Secular Orbital Element Variations Due to Continuous Low-thrust Control and Third-body Perturbations

An analytical method is investigated to evaluate the low-thrust orbit dynamics of a spacecraft under the influence of third-body perturbations in the absence of resonance. The orbital evolution is formulated as a combination of Lagragian and Gaussian variational equations with two distinct perturbing accelerations. The third-body effects are described by Legendre polynomials and truncated up to second-order terms. Components of the control terms are represented as Fourier series in eccentric anomaly. Then the variational equations are averaged over its period to yield secular effects. The work is also presented in non-singular elements. Numerical simulation verifies the efficiency of the methodology