Precision analytical equation to relative motion of formation flying satellites for J₂ perturbation

A precision analytical equation to relative motion of formation flying satellites for J₂ perturbation is presented. Introduced non-singular variable, mean elements analytical orbit theory for J₂ perturbation is described. General equation for relative motion of formation satellites is obtained by first-order Taylor series expansion about chief satellite. On the basis of J₂ analytical orbit theory, relative motion analytical equation for the J₂ perturbed near-circular reference orbit is derived by using initial relative non-singularity mean elements or osculating elements, and the state transition matrixes, from the relative mean to the relative osculating non-singular elements and from the initial relative mean to random time relative mean non-singular elements and from the true argument of latitude to the mean argument of latitude, are prescribed. Simulation indicated that the relative error precision of analytical equation is less than or equal to meter level, and max-relative position errors are less than by far its of Hill equation. The method preserves advantage of precision long-time prediction for formation configuration, low computational costs and autonomous control and maneuver scheme planning of formation satellites.