Differential Drag-Based Reference Trajectories for Spacecraft Relative Maneuvering Using Density Forecast

Abc = element of matrix Ad to which aDcrit is the most sensitive Ad = stable linear reference state-space matrix As = Schweighart and Sedwick model state-space matrix aDcrit = magnitude of the differential drag acceleration ensuring stability aDrel = magnitude of the differential aerodynamic drag acceleration aPrelx, aPrely = differential accelerations caused by orbital perturbations excluding drag, along x and y directions of the local vertical/local horizontal frame CDC, CDT = chaser and target spacecraft’s drag coefficients e = tracking error vector it = target’s initial orbit inclination J2 = second-order harmonic of Earth gravitational potential field (Earth flattening) lb, ub = lower and upper bounds for the optimization mC, mT = chaser and target spacecraft’s mass Re = Earth mean radius Rt = position vector of the target in relation to the Earth SC, ST = chaser and target spacecraft’s crosswind surface area u = on/off control signal V = Lyapunov function vs = spacecraft velocity vector magnitude with respect to the Earth’s atmosphere xn = state-space vector of the nonlinear system including relative position and velocity between the spacecraft in the local vertical/local horizontal orbital frame xt = reference state-space vector in the local vertical/ local horizontal orbital frame δAop = modifications made to matrix Ad for the optimized adaptation μ = Earth’s gravitational parameter ρ = atmospheric density ω = magnitude of the orbital angular velocity of the target