Lunar orbit VLBI modeling and application for orbit determination of deep space probes

<p indent="0mm">The Queqiao-2 relay satellite, launched in March 2024, is equipped with an interferometric antenna with a diameter of <sc>4.2 m</sc>, presenting an excellent opportunity to extend the baseline length of VLBI. By integrating the lunar orbit VLBI antenna with the ground VLBI antenna, the baseline length can be extended to approximately <sc>380000 km</sc>, approximately 100 times longer than the ground baseline length, thereby further enhancing the orbit determination accuracy. This article derives a model for measuring the time delay of the Earth-Moon VLBI within the framework of relativity theory. It analyzes the orbit determination accuracy of relay satellite through simulations and real data. Furthermore, it explores the application of Earth-Moon baseline VLBI data in precisely determining the orbit of deep space probes, such as Mars, through simulation analysis. The analysis reveals that the orbit determination accuracy of the relay satellite in a 24-h elliptical lunar orbit is approximately <sc>30 m</sc>. Compared with traditional ground-based ranging and VLBI data orbit determination method, incorporating <sc>2 h</sc> of daily Earth-Moon VLBI delay data can enhance the orbit determination accuracy of Mars probes from <sc>27</sc> to <sc>12 km</sc> prior to Mars capture. Additionally, the orbit determination accuracy of asteroid probes during transfer orbit is improved from <sc>10</sc> to <sc>6 km</sc>. The simulation analysis results confirm the potential of Earth-Moon VLBI technology in enhancing the orbit determination accuracy of deep space probes.