This thesis analyzes and develops the methods of accurate satellite orbits determination and estimation using adaptive Least Mean Squares (LMS), Kalman digital filters, and Adaptive Neural Networks (ANN). In addition, the thesis develops and implements satellite orbits controllers using an Adaptive Neural Network Predictive Control (ANNPC) technique. After a spacecraft has been placed in an operational orbit about the Earth, it will lose its orbit due to physical perturbation forces from the Earth, the Sun, and the Moon. Subsequent thrusting maneuvers will be required to correct the satellite orbit. Orbit estimation and determination are required with high accuracy, which are the first and the most important phase in preparation of the satellite-control-maneuver. The thesis specifically addresses the algorithmic implementation of the LMS and Kalman filters for the spacecraft orbit determination and estimation problem. The inherent advantages, disadvantages and trade-off, which are required to select the suitable method, have been analyzed. The orbit determination and estimation has been refined using multi-layers ANN with a non-linear function.