MOID USING NEW SETS OF UNIVERSAL FUNCTIONS

Authors

AYMAN HOMDA, Egyptian Space Agency, Cairo, Egypt, 130Follow
Hany R. Dwidar, Astronomy, Space Science and Meteorology Department Faculty of Science, Cairo University, Cairo, Egypt, 12613
Abdelaziz A. Bakry, Astronomy and Meteorology Department Faculty of Science, Al-Azhar University Nasr City, Cairo, Egypt, 11884
M.N. Mohamad Ismail, Astronomy and Meteorology Department Faculty of Science, Al-Azhar University Nasr City, Cairo, Egypt, 11884
AHMED El-RAFFIE, Egyptian Space Agency, Cairo, Egypt, 130

Corresponding Author

ayman.homda@EGSA.GOV.EG

Document Type

Original Article

Subject Areas

Astronomy and Meteorology

Keywords

Closest Approach; objective function; Universal functions; Numerical integration.

Abstract

In this paper, based on Goodyear's time transformation formula, we used a set of modified universal functions to construct the minimum distance function between any two celestial objects. We determined the distance between objects in space under a specific time constraint. We used the continued fractions method for quick convergence of the distance function. We used the inverse series to obtain a first initial guess to solve the convergence equation. Furthermore, the Lagrange multiplier method was used to determine the minimum distance between the two objects under the specified time constraint. We constructed an algorithm and applied it with the Matlab toolbox to numerically simulate the problem under consideration. We found that the deviation in the position and velocity vectors using both Ansys Systems Tool Kit (STK) and MATLAB are -7:52234e^-7 km and -7:6045e^-7 km=s; respectively for some satellites. Also, the deviation for distance function is 3:956E^-05 km.

How to Cite This Article

HOMDA, AYMAN; Dwidar, Hany R.; Bakry, Abdelaziz A.; Ismail, M.N. Mohamad; and El-RAFFIE, AHMED (2024) "MOID USING NEW SETS OF UNIVERSAL FUNCTIONS," Al-Azhar Bulletin of Science: Vol. 35: Iss. 1, Article 3.
DOI: https://doi.org/10.58675/2636-3305.1662