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
Kirkuk Journal of Science
Volume 21, Issue 2, June 2026, Pages 64-73 PDF (6.69 M)
Document Type: Research Paper
DOI: 10.32894/kujss.2026.172294.1333
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
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’ s Perturbations

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