This article presents a comprehensive and in-depth analysis of the integration of Reconfigurable Intelligent Surfaces (RIS) with Non-Terrestrial Networks (NTN), offering ground-breaking advancements in communication systems beyond terrestrial boundaries. Through rigorous theoretical analysis and extensive simulations, the potential of RIS to enhance the performance of 6 G NTN by dynamically manipulating electromagnetic wave propagation is meticulously examined. The effects of RIS on signal optimization, coverage expansion, and energy efficiency within NTN frameworks are scrutinized. Findings indicate that RIS markedly improves signal-to-noise ratio (SNR), throughput, and bit error rate (BER) in NTN, presenting a viable solution to the pervasive challenges of global connectivity. The implications of this research are far-reaching, suggesting a future where RIS-NTN integration could become a cornerstone of advanced communication networks.