University of Tehran Press Journal of the Earth and Space Physics 2538-371X 32 3 2006 10 23 Comparison of numerical integration methods in orbit determination of low earth orbiting satellites■ Comparison of numerical integration methods in orbit determination of low earth orbiting satellites■ 41 57 82217 FA Mehdi Eshagh Royal Institute of Technology (KTH), SE 100 44 Stockholm, Sweden and Islamic Azad University, Shahr-e-Rey branch, P.O. Box 18735-334, Tehran, Iran Mehdi Najafi Alamdari K. N. Toosi University of Technology, P.O. Box 15875-4416, Tehran, Iran Journal Article 2003 08 31 Comparison of some numerical integration methods of solving the differential equation of motion of a satellite is the main subject of this paper. Since the equation of motion of a satellite is a second order differential equation, therefore, six initial values should be introduced to the numerical solution. These six initial values are the components of position and velocity vectors in an inertial frame respectively. Comparing numerically integrated position and velocity vectors with Keplerian orbit; one can obtain the bias of the numerical integration method in a satellite-centered coordinate system. In this research, three methods of Runge-Kutta, Runge-Kutta-Nystrom, and the predictor-corrector method of Adams-Bashforth and Adams-Moulton are investigated for a low earth orbiting satellite. Numerical results show that with integration size of 30 seconds, the Runge-Kutta method, Adams-Bashforth and Adams-Moulton predictor-corrector algorithms, and Runge-Kutta-Nustrom provide closer orbit to the theoretical orbit respectively. Comparison of some numerical integration methods of solving the differential equation of motion of a satellite is the main subject of this paper. Since the equation of motion of a satellite is a second order differential equation, therefore, six initial values should be introduced to the numerical solution. These six initial values are the components of position and velocity vectors in an inertial frame respectively. Comparing numerically integrated position and velocity vectors with Keplerian orbit; one can obtain the bias of the numerical integration method in a satellite-centered coordinate system. In this research, three methods of Runge-Kutta, Runge-Kutta-Nystrom, and the predictor-corrector method of Adams-Bashforth and Adams-Moulton are investigated for a low earth orbiting satellite. Numerical results show that with integration size of 30 seconds, the Runge-Kutta method, Adams-Bashforth and Adams-Moulton predictor-corrector algorithms, and Runge-Kutta-Nustrom provide closer orbit to the theoretical orbit respectively. https://jesphys.ut.ac.ir/article_82217_0f91331b5a1203d230b62bd0e4518188.pdf