Using Heun's Method to Determine the Initial Conditions of Orbital Elements for Satellites in Low Earth Orbits

Ibrahim, Rasha ٌH.; Kadhim, Zina F.; Gburi, Sura I.; AL-Dahlaki, H. H.

doi:10.32894/kujss.2026.172294.1333

Using Heun's Method to Determine the Initial Conditions of Orbital Elements for Satellites in Low Earth Orbits

Document Type : Research Paper

Authors

Rasha ٌH. Ibrahim

Zina F. Kadhim

Sura I. Gburi

H. H. AL-Dahlaki

Astronomy and Space Department, College of Science, University of Baghdad, Baghdad, Iraq

10.32894/kujss.2026.172294.1333

Abstract

The study aims to determine the ideal starting value of eccentricity for satellites affected by atmospheric drag using Heun's method. Several altitudes from perigee were chosen for the satellites impacted by atmospheric drag. The process of transforming position and velocity components into dimensional and directional elements was described along with Heun's method. Based on the dimension and form of the orbit, the results showed that Heun's method is effective at very low values for eccentricity, less than or equal to 0.0000456. The results of the dimensional elements dropped rapidly, particularly in the next several days. The directional elements (Euler’s angles) were not affected using eccentricity at any given value. Over time, the semi-major axis displays secular declining behavior, whereas the eccentricity exhibits periodic falling behavior. The results demonstrated excellent matching with previously published data using the Adams-Bashforth and Runge-Kutta methods.

Keywords

Dynamic of the Orbit, eccentricity, Orbital Elements, Orbital Period of Satellite, Satellite&rsquo

s Perturbations