than that that that that

I N T E R N A L S T R U C T U R E O F T H E M O O N Z d e n e k K o p a l 1

U n i v e r s i t y of M a n c h e s t e r , M a n c h e s t e r , England, and Jet P r o p u l s i o n L a b o r a t o r y , C a l i f o r n i a Institute of T e c h n o l o g y ,

P a s a d e n a , C a l i f o r n i a A B S T R A C T

T h e s a l i e n t o b s e r v a t i o n a l facts b e a r i n g on the i n t e r n a l constitution of the m o o n l e a d to the f o l l o w i n g c o n c l u s i o n s :

T h e m e a n density of 3 . 34 g / c m ^ s u g g e s t s the m o o n to be of a c o m p o s i t i o n s i m i l a r to that of the t e r r e s t r i a l mantle ( o r the n o n v o l a t i l e f r a c t i o n of the s o l a r a t m o s p h e r e ) , but i s e i t h e r d e f i c i e n t in i r o n (containing about 12 + 1 % of F e by w e i g h t , as against 28% f o r E a r t h ) , o r e n r i c h e d by s o m e c o m - mon l o w - d e n s i t y substance ( H 2 O , o r C 2 ? )

D e v i a t i o n s of the m a s s of the m o o n f r o m h y d r o s t a t i c e q u i l i b r i u m a r e s m a l l but s i g n i f i c a n t . In p a r t i c u l a r , the d i f f e r e n c e of lunar angular m o m e n t a about the t h r e e p r i n c i p a l a x e s of i n e r t i a a r e i n c o n s i s t e n t w i t h a h y d r o s t a t i c e q u i l i b r i u m at any distance f r o m the E a r t h . T h e n e a r - s p h e r i c i t y of the moon r e v e a l s that i t s c r u s t cannot sustain l a r g e - s c a l e d i f f e r - e n c e s in l e v e l e x c e e d i n g 1 to 2 k m ; and the absence of f r e e p h y s i c a l l i b r a t i o n s i g n i f i e s that the r i g i d i t y of the lunar g l o b e must be s m a l l e r than that of the E a r t h ,

P r e s e n t e d at the A R S L u n a r M i s s i o n s M e e t i n g , C l e v e l a n d , Ohio, July 17-19, 1962. T h i s p a p e r p r e s e n t s the r e s u l t s of

one phase of r e s e a r c h c a r r i e d out at the Jet P r o p u l s i o n

L a b o r a t o r y , C a l i f o r n i a Institute of T e c h n o l o g y , under C o n t r a c t IjTAS 7-100, s p o n s o r e d by N A S A .

P r o f e s s o r of A s t r o n o m y *

R a d i o g e n i c heat p r o d u c e d by e x p e c t e d t r a c e s of l o n g - l i v e d r a d i o a c t i v e e l e m e n t s should have r a i s e d the p r e s e n t t e m p e r a t u r e of lunar i n t e r i o r to at l e a s t 1000°K; and the s a m e could have been a c c o m p l i s h e d by v i s c o u s d i s s i p a t i o n of E a r t h - r a i s e d b o d i l y t i d e s i f the m o o n b e h a v e s as p l a s t i c . M o r e o v e r , the t e m p e r a t u r e should s t i l l be e x p e c t e d to i n c r e a s e (though not by m o r e than a 100 d e g r e e s ) in the next 3 to 4 b i l l i o n y e a r s .

A s the conductive t e m p e r a t u r e g r a d i e n t c r e a t e d by r a d i o g e n i c o r g r a v i t a t i o n a l heating of lunar i n t e r i o r e x c e e d s the adiabatic g r a d i e n t of m o l t e n r o c k s by 1 to 2 o r d e r s of magnitude, s l o w c o n v e c t i o n c u r r e n t s should p r o v i d e at l e a s t as e f f e c t i v e m e a n s of o u t w a r d heat flow as conduction o r r a d i a t i o n . Surface d e f o r m a t i o n s c a u s e d by this flow a r e p r o b a b l y the m a i n cause of the o b s e r v e d d e p a r t u r e s f r o m h y d r o s t a t i c e q u i l i b r i u m .

Should the n e w l y - f o r m e d m o o n have contained a s u f f i - cient p r o p o r t i o n of s h o r t - l i v e d r a d i o a c t i v e e l e m e n t s to m e l t it c o m p l e t e l y in the f i r s t 10? y e a r s of i t s e x i s t e n c e , c o n v e c t i v e c o o l i n g would have enabled i t t o s o l i d i f y again in a c o m p a r a - ble p e r i o d of t i m e ; and the m o o n so f o r m e d should have been l a r g e l y d e p r i v e d of a l l v o l a t i l e e l e m e n t s . Should this not have o c c u r r e d , s e c u l a r heating by l o n g - l i v e d e l e m e n t s should have brought about a m o r e g r a d u a l e s c a p e of v o l a t i l e s f r o m the i n t e r i o r . O b s e r v a b l e s u r f a c e m a n i f e s t a t i o n s of such p r o - c e s s e s a r e b r i e f l y d i s c u s s e d .

