cargo transfer. The types of circulating transfer orbits found thus far (Niehoff, 1986) do not appear to be particularly useful. One type has low encounter velocities, but Earth-Mars and Mars-Earth passages of reasonable duration occur infrequently. The other type, a variation on the old 2-year Mars flyby trajectory with gravitationally assisted rotation of the line of apsides to make it repeat, has very high (~12 km/sec) encounter velocities at Mars. The aeroassist and propulsion penalties for such high encounter velocities would appear to outweigh any advantages of a permanent facility following this type of trajectory. Use of lunar resources in geosynchronous orbit for large construction projects has been advocated by many authors beginning with O'Neill's pioneering paper in Physics Today, (1974). The payoff as estimated by the method here is great. A related tradeoff must be conducted in this case, because labour in space is to be used to create manufactured products from the lunar resources; in the Earth launch alternative, that labour occurs on Earth. Woodcock (1982) discusses this problem in some depth, as noted above; it leads us to case study 3 for further treatment. Case Study 3: Self-Sufficiency of Space Colonies Through Export. A space colony offers potential economic advantages over a ‘company town'. A colony is an independent economic unit with import-export trade. The parent economy, i.e. on Earth, does not pay salaries and support costs for the settlers, but conducts trade such as computer chips, reactor cores and makeup biomass, for lunar products delivered to Earth orbits or to the Earth's surface. A large and mature extraterrestrial economy, with exotic and sophisticated value export products, potentially of great value on Earth, could exist in this fashion and probably only in this fashion. As we shall show, however, space settlements existing in this way must be very nearly self-sufficient. Industrialized economies produce and consume thousands of different products, ranging in unit value from a few cents per kilogram to thousands or even millions of dollars per kilogram. The question of self-sufficiency of a space settlement, i.e. its capability to produce enough of these products to obtain the rest through export trade, is difficult to deal with because of the large number of products. An analytical approach described in Woodcock (1972) offers some insight into the issues. This approach makes use of a unit value distribution function as depicted in Fig. 3. The integral of the function gives the total mass of products and the first moment integral gives the total value of the products. These integrals help to bound the form of the functions and select values. Estimates for known economies help to extrapolate to possible extraterrestrial ones. Since the mass of products with low unit value is much greater than that for products of high unit value, we should look for functions that decay rapidly as the abscissa increases. Functions of the form X"exp( —aX") and KX~n were investigated. The interest in the first form arises because it increases rapidly from zero at zero value and then decays. However, as shown in Fig. 4, the first yields distributions that are (intuitively) initially too flat, and then fall off too fast. The second form is more promising. The lower limit value for this form must exceed zero or the integrals are infinite. This seems OK as there are no products made of zero value. For this paper, I assumed a lower limit value of 10 cents per kg, $0.045/lb. Also, n must be greater than 2, or the first moment integral of the second form is infinite. When the distribution is normalized to one person, the integrals of the distribution and of its first moment, above selected lower limits, show the per capita product mass and value totals, above the lower limit value, produced by the economic unit. In other words, if we divide the US gross manufactured product value by the population, we
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