Primitive Planetary Atmospheres 17 



our present great difficulty in understanding how a planet could accumulate 

 without retaining certain gaseous constituents, e.g. krypton and xenon, it seems 

 most likely that the accumulation process required tens or hundreds of millions 

 of years and hence that the general temperature of the earth during its formation 

 was low. (The writer no longer accepts Kuiper's proto-planetary model at least 

 for the terrestrial planets [8] and in fact always had great difficulty in fitting the 

 great amount of chemical evidence into that theory.) The arrival of objects 

 containing metallic iron and water on the earth's surface would result in the 

 production of hydrogen gas, from the reaction Fe + H2O = FeO + H2, which 

 is strongly displaced to the right at high temperatures. At low temperatures 

 reactions to form methane from carbon and hydrogen, and ammonia from 

 nitrogen and hydrogen should occur and these substances should have been 

 present temporarily at least*. 



Thus a reducing atmosphere must surely have existed for a short period of 

 time at least. 



The escape of gases from planetary atmospheres is determined at the escape 

 layer by the formula of Jeans, 



Li = McCi / (I + Xi) e ^i, Xi = ~~^ 



^ 2tt [Xi KIc ac 



In this formula, Lt is the rate of escape of molecules of the ith. kind in mole- 

 cules per sec and cm^, Mc is the number of molecules per cm^ at the escape 

 layer, Ci is the fraction of these molecules at the escape layer which are of the 

 Ith kind, jlcj is the molecular weight of the escaping molecule, Tc is the tempera- 

 ture at the escape layer, ac is the radius of the planet at the escape layer, M is 

 the mass of the planet, and G the gravitational constant. The quantities in this 

 formula can be estimated approximately with the exception of a and this 

 depends particularly on the mixing in the atmosphere. Convection must stop 

 at a high level where diffusional separation becomes high. This level is estimated 

 to be at about 160 km above the Earth's surface and the rate of escape may be 

 limited by diffusion to the escape layer which for the Earth is some 300-500 km 

 above the Earth's surface. Also, condensible substances such as water will be 

 kept below the tropopause at 8-17 km above the Earth's surface. Finally, 

 condensible substances may be decomposed by ultraviolet Hght into non- 

 condensible substances which can then escape through a low temperature layer 

 to the higher atmosphere. In a recent paper, the writer [10] has reviewed this 

 problem for the Earth, Venus and Mars. The escape of planetary atmospheres 

 when these factors are considered is a very compUcated problem. The results 

 will be briefly summarized here. 



At the present time escape of hydrogen from the Earth is limited by conden- 

 sation of water at about 187 °Kat the tropical tropopause and by diffusion from 

 the 160 km level to the escape layer, the temperature of which must be high, 

 i.e. some 2000-4000 °K. The calculated rate of escape is lo"^ atoms/cm^/sec, 

 though this is uncertain by an order of magnitude probably. The escape rate 



* When these arguments were advanced some years ago [9] the brilliant work of Miller 

 had not been done and hence modifications of the discussion are necessary. 

 2 



