ABSTRACT
The motion of a spacecraft around the earth is affected with many forces. The major force affecting this motion is the gravity force resulting from a spherical central body (the earth). This motion is commonly known in the literature as the two-body problem. The main drive for this research is to select the best numerical integration algorithm of the two-body problem on the basis of quantitative measures. The error of each integration algorithm is measured with respect to the exact solution of the two-body problem and the test results were embarrassing. Also, the average execution time is compared for all of these algorithms.