利用天文軟體校註《過洋牽星圖》

To Collate and Footnote Zheng-Ho's Astronomical Navigation Charts through Stellarium Software

四幅過洋牽星圖是鄭和下西洋時船隻在印尼阿齊、錫蘭別羅里、印度丁得把昔、阿曼沙姑山、及伊朗忽魯謨斯等地的牽星定位圖解。每幅圖基本上繪有兩套星辰的仰角指數，一套為北辰星（勾陳一）與燈籠星（十字二星）組合，另一套為織女星與南北布司星（南河三與北河三）組合。當船隻抵達預定港口時，各套星辰組合的高度角應符合先前的觀測記錄，如此便完成了定位作業。牽星板（Kamal）用來度量星辰正切高度指數而非度數，因此利用天文軟體溯源牽星圖時，除了需要還原歲差外還要將指數換算成度數。本文從〈鄭和航海圖〉中優選16個印度西岸的北辰星觀測記錄，求得回歸方程式Y=1.094+1.601X，式中X為自變數，以星辰仰角指數為單位；Y為因變數，以星辰仰角度數為單位。運用此回歸式可換算牽星指數為仰角度數，如此便可利用天文軟體還原明代的牽星圖，進行驗證與修訂工作。牽星圖記錄的星辰指數大抵與計算結果相符，然而在1433年4月時木星位置靠近北布司星（北河三），可能造成觀測誤判，此外也有幾個星辰的高度指數被誤寫或誤讀，原因不明。在Stellarium天文軟體協助下，本文認為在錫蘭Beruwara所牽西南水平星即是水委一星，而在印尼阿齊所牽的華蓋星即是帝星。由於牽星圖當年刊印時，一些既存的觀測誤差以及明顯誤抄沒有被修訂過，本文相信這四幅圖雖然沒有記錄牽星季節與時刻，卻符合《前聞記》之日期與地點以及季風航海之經驗法則。因此，本文以1432-1433年鄭和最後一次下西洋訪問的港口與日程來進行各項說明與展示。

"Four astronomical navigation charts on Aceh Indonesia, Beruwara Sri Lanka, Dandi-Baxi India, Raas-Al-Hadd Oman, and Hormus Iran, were prepared for ship navigation purposes for Zheng-Ho's journey to western oceans. Each chart basically provides two sets of star elevation angles, the first set includes Polaris and Acrux while the other set includes Vega and Pollux. When a ship arrived at a port of call, the azimuth and the elevation for each assigned star in the navigation chart should meet the previous record to position the ship. In Ming dynasty a Kamal wood board was used to measure the star elevation in fingers instead of radian degrees with low precision, therefore the conversion from fingers to degrees and vice versa requires a regression curve and a stellar software. In order to convert fingers to degrees, this study employed 16 Polaris elevation angles in fingers observed around 1430 AD along the western Indian coast to establish a regression equation: Y=1.094+1.601X, where X is an independent variable in fingers and Y is a dependent variable in degrees. It is found that the figures recorded on these charts were comprehensive and explainable with help of the computed results. However, some obvious errors were found, which could be attributable to aiming at Jupiter instead of Pollux in April of 1433 AD, and other errors such as the misprinting of Chinese characters due to some unknown reasons. With the assistance of Stellarium software, a temporary named''Leveling''star observed at Beruwara is confirmed to be Achenar (αEri) while a''Canopy-Star''observed at Aceh is confirmed to be Kochab (βUMi). Due to the fact that some observational errors and writing errors appeared in these charts, which had not been corrected before publication, these stellar charts are consequentially thought to be the records of Zheng-Ho's last made journey between 1432 AD and 1433 AD."