I N T R O D U C T I O N

A f t e r spending s e v e r a l d e c a d e s in a s t r o n o m i c a l s e m i - o b s c u r i t y , the m o o n has of late e m e r g e d to c l a i m r e n e w e d and w i d e s p r e a d i n t e r e s t - - n o t only on the part of the students of many b r a n c h e s of p h y s i c a l s c i e n c e , but a l s o on the p a r t of the g e n e r a l public a l l o v e r the w o r l d . T h e r e a s o n s f o r this a r e i n d e e d of h i s t o r i c a l s i g n i f i c a n c e . On S e p t e m b e r 13, 1959, the s e c o n d R u s s i a n s p a c e ship c r a s h - l a n d e d on the s u r f a c e of our s a t e l l i t e to end its a g e - l o n g s e p a r a t i o n f r o m E a r t h ; on A p r i l 23 of this y e a r , it w a s f o l l o w e d by the A m e r i c a n R a n g e r I V which s i m i l a r l y c r a s h - l a n d e d on the f a r s i d e of the m o o n t h r e e days l a t e r ; M o r e o v e r , the continuing a d v a n c e s in r o c - ket p r o p u l s i o n and e n g i n e e r i n g m a k e it a v i r t u a l c e r t a i n t y that

these f l i g h t s soon w i l l be f o l l o w e d by o t h e r s , c a r r y i n g i n s t r u m e n t s - - a n d e v e n t u a l l y m e n - - t o the m o o n , thus inaugu- r a t i n g a new e r a of d i r e c t e x p l o r a t i o n of this f i r s t one of the h e a v e n l y b o d i e s outside the g r a v i t a t i o n a l confines of E a r t h .

T h e f a c e of the m o o n stands, h o w e v e r , f o r much m o r e than a t a r g e t at w h i c h to a i m y o u r r o c k e t s . F o r the s c i e n t i s t , it r e p r e s e n t s the c o m p o s i t e o u t c o m e of l o n g - d r a w n - o u t p r o - c e s s e s - - l a s t i n g f o r m o r e than four b i l l i o n y e a r s - - w h i c h have m o l d e d this f a c e to i t s p r e s e n t f o r m by p r o c e s s e s w h i c h a r e of both e x t e r n a l and i n t e r n a l o r i g i n .

F r o m the outside, the s u r f a c e of the m o o n — u n p r o - t e c t e d by any a t m o s p h e r e - - h a s s i n c e i t s f o r m a t i o n been e x p o s e d to a l l c o s m i c i n f l u e n c e s e x p e r i e n c e d on i t s p e r p e t u a l j o u r n e y in s p a c e , f r o m c o l l i s i o n s w i t h a s t e r o i d s and c o m e t s to s w e e p i n g out of i n t e r p l a n e t a r y dust and s u f f e r i n g f r o m e x p o s u r e to x - r a y s and c o r p u s c u l a r r a d i a t i o n , as w e l l as to the p r i m a r y c o s m i c r a y s of s o l a r o r i n t e r s t e l l a r o r i g i n . T h e c u m u l a t i v e e f f e c t s of the e x t e r n a l i n f l u e n c e s m a y dominate the p o c k - m a r k e d a p p e a r a n c e of the lunar f a c e , w h i c h i s r e p l e t e w i t h c r a t e r s in a w i d e r a n g e of s i z e s , and a l s o the v a r i a t i o n of the b r i g h t n e s s of the m o o n w i t h the phase, g o v e r n e d by the m i c r o s t r u c t u r e of i t s s u r f a c e w r o u g h t and r e c r e a t e d by the constant downpour of m i c r o m e t e o r i t e s and c o s m i c dust.

T h e f a c e of the m o o n as s e e n f r o m E a r t h , i s , h o w e v e r , m o r e than a m e r e i m p a c t counter of e x t e r n a l e v e n t s , f o r i t must r e p r e s e n t a l s o a boundary condition f o r a l l i n t e r n a l p r o - c e s s e s w h i c h must have been g o i n g on in the bulk of the m o o n ' s m a s s s i n c e the days of its o r i g i n as an autonomous a s t r o n o m i c a l body. T h e s e , although p e r h a p s l e s s r e a d i l y apparent at a g l a n c e , m a y be r e s p o n s i b l e to an e v e n g r e a t e r extent f o r the fundamental s u r f a c e c h a r a c t e r i s t i c s of our s a t e l l i t e than a l l e x t e r n a l i m p a c t s . T o identify and i n t e r p r e t t h e m , h o w e v e r , an understanding of the p r o c e s s e s o p e r a t i v e in the i n t e r i o r of the m o o n as a w h o l e must be n e c e s s a r i l y be g a i n e d f i r s t . T h e p u r p o s e of this p a p e r i s to outline these p r o c e s s e s , t o g e t h e r w i t h a s u r v e y of the phenomena which they a r e l i k e l y to p r o d u c e .

5

F U N D A M E N T A L D A T A A N D C H E M I C A L C O M P O S I T I O N A n i n v e s t i g a t i o n of the i n t e r n a l s t r u c t u r e of any c e l e s t i a l body, be it a s t a r o r a planet, p o s s e s s e s many f e a - t u r e s in c o m m o n and c o n s i s t s , e s s e n t i a l l y , of the c o n s t r u c - tion of p a r t i c u l a r solutions of d i f f e r e n t i a l equations that i n s u r e the c o n s e r v a t i o n of a ) the m a s s , b ) e n e r g y , and c ) m o m e n t u m , f o r g i v e n boundary c o n d i t i o n s . In point of fact, s t a r s and planets r e p r e s e n t t w o c l a s s e s of s e l f - g r a v i t a t i n g b o d i e s d i f f e r i n g m a i n l y in m a s s by s e v e r a l o r d e r s of m a g n i - tude; and a l l d i f f e r e n t e x t e r n a l m a n i f e s t a t i o n s (such as the s i z e of l u m i n o s i t y ) s t e m d i r e c t l y f r o m this s o u r c e .

S o m e f o r t y y e a r s a g o , in the e a r l y s t a g e of d e v e l o p - ment of the study of s t e l l a r s t r u c t u r e , R u s s e l l and V o g t d i s - c o v e r e d independently a t h e o r e m ( b e a r i n g t h e i r n a m e ) w h i c h a s s e r t s that the s t r u c t u r e of a s t a r i s c o m p l e t e l y d e t e r m i n e d by i t s m a s s and c h e m i c a l c o m p o s i t i o n . T h e v a l i d i t y of this t h e o r e m t r a n s f e r s r e a d i l y to a s t r o n o m i c a l b o d i e s of the m a s s of the m o o n o r the planets as w e l l .

