模型，得到最小的簡化卡方檢定 (reduced chi-square )為 2.14，所得到的凌星參考時間為2455647.63345 ± 0.00008 (BJD)，軌道週期為 1.4200236 ± 0.0000001 (day)。
對於 HAT-P-23b系統，我們觀測並提供了4條新的凌星光度曲線且研究分析凌星時間的變化。我們在假警報率 (false-alarm probability)為36%所對應的頻率在正弦模型下，得到最小的簡化卡方檢定 (reduced chi-square )為 0.94，所得到凌星參考時間為 2456135.49914 ± 0.00015 (BJD)，軌道週期為 1.2128866 ± 0.0000001(day)，另外我們更新了兩個系統的軌道半長軸與恆星的半徑比，並且計算了恆星潮汐因子。

Motivated by the unsettled conclusion on whether there are any transit timing variations (TTVs) for the exoplanet Qatar-1b and HAT-P-23b, we decided to study these two systems. For Qatar-1b, ten new light curves are presented and the TTV analysis with a baseline of 1400 epochs are performed. The sinusoidal model provides a good fitting with minimum reduced chi-square χ2red = 2.14, and the false-alarm probabilities of corresponding frequency is 35.2%. A new ephemeris with the reference time T0 = 2455647.63345 ± 0.00008 (BJD), the period P=1.4200236±0.0000001 (day) is obtained.
For HAT-P-23b, four light new light curves as presented, and the TTV analysis with a baseline of 1600 epochs are performed. The sinusoidal model provides a good fitting with minimum reduced chi-squareχ2red = 0.94 and the false-alarm probability of corresponding frequency is 36.3%. A new ephemeris with the reference time T0 = 2456135.49914 ± 0.00015 (BJD), the period P = 1.2128866±0.0000001 (day) In addition, the updated orbital semi-major axis and planetary radius in the unit of stellar radius are provided, and the lower limit of modified stellar tidal quality factor is also determined for these two systems.

1 Introduction .....1
2 Introduction to Qatar-1 and HAT-P-23 Systems .....7
3 The Observation and Data Reduction ..... 10
3.1 The Telescopes ..... 10
3.1.1 Palomar 60-inch telescope (P60) ..... 10
3.1.2 MTM-500 and RC-800 at Crimean Astrophysical Observatory .....11
3.1.3 Himalayan Chandra Telescope .... 12
3.2 Data Reduction .... 14
3.2.1 The Selection of Comparison Starts ..... 14
3.2.2 Other Data ..... 14
3.2.3 The Time Stamp ..... 15
3.3 Transit Analysis ..... 18
3.4 The Fitting Method ..... 18
4 Investigating Transit Timing Variation of Qatar-1b ..... 19
4.1 MCMC Parameter Setting ..... 19
4.2 Comparisons with Previous Works .....22
4.3 Transit Timing Variations ..... 27
4.3.1 New Ephemeris ..... 27
4.3.2 The Frequency Analysis ..... 30
4.3.3 The Rate of Orbital Decay ..... 35
5 Investigating Transit Timing Variation of HAT-P-23b ..... 39
5.1 TAP Parameters Setting ..... 39
5.2 Comparisons with Previous Works ..... 42
5.3 Transit Timing Variations .....46
5.3.1 New Ephemeris ..... 46
5.3.2 The Frequency Analysis ..... 49
5.3.3 The Rate of Orbital Decay ..... 58
6 The Conclusions and Future Work .....60
6.1 The Conclusions of Qatar-1b ..... 60
6.2 The Conclusions of HAT-P-23b ..... 61
6.3 Future Work ..... 62

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