Estimation of Impulsive Velocity for Nanosatellite Formation Keeping under Perturbation

In nanosatellite formation flying, the second geopotential harmonic gravitational acceleration is the dominant perturbation. In order to take this perturbation into account a set of linearized differential equations in Hill frame is presented. Based on these linearized equations, the estimation technique of the impulsive velocity to correct the relative position is newly presented, which only needs a set of the initial conditions. The estimated results are compared to those obtained by the integration of differential equations for the cases in which a corrective displacement exists either in the radial, in-track or cross track direction.