T h e m o s t i m p o r t a n t c h a r a c t e r i s t i c of any c e l e s t i a l body i s , i n d e e d , its m a s s ; f o r the m o o n i t i s known to be

7. 35 χ 1θ25 g o r 1. 2% of that of E a r t h . When c o m b i n e d with the lunar r a d i u s R = 1738 k m , it l e a d s to the m e a n density "p of the lunar g l o b e of 3. 34 g / c m . 3 . T h e p r e s s u r e Ρ i n s i d e the m o o n i s e s s e n t i a l l y h y d r o s t a t i c , m e a n i n g that the s t r e n g t h of i t s m a t e r i a l i s unable to withstand i t s w e i g h t a n y w h e r e except, p o s s i b l y , in the v e r y outer part of i t s c r u s t . If s o , h o w e v e r , an a p p l i c a t i o n of e l e m e n t a r y h y d r o s t a t i c s r e v e a l s that the i n t e r n a l p r e s s u r e in a g l o b e of the lunar m a s s and s i z e cannot e x c e e d its c e n t r a l v a l u e of

P^c = 2/3 π σ ρ ^² = 49000 atm

a p r e s s u r e attained at a m e r e 150 km b e l o w the s u r f a c e of E a r t h ; and this should be true r e g a r d l e s s of the kind of m a t e r i a l of which the m o o n c o n s i s t s .

P r e s s u r e s of this o r d e r of magnitude a r e nowadays attained r e a d i l y in t e r r e s t r i a l l a b o r a t o r i e s , and the changes in s p e c i f i c v o l u m e of c o m m o n r o c k s under such p r e s s u r e s have been m e a s u r e d . On the b a s i s of a l l e v i d e n c e now

p o s s e s s e d , i t i s r e a s o n a b l e to conclude that, i f the m o o n i s c h e m i c a l l y h o m o g e n e o u s throughout, the actual density of its subsurface m a t e r i a l i s p r o b a b l y 3. 28 g / c m ^ , i n c r e a s i n g to 3.41 g / c m ^ n e a r i t s c e n t e r ( l )². T h e r a d i u s of the m o o n at z e r o p r e s s u r e ( i . e . , in the a b s e n c e of g r a v i t y ) thus would be l a r g e r than the one w e o b s e r v e by 0. 61% o r 12 k m . Such a m o d e l l e a d s us to b e l i e v e that the m o o n c o n s i s t s of s i l i c a t e m a t e r i a l , s i m i l a r to the r o c k s constituting the outer p a r t of the m a n t l e of our own planet. Its m o s t abundant e l e m e n t s should b e , a c c o r d i n g to U r e y ( 2 ) , O , Si, M g , and F e , f o l l o w e d by S, A I , C a , N a , N i , and C r in a p p r o x i m a t e l y this o r d e r .

In one r e s p e c t , h o w e v e r , these v a l u e s do constitute a c h a l l e n g e : and this c o n c e r n s the r e l a t i v e abundance of i r o n in the m o o n . T h e m e a n density of the m o o n as a w h o l e t a l l i e s w e l l w i t h the p r o b a b l e c o m p o s i t i o n of the p r i m o r d i a l m a t t e r f r o m w h i c h the s o l a r s y s t e m w a s f o r m e d and w h o s e unadul- t e r a t e d s a m p l e a c c e s s i b l e to quantitative c h e m i c a l a n a l y s i s i s found now in the a t m o s p h e r e of the s u n - - u n a d u l t e r a t e d b e c a u s e the l a r g e s o l a r m a s s p r e v e n t e d the e s c a p e of any e l e m e n t s f r o m i t s g r a v i t a t i o n a l f i e l d e v e n at t e m p e r a t u r e s of s e v e r a l thousand d e g r e e s ; and y e t such t e m p e r a t u r e s a r e s t i l l f a r t o o l o w to b r i n g about n u c l e a r t r a n s f o r m a t i o n s on any a p p r e c i a b l e s c a l e . When a s a m p l e of the g a s e s now found in the s o l a r a t m o s p h e r e i s taken, the e s c a p e of i t s m o r e v o l a t i l e e l e m e n t s a l l o w e d f o r by r e l a x i n g the g r a v i t a t i o n a l f i e l d to that p r e v a l e n t on the m o o n , and the r e s t condensed, the r e s u l t i n g m a t t e r of density (at z e r o p r e s s u r e ) of 3. 3 g / c m ^ should contain, a c c o r d i n g to U r e y , b e t w e e n 11 to 14% of i r o n by w e i g h t ( 3 ) .

T h i s turns out to be l e s s than half of the r e c e n t e s t i - m a t e s f o r the i r o n content of E a r t h (which i s supposed to be about 2 8 % ) . T h e r e f o r e , e i t h e r the m o o n i s of a p p r o x i m a t e l y s o l a r c o m p o s i t i o n as f a r as i r o n i s c o n c e r n e d , w h i l e E a r t h (and other t e r r e s t r i a l p l a n e t s ) s e e m to p o s s e s s a d i s t i n c t l y h i g h e r c o n c e n t r a t i o n of this i m p o r t a n t e l e m e n t , o r - - i f i t s i r o n content i s c o m p a r a b l e w i t h that of E a r t h - - t h e m o o n ' s m a s s must contain an a n o m a l o u s l y high p r o p o r t i o n of s o m e

2

N u m b e r s in p a r e n t h e s e s i n d i c a t e R e f e r e n c e s at end of p a p e r .

