A quick and efficient method for computing the optimal vehicle-trajectory combination for lunar missions using electric propulsion is developed. The problem involves computing the optimal spacecraft sizing parameters and trajectory shaping parameters that maximize the payload for a one-way, fixed-trip-time, planar transfer from circular Earth orbit to circular low lunar orbit. The computational load of the problem is reduced by utilizing universal low-thrust trajectory solutions to approximate the Earth-escape and moon-capture spiral trajectories. Several maximum-payload solutions are obtained for both nuclear electric-propulsion and solar electric-propulsion spacecraft. The nuclear results show a very good match with published exact trajectories. A sensitivity analysis of the assumed electric-propulsion technology level is also performed. Nomenclature a T -thrust acceleration, m/s 2 b = propellant-dependent coefficient c = engine exhaust velocity, km/s D = constant Earth-moon separation distance, km d = propellant-dependent coefficient, km/s g = sea-level gravitational acceleration, m/s 2 7 sp = specific impulse, s Kt -tankage fraction m net = net mass of spacecraft, kg Wp p = mass of power and propulsion system, kĝ prop . = propellant mass, kĝ tank = mass of tank and propellant feed system, kg m 0 = initial mass of spacecraft in Earth orbit, kg P = input power, kW r = radial position, km T/W = thrust-to-weight ratio kapt = powered moon-capture spiral time, days koast = translunar coast time, days £ esc = powered Earth-escape spiral time, days tf = total trip time, days v r = radial velocity, km/s VQ = circumferential velocity, km/s a = power and propulsion system specific mass, kg/kW Y] = thruster efficiency 9 = polar angle, deg IJL = gravitational parameter net = net mass fraction CD = constant Earth-moon system angular rate, rad/s Subscripts e = Earth m = moon LEO = low Earth orbit LLO = low lunar orbit Superscript * = nominal or optimal value
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