Improvement of the Accuracy of the Perturbed Orbital Elements for LEO Satellite by Improving 4th Order Runge–Kutta’s Method

Abstract
Background/objectives: To study the motion equation under all perturbations effect for Low Earth Orbit (LEO) satellite. Predicting a satellite’s orbit is an important part of mission exploration.

Methodology: Using 4thorder Runge–Kutta’s method this equation was integrated numerically. In this study, the accurate perturbed value of orbital elements was calculated by using sub-steps number m during one revolution, also different step numbers nnn during 400 revolutions. The predication algorithm was applied and orbital elements changing were analyzed. The satellite in LEO influences by drag more than other perturbations regardless nnn through semi-major axis and eccentricity reducing.

Findings and novelty/ improvement: The results demonstrated that when m for Runge– Kutta’s method is large; the perturbed value for orbital element considers more acceptable. Furthermore, as nnn increases the step will reduce.

Keywords: 4thOrder Runge–Kutta’s Method, Orbital Elements, LEO Satellite, Perturbations, Perturbed Equation of Motion.