c o s m i c a l l y s u f f i c i e n t l y abundant l o w - d e n s i t y substance, such as w a t e r (2 to 3%) o r g r a p h i t e (10%), to m a k e up f o r the

o b s e r v e d m e a n density of i t s g l o b e . S u r p r i s e s m a y s t i l l be in s t o r e when the f i r s t s a m p l e s of lunar r o c k s a r e r e t u r n e d by r o c k e t s to E a r t h ; but U r e y c o n s i d e r s it p r o b a b l e that the moon contains substantially l e s s i r o n than the t e r r e s t r i a l p l a n e t s . T h i s would s u g g e s t a m a r k e d d i f f e r e n c e in the c h e m i c a l p r o c e s s e s p r e c e d i n g the f o r m a t i o n of the lunar and p l a n e t a r y g l o b e s (which w o u l d , i n d e e d , be e q u a l l y t r u e i f t h e r e w e r e e x c e s s w a t e r o r c a r b o n in the m o o n ) , r e n d e r i n g E a r t h ' s s a t e l l i t e a v e r y s p e c i a l o b j e c t .

P R O B L E M S O F H Y D R O S T A T I C E Q U I L I B R I U M

How c l o s e l y does the p r e s e n t state of the lunar i n t e - r i o r approach that of h y d r o s t a t i c e q u i l i b r i u m ? T h e s i m p l e s t and m o s t d i r e c t l y o b s e r v a b l e fact attesting this situation i s , of c o u r s e , the s p h e r i c a l f o r m of the m o o n . E x t e n s i v e e v i - dence b e a r i n g on the subject r e v e a l s the m o o n to be a s p h e r e of the r a d i u s of 1738 ±1 k m . D e p a r t u r e s of the actual lunar s u r f a c e f r o m a s p h e r e of this m e a n r a d i u s a r e , at b e s t , of the o r d e r of ±1 km (being v e r y difficult to a s c e r t a i n f r o m s m a l l s t e r e o s c o p i c e f f e c t s e x h i b i t e d during l i b r a t i o n s ) a n d - - if the s i g n i f i c a n c e of such m e a s u r e s can be t r u s t e d - - a r e apparently quite c o m p l i c a t e d . N o a p p r o p r i a t e h a r m o n i c a n a l y s i s of the d e p a r t u r e s of the lunar s u r f a c e f r o m a s p h e r e , as b o r n e out by the r e c e n t w o r k of Hopmann and Schrutka- R e c h t e n s t a m m ( 4 ) o r Joksch ( 5 ) s o f a r has been m a d e . O b v i - ous i n c o n s i s t e n c i e s b e t w e e n t h e m and the s t i l l m o r e r e c e n t r e s u l t s of B a l d w i n ( 6 ) o r the U . S . A r m y M a p S e r v i c e ( 7 ) l e a d one to suspect that, on account of the m i n u t e n e s s of the m e a s u r a b l e d i s p l a c e m e n t s , the s t e r e o s c o p i c m e t h o d can furnish r e s u l t s of but m a r g i n a l s i g n i f i c a n c e , e v e n when b a s e d on the best photographic data a v a i l a b l e in the p a s t .

T h e a x i a l r o t a t i o n , in the p e r i o d of one s i d e r i c month, of a h o m o g e n e o u s m o o n r e g a r d e d as a f i g u r e of e q u i l i b r i u m should g i v e r i s e to an e l l i p t i c i t y e of the m e r i d i o n a l s e c t i o n c l o s e to e ~ l = 105500--as c o m p a r e d with e ~ l = 297 f o r E a r t h - - c o r r e s p o n d i n g to a d i f f e r e n c e b e t w e e n the e q u a t o r i a l and p o l a r s e m i a x i s of only 16.5 m ( 8 ) . S i m i l a r l y , the e q u i - l i b r i u m t i d e s r a i s e d on the m o o n by E a r t h ' s a t t r a c t i o n should p r o d u c e a s e c o n d - h a r m o n i c d i s t o r t i o n of the lunar e q u a t o r ,

c o r r e s p o n d i n g (at a m e a n distance of the m o o n ) to a d i f f e r e n c e b e t w e e n e q u a t o r i a l s e m i a x e s of 49 m - - w h i c h i s about 100 t i m e s as much as the height of the b o d i l y t i d e r a i s e d by the m o o n on E a r t h . T h e height of this bulge f a c i n g E a r t h should be e x p e c t e d , m o r e o v e r , to o s c i l l a t e by ±5 m in the c o u r s e of a month, b e c a u s e of the e c c e n t r i c i t y of the lunar r e l a t i v e o r b i t . N e e d l e s s to s a y , the a v a i l a b l e data a r e as y e t u t t e r l y insufficient to v e r i f y s o s m a l l a flattening at the p o l e s (which would appear as a d i f f e r e n c e of 0^T.^f009 b e t w e e n the e q u a t o r i a l and d i a m e t r a l s e m i a x i s of the m o o n ' s apparent disk as s e e n f r o m E a r t h ) o r so i n s i g n i f i c a n t a t i d a l bulge w h i c h w o u l d be v i r t u a l l y c o n c e a l e d by f o r e s h o r t e n i n g . T h e o b s e r v a t i o n s a r e sufficient, h o w e v e r , to r u l e out the e x i s t e n c e of a substan- t i a l l y l a r g e r d e f o r m a t i o n .

