使用Johnson UBV光度資訊推算疏散星團的距離和年齡，首要工作是能夠分辦出星團的成員星。 本研究使用雙變數常態分布之數學模式分析恆星自行運動，計算出每顆恆星為星團成員的或然率。
本研究使用2003年8月7日和2012年7月8日在中央大學鹿林前山天文台的一米望遠鏡觀測之疏散星團NGC 7142之影像，得出其中1697顆恆星的UBV光度及自行運動資訊。而本研究同時也選擇擇了M45(昴宿星團)作為距離、星際紅化消光已知之對照星團，採用Tycho-2星表記載之亮度及自行資訊。
在分析恆星自行運動後得到每顆恆星為成員星之或然率，將或然率較高之恆星挑選出來繪製星等-星色圖和雙色圖。 由星團之雙色圖擬合，以及文獻之UBV紅化斜率0.72，得到NGC 7142的金屬豐度[Fe/H] = -0.37以及紅化係數E(B-V) = 0.36。而星等-星色圖由主序帶擬合之結果可得出距離模數(m-M)0 = 11.02，等同於1600pc。而年齡由星等-星色圖之等時線擬合而得出，約為79億年。
在M45之星等-星色圖代入文獻值E(B-V) = 0.04、[Fe/H] = 0.022以及(m-M)0 = 5.66後，由等時線擬合得到年齡1.26億年。 本研究比較M45和NGC 7142之主序帶星等，代入M45之文獻值136pc，得到NGC 7142之距離為1920pc。

For accurately estimating the distance and age of an open cluster with Johnson UBV photometry, the membership of the cluster should be determine first. The probability of membership for each star in the two open clusters: NGC 7142 and M45 are determined in terms of the normal bivariate frequency function with proper motion data. The database of proper motion and UBV photometry calculated from the images for NGC 7142 observed in this work, and proper motion database of M45 taken from the Tycho-2 catalog.
The observations of NGC 7142 carried out with the Lulin-One meter Telescope of National Central University on August 7, 2003 and July 8, 2012, respectively. A catalog contained 1697 stars with UBV photometry, proper motion and membership probability data is set up. From the main-sequence fitting on the Two-Color Diagram with the UBV reddening slope 0.72, the estimate value of the metallicity Z is 0.008, represents [Fe/H] = -0.37, and the E(B – V) = 0.36. The distance modulus is (m-M)0 = 11.02, represents distance is about 1600pc. From the isochrones fitting, the age of NGC 7142 is 7.9 Gyr.
The M45 been chosen for comparison with almost no extinction and distance well known. With the E(B-V) = 0.04, (m-M)0 = 5.66 and [Fe/H] = 0.022, the isochrones fitting of age is 126 Myr. From the main-sequence comparison with the distance of M45 (136 pc), the distance of NGC 7142 is 1920 pc.

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