Purpose: This paper presents a full fourth-order model of the gravity gradient torque of spacecraft around asteroids by taking into consideration of the inertia integrals of the spacecraft up to the fourth order, which is an improvement of the previous fourth-order model of the gravity gradient torque. Design, methodology and approach: The fourth-order gravitational potential of the spacecraft is derived based on Taylor expansion. Then the expression of the gravity gradient torque in terms of gravitational potential derivatives is derived. By using the formulation of the gravitational potential, explicit formulations of the full fourth-order gravity gradient torque are obtained. Then a numerical simulation is carried out to verify our model. Findings: We find that our model is more sound and precise than the previous fourth-order model due to the consideration of higher-order inertia integrals of the spacecraft. Numerical simulation results show that the motion of the previous fourth-order model is quite different from the exact motion, while our full fourth-order model fits the exact motion very well. Our full fourth-order model is precise enough for high-precision attitude dynamics and control around asteroids. Practical implications: This high-precision model is of importance for the future asteroids missions for scientific explorations and near-Earth objects mitigation. Originality and value: In comparison with the previous model, a gravity gradient torque model around asteroids that is more sound and precise is established. This model is valuable for high-precision attitude dynamics and control around asteroids.
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