Increasing demand of satellites usage, our community raises awareness of space debris, which could collide with our space inventions. To avoid an unnecessary cost, many engineers resolve this issue with a ground-based observation, which is one of the inexpensive ways of tracked celestial bodies in the Earth vicinity. To use a plain optical telescope without laser ranging to determine orbital parameters by using angles only through Gauss method, and with appropriate calibrating a telescope mounting on a ground station. In this paper, we propose three main parts by first, presenting a concept of calibrating technique on how to obtain observation angle pair when an object is not at the center of image sensor. Second, we optimize the Gauss method’s execution time. Third, we validate that our generated Two-Line Element can be used to track celestial bodies. In our experiment, an 0.7-meter optical telescope equips with image sensor which is located at National Astronomical Research Institute of Thailand, Chiang-Mai, Thailand to project stars on image sensor. The image is mapped to stars database to correct the magnification, shear, and rotation of the image sensor respective to the Cartesian coordinates as a function of astrometry engineering. The result of the method is a plate constant. It is used to correct positions of an interesting celestial body tracked. In this second main part, we investigate the execution time with the same accuracy to other solver of the Gauss method in the famous eight order polynomial. The proposed solver is Laguerre method to find a root finding with convergence rate of cubic. Finally, Our result is proved to be reliable to use as a Two-Line Element update in our telescope system.
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