本文以向量代數建構球面三角公式，針對單一天體觀測高度發展出求解天文位置線不用截距的新計算方法，可直接求出計算方位線與觀測等高度線的垂足交點，來繪製天文位置線。同時，本方法可應用在已知時間下，觀測兩個天體高度來決定天文觀測船位。此外，該新方法亦可透過迭代運算大幅消除截距法在其兩項基本假設上對天文觀測船位計算準確度之影響。文中並舉出一個算例做為該法之驗證與說明，在觀測高度小於70度以下時，本法與傳統使用之截距法比較，發現兩者均具有相同之準確性，但從計算速度與繪製天文位置線等兩項指標比較之，本法均較快；在觀測高度大於70度以上時，截距法則有誤差之產生，更顯出本法之優越性。本法因已將理論透過數值計算，若能再結合航海曆資料庫預測系統，未來將可進一步發展成商用套裝軟體，改善目前商船教育訓練或海上實務作業上天文航海的現況。

In this paper, a new calculation method, based on spherical triangular equations by using the vector algebra, is developed to solve the celestial line of position (LOP) for the altitude of a single celestial body without the intercept. By using the proposed approach, the LOP can be directly plotted by the calculation of the perpendicular intersection of the computed azimuth arc and observed equal altitude arc. Besides, this approach with the observed altitudes of two celestial bodies can also be applied to determine the astronomical vessel position when the time is given. Moreover, this new approach in conjunction with the iteration method can largely reduce the inaccuracy of the calculation of the astronomical vessel position, which is resulted from the intercept method. A computed example is included to validate the approach. It is found that for the case of the observed altitude not over 70 degrees, the result of the proposed approach is as accurate as that of the intercept method, however, our method is quite faster than the counterpart when the indices of calculation speed and plotting the LOP are chosen to compare. As for the case of altitude over 70 degrees, the intercept method may lead to inaccuracy, and thus, it shows the superiority of the current approach. Since the approach has been coded into the program, if it can be combined with the predication system of the nautical almanac data, the combined two systems can be further developed in a commercial package and dramatically improve the training or education of the current celestial navigation.