Establishing GEO and LEO Orbits with Parameter Calculations

When designing satellite orbital configurations, numerous factors must be considered. This involves establishing both GEO (Geosynchronous Earth Orbit) and LEO (Low Earth Orbit) trajectories, along with calculating essential parameters such as inter-orbit azimuth angles, elevation angles, angular velocities, accelerations, and Doppler shifts. These calculations typically employ orbital mechanics algorithms using coordinate transformation matrices and numerical differentiation methods. The implementation requires accounting for diverse factors including Earth's geoid shape and rotational velocity (using WGS-84 model parameters), atmospheric thickness and density profiles (via empirical models like NRLMSISE-00), and other astrophysical considerations. Key functions involve propagation algorithms (e.g., SGP4 for LEO, analytical solutions for GEO) and frequency shift calculations using relative velocity vectors. Consequently, satellite orbit planning constitutes a complex engineering task demanding meticulous computational planning and validation through simulation frameworks.