The problem of small spacecraft minimum-fuel heat-rate-constrained aeroassisted orbital transfer between two low Earth orbits with inclination change is considered. Assuming impulsive thrust, the trajectory design is described in detail and the aeroassisted orbital transfer is posed as a nonlinear optimal control problem. The optimal control problem is solved using an hp-adaptive pseudospectral method, and the key features of the optimal trajectories are identified. It was found that the

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... impulse solutions are obtained when the vehicle enters the atmosphere exactly twice. Furthermore, even for highly heat-rate-constrained cases, the final mass fraction of the vehicle was fairly large. Finally, the structural loads on the vehicle were quite reasonable, even in the cases where the heating rate was unconstrained. drag specific force magnitude, m=s 2 e = eccentricity g 0 = standard acceleration due to gravity, m=s 2 h = altitude over spherical Earth, m or km h atm = maximum altitude of sensible atmosphere, m or km i = inclination, deg or rad K = drag polar constant L = lift specific force magnitude, m=s 2 ' _ Q = natural logarithm of stagnation point heating rate n = number of atmospheric passes _ Q = stagnation point heating rate, W=cm 2 _ Q = stagnation point heating-rate multiplier, W=cm 2 _ Q = maximum allowable stagnation point heating rate, W=cm 2 r = geocentric radius, m or km R e = radius of Earth, m S = standard gravity-normalized specific force magnitude S = maximum standard gravity-normalized specific force magnitude t = time, s or h u 1 ; u 2 = alternative control parameterization v = speed, m=s or km=s v c = Earth radius circular speed of spacecraft, m=s or km=s = angle of attack, deg or rad = maximum allowable angle of attack, deg or rad = inverse of density scale height, m=s V = instantaneous impulse, m=s or km=s V 1 = instantaneous deorbit impulse, m=s or km=s V 2 = instantaneous boost impulse, m=s or km=s V 3 = instantaneous recircularization impulse, m=s or km=s = flight-path angle, deg or rad = longitude, deg or rad = gravitational parameter, m 3 =s 2 = true anomaly, deg or rad = atmospheric density, kg=m 3 0 = atmospheric density at sea level, kg=m 3 = bank angle, deg or rad = latitude, deg or rad = heading, deg or rad = longitude of ascending node, deg or rad ! = argument of perigee, deg or rad