Describing Kepler Orbits with the Ulianov Orbital Model

This paper presents the Ulianov Orbital Model (UOM), a simplified approach to two-body orbital mechanics. The UOM provides equations to calculate the standard ellipse parameters (a and b) and orbital trajectories and velocities from three UOM basic parameters (Ue, R0, and V0). It introduces a new kind of elliptical trigonometric functions, which simplify plotting orbital trajectories and their velocities over time and in elliptical angular steps. The Ulianov Elliptic Transform (UET), generates an impressive effect of rotating and scaling an ellipse, transferring its center from one of the foci to the geometric center of the ellipse. The UET offers a new and easy way to create and manipulate ellipses using both numerical and analytical methods.