Selection of Launch Vehicle Motion Model Parameters for Spacecraft Insertion into Circular Orbits

Purpose. This study aims to justify the selection of parameters for a launch vehicle's pitch angle program during the insertion of spacecraft into circular orbits. The goal is to improve the accuracy and efficiency of the insertion process, optimizing the delivery of payloads to their target orbits. Design / Method / Approach. The research develops a detailed mathematical model that defines the pitch angle of a launch vehicle, specifically focusing on the relationships between the vertical and horizontal velocity components. These velocity components are represented as parabolic functions, and the model's coefficients are chosen based on numerical simulations using real flight data from the Falcon 9 rocket. Additionally, an analytical approach is presented to evaluate how different parameters influence the final orbit insertion. Findings. Analytical dependencies for model parameter selection are established, closely matching numerical simulations and confirming the validity of the approach for ensuring precise spacecraft insertion into circular orbits. Theoretical Implications. The model provides a new approach to calculating pitch angle programs using parabolic functions, contributing to the theoretical understanding of launch vehicle dynamics during orbital insertion. Practical Implications. The method can improve the efficiency of pitch angle programs for launch vehicles during the active phase of flight, optimizing payload delivery and enabling higher orbital insertions. Originality / Value. This research presents a novel methodology for modeling pitch angle programs, improving accuracy and efficiency in spacecraft orbit insertion. Research Limitations / Future Research. The model assumes simplified velocity profiles and does not account for atmospheric drag or real-time adjustments, which could be included in future research. Paper Type. Methodological.