M o r e definite i n f o r m a t i o n c o n c e r n i n g lunar d i s t o r t i o n can be i n f e r r e d f r o m the extent to w h i c h such d i s t o r t i o n i n f l u - e n c e s the m o t i o n of the m o o n , both in s p a c e and around i t s c e n t e r of g r a v i t y . Thus i f A , B , and C denote the m o m e n t s of i n e r t i a of the lunar g l o b e w i t h r e s p e c t to a set of the a x e s o r i e n t e d t o w a r d s E a r t h (at the t i m e of the nodal p a s s a g e ) , n o r m a l l y to i t in the plane of the e q u a t o r , and p a r a l l e l w i t h the a x i s of r o t a t i o n , r e s p e c t i v e l y , then t h e i r t h e o r e t i c a l e q u i l i b r i u m v a l u e s f o r a h o m o g e n e o u s m o o n under p r e v a i l i n g r o t a t i o n a l and t i d a l f o r c e s should b e a r to each other the r a t i o s

(C - A ) / C = 0. 0000375 [ l ] and

(C - B ) / C = 0. 0000095 [2J such that

(C - B ) / ( C - A ) = f = 1/4 [3]

In actual fact, the o b s e r v e d v a l u e of (C - A ) / C as deduced f r o m the s e c u l a r m o t i o n of the m o o n ' s node and p e r i g e e w a s found to be 0. 000628 ± 0 . 000002(p. e . ) - - i . e . , 17 t i m e s as l a r g e as the c o m p u t e d e q u i l i b r i u m v a l u e and c o r r e - sponding to a t i d a l bulge of 1. 09 k m e l o n g a t e d t o w a r d s E a r t h ( 9 ) . Such bulge w o u l d r e p r e s e n t the height of an e q u i l i b r i u m

t i d e i f the m o o n w a s e v e r ( 1 7 ) 1 / 3 = 2.57 t i m e s c l o s e r to E a r t h than it i s n o w . H o w e v e r , at this distance the m e a n K e p l e r i a n angular v e l o c i t y of i t s o r b i t w o u l d have been ( 1 7 ) ^ / 2 = 4. 12 t i m e s l a r g e r , and the p o l a r flattening in the c a s e of s y n c h r o n i s m b e t w e e n r o t a t i o n and r e v o l u t i o n would have been 0. 28 k m . N e i t h e r this flattening nor the c o r r e - sponding t i d a l bulge s e e m to be b o r n e out by o b s e r v a t i o n s , though the e v i d e n c e i s not y e t c o n c l u s i v e .

T h e r a t i o (C - B ) / C i s much m o r e difficult to d e t e r - m i n e f r o m the m o t i o n of the m o o n in s p a c e , but the m o o n ' s o b s e r v e d p h y s i c a l l i b r a t i o n l e d , at the hands of K o z i e l , to a d e t e r m i n a t i o n of the r a t i o f to be 0. 60 ± 0 . 05 o r 0. 71 ± 0 . 05 ( 1 0 ) . T o this extent the solution i s s o f a r a m b i g u o u s , and the a n s w e r m a y be in the n e i g h b o r h o o d of e i t h e r v a l u e . W h a t e v e r the c a s e m a y b e , h o w e v e r , the o b s e r v e d f d e v i a t e s s o w i d e l y f r o m i t s e q u i l i b r i u m v a l u e ( E q . 3) of 0. 25 as to r u l e out not only the e x i s t e n c e of an e x a c t h y d r o s t a t i c e q u i l i b r i u m at the p r e s e n t t i m e , but a l s o any p o s s i b i l i t y that the m o o n ' s d y n a m i - c a l c h a r a c t e r i s t i c s m a y have p r e s e r v e d f o r us a f o s s i l f o r m of h y d r o s t a t i c e q u i l i b r i u m p r e v a i l i n g in the p a s t .

T h e hypothesis that the s u r f a c e of the m o o n r e p r e s e n t s a " f r o z e n t i d e , " so popular in the l i t e r a t u r e of o l d e r v i n t a g e , thus must be d i s c a r d e d , as w e l l as another f a l l a c y w h i c h m a y s t i l l s o m e t i m e s c r e e p in our thinking: n a m e l y , that C a s s i n i 's l a w s of m o t i o n of the m o o n about i t s c e n t e r of g r a v i t y - - a n d , in p a r t i c u l a r , the s y n c h r o n i s m b e t w e e n i t s r o t a t i o n and r e v o - lution obtaining now within b e t t e r than one p a r t in 10? ( 1 1 ) - - p r o v e the m o o n to be an e l l i p s o i d o r e v e n a s p h e r o i d . A c t u - a l l y , this fact s i g n i f i e s only that the distribution of m a s s in the lunar i n t e r i o r d e p a r t s f r o m s t r i c t r a d i a l s y m m e t r y - - w h a t e v e r the f o r m of the s u r f a c e . Once the m o m e n t of i n e r - tia about a g i v e n r a d i u s - v e c t o r b e c o m e s a function of i t s d i r e c t i o n , the body so c h a r a c t e r i z e d i s bound to o r i e n t i t s e l f , in the c o u r s e of t i m e , s o as to attain the state c o r r e s p o n d i n g to the m i n i m u m e n e r g y of the d y n a m i c a l s y s t e m of w h i c h it i s a p a r t .

