Moid Using New Sets of Universal Functions

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.