Finding the Exact Solution of Kepler’s Equation for an Elliptical Satellite Orbit Using the First Kind Bessel Function

• Published in: Iraqi journal of science pp. 1129 - 1137
• Main Authors: Ibrahim, Rasha H., Saleh, Abdul-Rahman H.
• Format: Journal Article
• Language: English
• Published: 29.02.2024
• ISSN: 0067-2904; 2312-1637
• DOI: 10.24996/ijs.2024.65.2.42

     In this study, the first kind Bessel function was used to solve Kepler equation for an elliptical orbiting satellite. It is a classical method that gives a direct solution for calculation of the eccentric anomaly. It was solved for one period from (M=0-360)° with an eccentricity of (e=0-1) and the number of terms from (N=1-10). Also, the error in the representation of the first kind Bessel function was calculated. The results indicated that for eccentricity of (0.1-0.4) and (N = 1-10), the values of eccentric anomaly gave a good result as compared with the exact solution. Besides, the obtained eccentric anomaly values were unaffected by increasing the number of terms (N = 6-10) for eccentricities (0.8 and 0.9). The Bessel function's solution appeared to be close to the exact solution for eccentricity of 1 and more than 10 number of terms. Finally, the representation of the first kind Bessel function J1(x) was closer to the exact representation only for eccentricity 0.5 and (N=1-10).