T h e s m a l l but unmistakable d e p a r t u r e s of the i n t e r n a l s t r u c t u r e of the m o o n f r o m h y d r o s t a t i c e q u i l i b r i u m h a v e b e e n i n t e r p r e t e d by many authors ( J e f f r e y s , Opik, U r e y , e t c . ) as i n d i c a t i o n s that at l e a s t the c r u s t of the m o o n b e h a v e s as a

s o l i d body and p o s s e s s e s a sufficient d e g r e e of r i g i d i t y to withstand the s t r a i n o r i g i n a t i n g f r o m this c a u s e . T h i s m a y i n d e e d be t r u e of the c r u s t (though e v e n that s e e m s i n c a p a b l e of sustaining l a r g e - s c a l e d i f f e r e n c e s in l e v e l of m o r e than 1 k m ) but s c a r c e l y s o of the bulk of the m a s s of the m o o n f o r the f o l l o w i n g r e a s o n . A s it i s w e l l known, the M a x w e l l i a n r e l a x a t i o n t i m e t* r e q u i s i t e f o r the d i s a p p e a r a n c e of s t r e s s in a m e d i u m that i s not m a t h e m a t i c a l l y r i g i d i s g i v e n by the product

t* = μβ [4]

w h e r e μ i s the c o e f f i c i e n t of v i s c o s i t y of the r e s p e c t i v e m e d i u m , and

β

- h f i

^T

^Ν

i s the c o e f f i c i e n t of i s o t h e r m a l c o m p r e s s i o n (bulk c o m p r e s - sion m o d u l u s ) . F o r s i l i c a t e r o c k s of density c o m p a r a b l e w i t h the m e a n density of the m o o n , β ~ 10 "12 c m ^ / d y n e ( 1 2 ) . T h e m a x i m u m v a l u e of μ, c o n s i s t e n t with the g e o l o g i c a l e v i d e n c e b e a r i n g on the m o t i o n s in the outer c r u s t of E a r t h , a p p e a r s to be of the o r d e r of 10^2 g / c m s e c . If s o , the v a l u e of the product t* = should not e x c e e d 10*0 sec, o r s o m e 10^ y r .

T o i m p u l s e s lasting f o r a t i m e t » t * - - s u c h as a moonquake o r the i m p a c t of a r o c k e t o r a m e t e o r i t e - - t h e m o o n t h e r e f o r e , should r e a c t e s s e n t i a l l y as an e l a s t i c s o l i d and exhibit a full d i s c r e t e s p e c t r u m of not only s p h e r o i d a l (13) but a l s o t o r o i d a l (14) o s c i l l a t i o n s , l i m i t e d at the h i g h -

f r e q u e n c y end by the w e l l - k n o w n R a y l e i g h and L o v e w a v e s . H o w e v e r , when subject to the action of f o r c e s lasting f o r t » t # - - s u c h as g r a v i t a t i o n a l f o r c e s o r s t r a i n c a u s e d by i n t e r n a l h e a t i n g - - t h e m o o n ( a s w e l l as other t e r r e s t r i a l p l a n e t s ) should b e h a v e as a g l o b e of v i s c o e l a s t i c m a t e r i a l . When, m o r e o v e r , w e c o n s i d e r the fact that the a g e of the moon i s not l e s s than 4. 5 χ 1 0⁹ y r o r 1 0⁷t ^ , t h e r e s e e m s no e s c a p e f r o m the c o n c l u s i o n that, o v e r such long i n t e r v a l s of t i m e , the bulk of the m a s s of the m o o n should obey the l a w s of h y d r o d y n a m i c s r a t h e r than those of the t h e o r y of e l a s t i c i t y . T h e r e a l c l u e to i t s p r e s e n t m a n i f e s t a t i o n s as w e l l as to i t s

past h i s t o r y a c c o r d i n g l y should be e m b o d i e d in the w e l l - k n o w n N a v i e r - S t o k e s equations of v i s c o u s f l o w r a t h e r than the e q u a - tions g o v e r n i n g e l a s t i c d e f o r m a t i o n s .

T h a t this i s i n d e e d l i k e l y i s e v i d e n c e d a l s o by a w e l l - nigh c o m p l e t e a b s e n c e of f r e e l i b r a t i o n of our s a t e l l i t e . A s i s w e l l known, the g r a v i t a t i o n a l pull of both E a r t h and the sun c a u s e s the m o o n to p e r f o r m a c o m p l i c a t e d s p e c t r u m of f o r c e d l i b r a t i o n s , w i t h p e r i o d s w h i c h a r e g i v e n m u l t i p l e s of those of the disturbing f o r c e . M a n y d o z e n s of f o r c e d l i b r a t i o n t e r m s of this nature have been p r e d i c t e d and i d e n t i f i e d in the m o t i o n of the m o o n ( 1 0 ) - - b u t not a s i n g l e t e r m of a f r e e l i b r a t i o n in latitude o r longitude ( c h a r a c t e r i s t i c of r i g i d b o d i e s ) has s o f a r been i s o l a t e d in a s i g n i f i c a n t amount. A n analogy of E u l e r i a n f r e e p r e c e s s i o n ( o r , r a t h e r , the " C h a n d l e r i a n w o b b l e " ) in the m o t i o n of E a r t h i s c o n s p i c u o u s l y absent in the m o t i o n of the m o o n - - a n i n d i c a t i o n that our s a t e l l i t e as a w h o l e b e h a v e s as if it w e r e l i q u i d - - o r , at any r a t e , c o n s i d e r a b l y l e s s r i g i d than our own planet.

T H E R M A L H I S T O R Y O F T H E M O O N

Once a m o d e l of a r i g i d m o o n , as w e l l as one of a fluid moon in e x a c t h y d r o s t a t i c e q u i l i b r i u m , i s thus d i s c a r d e d as being i n c o m p a t i b l e w i t h the d e t a i l s of o b s e r v a t i o n a l e v i - dence and known b e h a v i o r of m a t e r i a l under conditions p r e - v a i l i n g in the lunar i n t e r i o r , the c a u s e of the m o t i o n w h i c h m a y disturb this e q u i l i b r i u m to the o b s e r v e d extent must be sought. By e l i m i n a t i o n of a l t e r n a t i v e h y p o t h e s e s , i t w i l l be a t t e m p t e d in the next s e c t i o n t e n t a t i v e l y to identify this m o t i o n with t h e r m a l c o n v e c t i o n i n v o k e d by s u p e r a d i a b a t i c t e m p e r a - ture g r a d i e n t . B e f o r e such a p o s s i b i l i t y i s f o l l o w e d up any further, h o w e v e r , a few w o r d s must be s a i d c o n c e r n i n g the p r e s e n t lunar heat b a l a n c e .

