In the domain of maritime surveillance, the continuous tracking and monitoring of vessels are imperative for the early detection of potential threats. The Automatic Identification System (AIS) database, which collects vessel movement data over time, including timestamps and other motion details, plays a crucial role in real-time maritime monitoring. However, it frequently exhibits irregular intervals of data collection and intricate, intersecting trajectories, underscoring the importance of analyzing long-term temporal patterns for effective vessel tracking. While Kalman filters and other physics-based models have been employed to tackle these issues, their effectiveness is limited by their inability to capture long-term dependence and nonlinearity in the historical data. This paper introduces a novel approach that leverages Long Short-Term Memory (LSTM), a type of recurrent neural network, renowned for its proficiency in recognizing patterns over extended periods. Recognizing the strengths and limitations of the LSTM model, we propose a hybrid machine learning algorithm that integrates LSTM with a physics-based model. This combination harnesses the physical laws governing vessel movements, thereby enhancing the predictive accuracy of vessel locations. To simulate real-world conditions, time gaps are introduced into the dataset. We evaluate the performance of both standalone and hybrid models on datasets with and without these data gaps. Our results reveal that while the LSTM model alone outperforms the physics-based model in scenarios with data gaps, the hybrid model significantly surpasses both standalone models. This study not only demonstrates the potential of combining data-driven and physics-based approaches but also sets a new benchmark for maritime vessel tracking.