The Titius-Bode law, initially proposed as an empirical relationship describing planetary distances from the Sun, has been a subject of both fascination and scrutiny in the field of celestial mechanics. Over time, variations and modifications to the original law have emerged, aiming to enhance its predictive accuracy and explanatory power. This research paper presents a comparative analysis of the original Titius-Bode law and a modified version proposed in recent literature. The study assesses the predictive performance and goodness of fit of both laws using statistical metrics such as mean squared error (MSE) and R 2 score. Additionally, graphical representations of observed and predicted distances for various planet positions are analyzed to discern patterns and deviations. The findings reveal significant differences between the original and modified laws in terms of predictive accuracy and model fit. While the original law demonstrates superior performance in capturing the observed data patterns and providing accurate predictions, the modified law exhibits limitations, potentially stemming 1 from over-fitting or simplifications. The implications of these findings for understanding planetary dynamics and the broader field of celestial mechanics are discussed, highlighting the importance of rigorous model evaluation and refinement in advancing our understanding of the cosmos. Furthermore, this study introduces a novel polynomial equation derived from observational data, offering insights into potential refinements of existing models and avenues for future research.