What i s the absolute t e m p e r a t u r e p r e v a i l i n g now i n s i d e the m o o n at the p r e s e n t t i m e ? In o r d e r to a n s w e r this question, the a v a i l a b l e s o u r c e s of heat, as w e l l as i t s s u b - sequent flow by a l l p h y s i c a l p r o c e s s through the i n t e r i o r must f i r s t be c o n s i d e r e d . F i r s t , i t must be s t a t e d that the m o o n - in c o m m o n with a l l other b o d i e s of the s o l a r s y s t e m - - o r i g i - nated p r o b a b l y by an a g g l o m e r a t i o n of s o l i d p a r t i c l e s of s m a l l s i z e s at r e l a t i v e l y low t e m p e r a t u r e s (not m o r e than a f e w

hundred d e g r e e s on the absolute s c a l e ) and decidedly less than those r e q u i r e d for v o l a t i l i z a t i o n . It does not s e e m possible to envisage a physical p r o c e s s which could have led to the formation of planetary bodies let alone of so s m a l l a m a s s as that of the moon, by a condensation of gas at high t e m p e r a t u r e but a gravitational collapse of an a g g l o m e r a t i o n of préexistent solid p a r t i c l e s into the moon could have been a c c o m p l i s h e d - - a s t r o n o m i c a l l y speaking--in a r e l a t i v e l y short t i m e (106 - 1 0⁷ y r ) .

Once the body of the moon thus g r e w up by c o a l e s c e n c e of solid p a r t i c l e s at low t e m p e r a t u r e s , additional heat must have been generated continuously throughout the m o o n ' s i n t e - r i o r by spontaneous decay of such t r a c e s of l o n g - l i v e d r a d i o - active elements (such as potassium K^O, thorium T h ^ ^ ^{o r} the two isotopes of uranium υ^35 ^{a n c}

j

^{\]238) a s a r e} l i k e l y to be p r e s e n t in the lunar m a s s in amounts c o m p a r a b l e , p e r h a p s , with those found in c h o n d r i t i c m e t e o r i t e s . T h e amount of r a d i o g e n i c heat l i b e r a t e d p e r g r a m p e r s e c o n d of such e l e - m e n t s i s known f r o m l a b o r a t o r y m e a s u r e m e n t s and s o i s the r a t e of t h e i r spontaneous decay (10^ - 1 0 ^ y r ) . T h e heat so d i s p e r s e d in m i c r o s c o p i c amounts through the e n t i r e m a s s of the m o o n then f l o w s t o w a r d s the s u r f a c e but its e s c a p e i s i m p e d e d by a l l kinds of p h y s i c a l o b s t a c l e s ( l o w t h e r m a l c o n - ductivity, high o p a c i t y , and v i s c o s i t y of lunar r o c k s ) w h i c h t o g e t h e r r e n d e r this c o o l i n g an e x c e e d i n g l y s l o w p r o c e s s .

In m o r e s p e c i f i c t e r m s , the e n e r g y equation which c o n t r o l s the r a t e of heat flow can be e x p r e s s e d in the f o r m

p C^v ^ = d i v ( K g r a d Τ ) + p € - Ρ Δ + μ φ [6]

I I I I I I I V w h e r e Τ denotes the l o c a l t e m p e r a t u r e , t the t i m e , C ^v the s p e c i f i c heat of the m a t e r i a l at constant v o l u m e , Κ the c o e f f i - cient of heat c o n d u c t i o n - - w h i c h , in the c a s e of a r a d i a t i v e t r a n s f e r , should be i d e n t i f i e d (15) with

w h e r e a denotes the S t e f a n - B o l t z m a n n constant, c the v e l o c i t y of light, and k the a b s o r p t i o n c o e f f i c i e n t p e r unit m a s s . T h e t e r m € r e p r e s e n t s the r a t e of spontaneous l i b e r a t i o n of

e n e r g y p e r unit m a s s ; Δ = d i v V i s the d i v e r g e n c e of the v e l o c i t y v e c t o r of fluid flow ( i f a n y ) ; and $ > a function r e p r e - senting the dissipation of kinetic e n e r g y of v i s c o u s f l o w into heat, w h i c h i s a known quadratic function of the v e l o c i t y c o m - ponents of m o t i o n . M o r e o v e r , the s y m b o l D / D t on the l e f t - hand s i d e of E q . 6 stands, as usual, f o r the L a g r a n g i a n t i m e d e r i v a t i v e ( f o l l o w i n g the m o t i o n ) .

If the i n t e r i o r of the m o o n could be r e g a r d e d as r i g i d , the t e r m s I I I and I V on the r i g h t - h a n d s i d e of E q . 6 would be i d e n t i c a l l y z e r o , and the only t e r m s balancing the left-hand s i d e would be I + I I . T h e l a t t e r c o n s i s t s of a l i n e a r c o m b i n a - tion of d e c r e a s i n g t i m e - e x p o n e n t i a l s w h i c h c h a r a c t e r i z e the spontaneous r a d i o a c t i v e d e c a y . T h i s , i n c i d e n t a l l y , d e m o n - s t r a t e s again a c l o s e f o r m a l a n a l o g y b e t w e e n the c o r r e s p o n d - ing s t e l l a r and l u n a r - p l a n e t a r y p r o b l e m s . A s in the s t a r s , the e n e r g y now p r o d u c e d i n s i d e the m o o n i s a l s o due to

n u c l e a r t r a n s f o r m a t i o n s , but w h e r e a s , i n s i d e the s t a r s , t h e s e r e a c t i o n s a r e e s s e n t i a l l y of the fusion t y p e , and the p r e v a i l i n g conditions a r e s u f f i c i e n t l y e x t r e m e f o r the r a t e of these r e a c - tions to be a f f e c t e d a p p r e c i a b l y by the l o c a l density and t e m - p e r a t u r e , a l l e x o t h e r m i c n u c l e a r r e a c t i o n s o c c u r r i n g now in the m o o n a r e l i m i t e d to spontaneous d i s i n t e g r a t i o n of h e a v y n u c l e i , the o r i g i n of w h i c h must be sought in the p r i m o r d i a l state of the lunar m a t t e r b e f o r e its body w a s f o r m e d .

