National Academies Press: OpenBook

Organic Matter and the Moon, by Carl Sagan (1961)


Suggested Citation:"X. APPENDIX: SURVIVAL TIME OF AN IRRADIATED POPULATION." National Research Council. 1961. Organic Matter and the Moon, by Carl Sagan. Washington, DC: The National Academies Press. doi: 10.17226/18476.
Page 43
Suggested Citation:"X. APPENDIX: SURVIVAL TIME OF AN IRRADIATED POPULATION." National Research Council. 1961. Organic Matter and the Moon, by Carl Sagan. Washington, DC: The National Academies Press. doi: 10.17226/18476.
Page 44

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X. APPENDIX: SURVIVAL TIME OF AN IRRADIATED POPULATION We consider a population of No organisms, each having mean density p gm cm"^, characteristic size a cm, and mean lethal dose for a given kind of electromagnetic or corpuscular ionizing radia- tion of D rep. The population is irradiated with an intensity of I erg cm"2 sec"1 of the given kind of radiation, which has a mass absorption coefficient in organic matter of \j-lp cm2 gun"1. We are interested in the time, t, in seconds, for the population to be de- pleted from N0 to N organisms. Let J be the energy absorbed by unit cross-section of or- ganism due to a dose of d rep. Then, since one rep corresponds to the absorption of 93 ergs gm"1, J^ 93 p a d. (A-l) On the other hand, if the energy incident on unit cross-section of the organism is EQ, then, by Beer's law, the energy transmitted through the organism is Et = EQ e-pa . (A-2) Consequently, the energy absorbed by the organism is Ea= EQ -Et= EQ [l - e-(^M<>a] . (A-3) Now if Ea ergs absorbed by 1 cm2 corresponds to a dose of d rep, Ea = J, and from equations (A-l) and (A-3), i-l Eo /d = 93 p a [ 1 - e"(ti/p)pa J erg cm-2 rep-l . (A-4) Consequently, the time, T , for one organism to accumulate D rep due to an incident flux of I erg cm"2 sec"1 is r= (D/I) (E0/d) . (A-5) Assuming an exponential survival curve for the population of organ- isms, the number surviving after time t will be N = N0 e -t/r . (A-6) 43

Solving equation (A-6) for t, substituting from equations (A-4) and (A- 5), and converting from natural to common logarithms, we ob- tain for the time in which the population will have been depleted to N organisms, t=214ap(D/I) f 1 - e-fc/'J'aJlogjo (NQ/N). (A-7) In the case that the mean lethal dose, D, is given directly in units of erg cm"2 instead of rep, as is the case for ultraviolet ir- radiation, equation (A-7) is replaced by t = 2. 3 (D/I) [ 1 - e-(n/p)pa | lOglQ (NQ/N). (A-8) Table II was constructed from equations (A-7) and (A-8); p was taken as unity throughout. For an organism opaque in the given radiation, (\i./p)pa » 1, and equations (A-7) and (A-8) reduce respectively to t = 214 a p (D/I) logic (N0/N), (A-9) and t- 2.3 (D/I) 1og10 (NQ/N) . (A- 10) For an organism which is almost transparent in the given radiation, (n/p)pa « 1, and a Taylor series expansion of the exponential re- duces equations (A-7) and (A-8) respectively to t = 214 (,/ji) (D/I) log10(N0/N) (A-ll) and t=(2.3/^a) (D/I) 1og10 (N0/N). (A"12) 44

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The immediate future seems to hold both the promise and the responsibility of extensive contact between man-made objects and the Moon.

Current United States plans tentatively call for the soft landing on the Moon of instrumentation designed to detect indigenous organisms or organic matter, possibly in a roving vehicle, by 1964-67 in the Surveyor and Prospector Programs. The Soviet Union apparently has the capability of performing similar experiments at an earlier date. It is clear that positive results would give significant information on such problems as the early history of the Solar System, the chemical composition of matter in the remote past, the origin of life on Earth, and the distribution of life beyond the Earth. By the same token, biological contamination of the Moon would represent an unparalleled scientific disaster, eliminating possible approaches to these problems. Because of the Moon's unique situation as a large unweathered body at an intermediate distance from the Sun, scientific opportunities lost on the Moon may not be recoupable elsewhere.

This monograph is concerned with the possibility of finding indigenous lunar organisms or organic matter, and with the possibility of their contamination by deposited terrestrial organisms or organic matter.

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