To achieve an on-orbit service mission, the mission spacecraft must approach the target spacecraft first, which is based on the spacecraft’s relative motion. To enhance the safety and reliability of on-orbit service missions, the relative hovering orbit was proposed and needed to be studied further. A high-precision design method for hovering orbit is presented based on the relative dynamics model of spacecraft in this paper. Firstly, based on the stability analysis of the spacecraft relative dynamics model, a method to determine the initial value of periodic relative motion orbit is explored, and an example is given to verify the validity of the method. Then, through theoretical analysis, the formulae of control acceleration required during the hovering flying mission were put forward for both without considering perturbation and with considering J₂ perturbation, and numerical simulations for hovering orbit were made to verify the feasibility of the approaches proposed. Simulation results show that the control acceleration curves are smooth, which indicates that the hovering flying mission is easier to achieve, and the control method based on sliding mode control theory is adopted for hovering control. The relative hovering method proposed can provide references in space on-orbit service missions for practical engineers.

Due to perturbation forces and control forces, trajectories of spacecraft around the Earth are usually non-Keplerian orbits, which may result in a gyroscopic effect. To meet the complex demands of space operations in the future, the trajectory prediction of spacecraft under the influence of the gyroscopic effect generated during non-Keplerian motion needs to be studied in depth. The paper investigated the trajectory of spacecraft under the gyroscopic effect generated during non-Keplerian motion. Firstly, according to the similarity between the spacecraft precession motion and the gyroscopic precession, as well as the definition of the “gyroscopic effect” of high-speed rotating bodies, the “gyroscopic effect” generated during the non-Keplerian motion of spacecraft around the earth was defined. Then, taking a continuous radial thrust orbit as an example, the dynamics equations of spacecraft under the influence of gyroscopic effect were deduced. Through theoretical analysis and numerical simulation, the trajectory of spacecraft under the influence of the gyroscopic effect generated during non-Keplerian motion was investigated. Finally, the paper simulated the examples and tested the performance of the proposed method. Simulation results show that a large gyroscopic moment may be generated in some non-Keplerian motion of the spacecraft. The greater the rotational angular velocity of the orbital plane, the greater the gyroscopic moment. Due to the gyroscopic effect, there is a significant deviation in the orbit and the orbital elements compared to those without considering the gyroscopic effect, which indicates that the influence of the gyroscopic effect generated during non-Keplerian motion on the orbit of the spacecraft cannot be ignored. It can be seen from the simulation results that the gyroscopic effect has a significant influence on the trajectory of spacecraft. In some special cases, the gyroscopic effect can be utilized reasonably to save fuel and realize low-energy orbit maneuver control technology in actual space missions; but the control should be considered for the spacecraft to bring it back to the desired orbit in most cases. It is necessary to study the trajectory of spacecraft under the influence of gyroscopic effect. The method and conclusions proposed can provide a theoretical reference for spacecraft trajectory prediction and future large-scale fast orbital maneuvers to meet the needs of complex space operations.