Development of the new approach of formation initialization using spring separation mechanism considering J2 perturbation

A new approach of formation initialization called separation initialization method was presented, using spring separation mechanism to release payload satellites one by one and enable them formation flying without any orbital maneuver. Firstly, the effect of relative motion caused by on-orbit separation was analyzed ideally by Hill-Clohessy-Wiltshire equations, while considering each separation as a velocity increment for payload satellite. Based on this analysis, the initial formation configuration was described in a series of closed relative motion ellipses by separation parameters, including the direction and size of ΔV for each payload satellite, and the time interval between two separations. Then, typical schemes of separation initialization were designed for the incompact formation and the combined incompact CartWheel formation. For separation ΔV of 1-3 m/s, the short semi axis of the formed relative motion ellipses are about 1-10 km in Low Earth Orbit, and 15-40 km in Geostationary Earth Orbit. At last, the stability of formed initial configurations was analyzed considering J2 perturbation. In order to prevent their along-track secular drifts, the constraints of separation ΔV based on linearized equations of relative motion were also improved by the constraint of J2-invariant. A few examples were developed to verify the theoretical analysis and to evaluate application schemes. Results show that the separation initialization method could provide stable formations in two weeks or more in Low Earth Orbit for small satellites cooperation without propulsion systems, and the formations could be kept even longer for a higher reference orbit.