In many cases, we have few optical observations over a short time span, and most of the information generated is too limited to compute a full orbit according to the angles-only method. This study aims to develop a mathematical model to determine the precise orbit from the optical observation data by the least squares method. We have used a set of the Global Navigational Satellite Systems, which are tracked by the Optical Satellite Tracking Station (OSTS) at the National Research Institute of Astronomy and Geophysics (NRIAG), Egypt, to access high-quality predictions for the orbits. We analyzed the orbit predictions from the observations of these satellites that are tracked from seven world stations using the laser ranging method, and the obtained results are compared with orbital elements produced using the Two-Line Element (TLE). The results showed that the orbital prediction accuracy differs for optical observations from laser observations because of the inaccuracy of the NORAD catalog information used; this is due to the difference between the time of observation and the epoch time of TLE.

In recent years, studying Lorentz’s force has become a possible good means to control the spacecraft to reduce the fuel cost by modulating spacecraft electrostatic charge (magnetic and electric fields). The generation of Lorentz force is finite by the natural magnetic field and the relative velocity of the spacecraft. Therefore, the Lorentz force cannot fully occur from conventional propulsion technologies. Previous studies are concerned with studying Lorentz’s strength in the magnetic field only. In this work, we developed a mathematical model for a new technique establishing a raise in the level of charging in the spacecraft surface that is moving in the Earth’s magnetic field and provided by modulating spacecraft’s electrostatic charge that induces acceleration via the Lorentz force. The acceleration will be used to find the relationship between capacitance and power required to minimize the consumption of control energy used in such cases or to replace the usual control thruster by Lorentz force.

This manuscript presents an approach to accurately determine the orbits of Medium Earth Orbit (MEO) and Geosynchronous Earth Orbit (GEO) space objects by utilizing data from an electro-optical sensor (Optical Satellite Tracking Station (OSTS), Kottamia Observatory station). The proposed method combines an extended and unscented Kalman filter with a semi-analytical propagation model. The effectiveness of this approach is demonstrated through numerical simulations and comparisons with traditional orbit determination techniques. The results drawn from this study show that when comparing both methods, the unscented semi-analytical Kalman filter provided more accurate orbital state estimates and required less time and fewer observations to converge.

The electrostatic charge became a possible method to control both orbital and attitude motion without fuel consumption or reduce the fuel cost. This study needs to install an ion collector on the satellite to increase the level of charging as artificial charging. In this paper, we developed a linearised satellite relative motion and a combination of Lorentz forces provided by modulating spacecraft's electrostatic charge (magnetic and electric fields) that can be used to keep the desired relative distances and orientations considering J