A NUMERICAL APPROACH TO SOLVE THE INITIAL-VALUE PROBLEM OF TWO-BODY WITH UNIVERSAL VARIABLE

Authors

1 Space Science Dep., Fac., of navigation Science and Space Technology (NSST), Beni-Suef Uni., Egypt

2 Applied Mathematics Dep., National Research Centre (NRC), Egypt

3 Astronomy and Meteorology Dep., Fac. Sci., Al-Azhar Uni., Egypt

4 Astronomy, Space and meteorology Dep., Fac. Sci., Cairo Uni., Egypt

Abstract

The solution of the initial-value problem of two-body gives inaccurate final state predictions for the orbital motions of artificial satellites. This is due to the presence of singularities and the poor selection of variables. In the current study, we numerically investigated the initial-value problem using the universal anomaly approach. To clarify the problem under concern, we carried out several numerical examples using a homemade software package. We considered five space missions, around the two planets Earth and Venus, which represent circular, near circular and ellipse orbits. We showed that the universal anomaly approach facilitates the numerical and analytical treatments of the two-body dynamics and works equally well for different types of orbits. Moreover, we developed a computation algorithm to handle the perturbed problem in cylindrical coordinates for the initial value problem taking into consideration the geopotential of the two planets up to the third zonal harmonic and the tesseral coefficient .
Al-Azhar Bulletin of Science
Volume 2023, Issue 1
January and February 2023

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