Artificial Frozen Orbits Around Small Bodies via Solar Sailing

Small bodies such as asteroids and comets present highly perturbed environments that pose significant challenges to spacecraft operations. Frozen orbits offer a practical means to maintain periodic motion; however, conventional frozen orbits are typically limited to the terminator or ecliptic planes. This paper introduces artificial frozen orbits (AFOs) around small bodies, realized by actively controlling solar radiation pressure (SRP) perturbations through solar sailing. Semi-analytical solutions for AFOs are derived using averaged Gauss variational equations incorporating dynamic SRP variations, with sail steering laws formulated as Fourier series in terms of the eccentric anomaly. The results reveal new families of AFOs that deviate from the terminator and ecliptic planes, allowing for variable orbital radii and eccentricities. A comprehensive exploration of the AFO solution space was conducted using randomly generated control profiles. Furthermore, a machine learning-based global sensitivity analysis identified that lower-order terms of the Fourier series dominate AFO formation. Finally, we present a design method to determine the optimal steering law for specified orbital elements, even when considering higher-order gravity perturbations.