Calculating Satellite Velocity in Earth-Centered Earth-Fixed Frame Using 15 Ephemeris Parameters

This document addresses the calculation of satellite velocity and position in the Earth-Centered Earth-Fixed (ECEF) coordinate system using 15 ephemeris parameters. These parameters consist of 6 Keplerian orbital elements and 9 perturbation parameters. The Keplerian elements define the fundamental characteristics of satellite motion along elliptical orbits, including semi-major axis, eccentricity, orbital inclination, right ascension of ascending node, argument of perigee, and mean anomaly. In code implementation, these elements are typically processed using Kepler's equation solvers and coordinate transformation matrices to convert from orbital plane to ECEF coordinates.

The perturbation parameters account for non-uniform effects on satellite motion, such as Earth's gravitational tides, solar radiation pressure, atmospheric drag, and third-body gravitational perturbations from the Sun and Moon. Algorithmically, these are incorporated through perturbation models that modify the basic Keplerian motion, often using numerical integration techniques like Runge-Kutta methods. The complete calculation typically involves initial orbit propagation using Keplerian elements, followed by iterative application of perturbation corrections to achieve precise position and velocity vectors.

By integrating all 15 parameters through appropriate orbital mechanics algorithms, precise satellite ephemerides can be generated. This computational process is fundamental for satellite navigation systems, providing critical support for accurate positioning, navigation, and timing services. The implementation typically requires coordinate transformation functions between different reference frames and careful handling of time-dependent parameter updates.