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under the constraints of starting point, target point, total travel time, total initial mass, total available power, and specific mass of the power source, makes the integral a minimum. This problem can be solved with the methods of variational calculus. In fact, computer programs exist already for numerous planetary trajectories and their optimization, and specific missions (for example, a rendezvous with asteroid Eros in 1975 or 1977) can be programed and computed easily. The computation results in optimum figures for the exhaust velocity, the program for thrusting and coasting periods, the guidance program, the actual payload capability, etc. It is obvious from equations (1) and (4) that the thrust acceleration of an electrically propelled spacecraft will always be low, on the order of 107* go. However, the thrust force on planetary missions will always act over a long period of time, on the order of months or even years. For this reason, the total impulse generated by an electric-propulsion system is of considerable magnitude. In fact, an ion thrustor powered with 16 kW of electric power and operating for 350 days generates the same total impulse as the hydrogenoxygen rocket engine RL 10 used on the second stage of the Saturn I rocket (six engines) and on the Centaur rocket stage (two engines). (See table II.) Before the propellant particles can be subjected to the accelerating force of an electric field, they must be ionized. Three different ionization methods have been developed to a high degree of efficiency and reliability: the electron bombardment method (Kaufman engine), developed at the NASA Lewis Research Center; the radiofrequency ion source (Loeb engine), developed at the University of Giessen in West Germany; and the contact ionization method, developed mainly at Electro-Optical Systems Corp. and at Hughes Research Laboratory. All three systems fulfill the requirements of an electric propulsion system, and all have undergone long-time laboratory testing. Furthest advanced in development, testing, and flight applications is the Kaufman engine in which ionization of the vaporized propellant is accomplished by electron bombardment; it is shown in figures 3 and 4. The first application of an electric propulsion system to a space probe, as far as publicly known, occurred in 1964 on the Soviet spacecraft Zond 2. Numerous electric thrustors for attitude and station control were used on U.S. satellites, as shown in table III. An ion thrustor for prime propulsion was applied on the U.S.S.R. space probe Yantar in 1969. Two American test vehicles for ion thrustors, SERT 1 and 2, were launched in 1964 and 1970. Although not completely successful, they definitely proved the proper functioning of ion propulsion systems under space conditions, and they established full confidence in this method of rocket propulsion. The SERT 2 test vehicle with two 1 kW ion engines is shown in figure 5. Design lifetime of SERT 2 was 1 yr. Project cost, including the Atlas/Agena carrier vehicle, amounted to approximately 12 million dollars. Experience shows that a thrustor designed for about 2.5 to 3 kW power consumption represents an optimum thrustor size. Thrustors of this type can TABLE II.-Comparison of Chemical and Electric Rockets With Equal Propulsion Capabilities
Mass of Mass
*Total impulse = thrust x time.
Figure 4.—Cluster of two ion engines (electron bombardment or Kaufman type).
be clustered easily for higher power and thrust levels. A propulsion system with three thrustors, consuming 8 kW of power, would be an adequate system for “easy” planetary missions. More demanding missions could be carried out with vehicles consisting of two or three modules of the 8 kW type. An artist's conception of an electrically propelled spacecraft is depicted in figure 6.
TABLE III.-Flights Having Electric Thrustors for Spacecraft Control
Vehicle Date of launch Functions of thrustors Type Propellant
Zond 2 (U.S.S.R.) 1964 Attitude control Plasmajet o
Department of Ion (bombardment) Hg
Defense Resistojet NH3
Table IV lists a number of desirable flight missions throughout the solar system that could be accomplished with electrically propelled vehicles. The first part contains missions powered with solar electric power; three different vehicle sizes and power levels are envisioned. The second part, containing more demanding missions to the outer planets, is based on a future nuclear electric power source of about 150 kW.