###### Published in Scientific Papers. Series "Journal of Young Scientist", Vol. 3

Written by Razvan Alex CIORBA, Radu Alexandru CRETU, Mircea Emil NAP, Andreea Carmen ZAGOR

The object of our study is the spherical excess and the national geodetic network for the city of Cluj-Napoca. As a proof of the earth's rotundity, many place great reliance upon what is called the "spherical excess," which has been observed on making trigonometric observations on a large scale. The angles taken between any three points on the surface of the earth by the theodolite are, strictly speaking, spherical angles, and their sum must exceed 180 degrees; and the lines bounding them are not the chords as they should be, but the tangents to the earth. This excess is inappreciable in common cases, but in the larger triangles it becomes necessary to allow for it, and to diminish each of the angles of the observed triangle by one-third of the spherical excess. In other words, the spherical excess is represented by the difference between the sum of the angles of a spherical triangle and the sum of the angles of a plane triangle. The national geodetic network and the triangulation network represent the fixed points which form the base of all leveling procedures. Considering the distance between the points and the measurements accuracy, the points that form the geodetic network are classified in five categories: first order: the points are situated between 20-60 km, average 30 km, second order: the tips of the triangles are intercalated in the points of first order at distances between 10-20 km, average 15km,third order: the points are situated inside of the triangles of the second order at distances between 5-10 km, average 7 km, forth order: the points are situated inside of the triangles of the third order at the average distance of 3 km, fifth order: the points are situated inside of the triangles of the forth order at the average distance of 1.5 km. In our project we are using the points of the third order to determine the spherical excess in the city of Cluj-Napoca.

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