where: P is the break-even price per mission Cv is the cost of the vehicle tm is the time taken in per mission maintenance u is the exhaust velocity is the velocity change from LEO to GEO mp is the mass of the payload /Hpropis the mass of the propulsion system Rtm is the thrust to mass ratio for the propulsive technology vm is the cost of per mission maintenance F is the cost of fuel in orbit (about $1000) Au6 is the velocity change needed for the aerobraking return (this is the velocity decrement to bring perigee from GEO to LEO) tb is the time to circularize the orbit with an aerobraked system after the perigee is at LEO. The .005 term is an estimate of the time required to wait for burns in the case of a Hohmann transfer. With these equations a comparison can be made of three propulsive systems under consideration for OTV’s. These systems are chemical, nuclear, and electric. A lack of data for some of the required values will prevent us from coming to any final answers for the break-even price, but we will be able to make some conclusions about the comparative performance of the technologies, and the value of the formulae for examining these technologies. Below are listed the exhaust velocities and thrust to mass ratios of the three systems. Type of Propulsion Exhaust Velocity Thrust to Mass Ratio Chemical 500 m/s 800 N/kg Nuclear 700 100 Electric 1500 10“3 At present, a 10,000 kg payload is at the outer limits of current throw-away boosters. This will be the mass of the payload in the analysis that follows. We must have some way of choosing the size of the vehicle (propulsion system). Arbitrarily we will choose a 1,000 kg system for all three. This yields these expressions for the break-even price:
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