If the a s s u m p t i o n - - h o w r e a s o n a b l e i s not y e t k n o w n - - i s m a d e that t h e s e unstable h e a v y e l e m e n t s w e r e f o r m e d at a p p r o x i m a t e l y the s a m e t i m e as the m o o n ( o r , at any r a t e , did not antedate it by a w i d e m a r g i n ) , s o r e s t r i c t e d a p r o b l e m of heat t r a n s f e r a d m i t s i n d e e d of an a n a l y t i c solution w h i c h w a s f i r s t g i v e n by L o w a n (16) and subsequently used f o r quan- t i t a t i v e p r e d i c t i o n s by U r e y ( 1 7 ) , L e v i n ( 1 8 ) , M a c D o n a l d (19), and o t h e r s . P e r h a p s the m o s t e x t e n s i v e computations of this kind w e r e c a r r i e d out by the author ( 2 0 ) . T h e o u t c o m e of t h e m a l l r e v e a l s that, e v e n i f the m o o n s t a r t e d i t s l i f e as an a s t r o n o m i c a l body i n i t i a l l y at absolute z e r o t e m p e r a t u r e , the r a d i o g e n i c heating i t should have e x p e r i e n c e d s i n c e should be sufficient to r a i s e the t e m p e r a t u r e of the bulk of its m a s s in e x c e s s of 1000°K and up to 1500 to 2000°K n e a r the c e n t e r . I f

it could be s e e n , the i n t e r i o r of the m o o n , t h e r e f o r e , should g l o w much l i k e the i n s i d e of a t e r r e s t r i a l blast f u r n a c e , and r a d i a t e light w h i c h f a c i l i t a t e s the o u t w a r d t r a n s p o r t of heat.

Such i s , h o w e v e r , the o p a c i t y of lunar r o c k s to e s s e n t i a l l y light [kp b e i n g the o r d e r of 100 to 1000 c m^{- 1} ( 1 9 ) ] that the r a d i a t i v e t r a n s f e r of heat, though s i g n i f i c a n t , cannot p r e v e n t the i n t e r n a l buildup of heat which, on account of the long l i f e - t i m e s (1θ9 to 10*0 y^r)⁰f -the n u c l e i p r o v i d i n g r a d i o g e n i c heat, i s s t i l l on the i n c r e a s e . I f t h e s e e l e m e n t s i n d e e d o r i g i n a t e d at a t i m e when the m o o n w a s f o r m e d , and i f conduction and r a d i a t i o n w e r e the only m e a n s of heat t r a n s p o r t , the m o o n should s t i l l be s e c u l a r l y w a r m i n g up in the i n t e r i o r (20) to attain m a x i m u m t e m p e r a t u r e about 2500 m i l l i o n y e a r s f r o m our t i m e . T h i s m a x i m u m , h o w e v e r , should not e x c e e d the t e m p e r a t u r e s now obtaining by m o r e than a f e w hundred d e g r e e s .

M o r e o v e r , a p o s s i b i l i t y has r e c e n t l y e m e r g e d that an a p p r e c i a b l e - - o r e v e n l a r g e - - a m o u n t of heat m a y be g e n e r a t e d in the i n t e r i o r of the m o o n by p u r e l y m e c h a n i c a l a c t i o n :

n a m e l y , by the d i s s i p a t i o n of m o t i o n due to b o d i l y t i d e s r a i s e d in the m a s s of the m o o n by t e r r e s t r i a l a t t r a c t i o n . It w a s m e n t i o n e d e a r l i e r in this p a p e r that the e c c e n t r i c i t y of the lunar o r b i t c a u s e s a " b r e a t h i n g " of the m o o n in the p e r i o d of one month, w h o s e m o s t i m p o r t a n t ( s e c o n d - h a r m o n i c ) c o m - ponent attains the amplitude of

Y²( r ) = [ 4 e h² q ( r / A )³] r Ρ²( λ ) [ β ] w h e r e e stands f o r the e c c e n t r i c i t y of the lunar o r b i t ; h², f o r

the r a d i a l L o v e n u m b e r ; q the m a s s - r a t i o E a r t h . m o o n ; A the m e a n E a r t h - m o o n d i s t a n c e ; and ( λ ) the c o s i n e of the angle b e t w e e n an a r b i t r a r y point on the lunar s u r f a c e and the d i r e c - tion of the a t t r a c t i n g f o r c e .

W i t h e = 0.0549, q = 8 1 . 3 7 , A = 384402 km and h² — 2 . 5 ( f o r a h o m o g e n e o u s c o n f i g u r a t i o n ) the a m p l i t u d e of the monthly t i d a l b r e a t h i n g at the s u r f a c e of the m o o n ( r = R = 1738 k m ) amounts to 5. 5 Ρ²( λ ) m e t e r s . A s the p e r i o d of this m o t i o n i s equal to 27. 321661 d a y s , the v e l o c i t y of r a d i a l m o t i o n g e n e r a t e d by s e c o n d - h a r m o n i c b o d i l y t i d e s turns out to p o s s e s s an amplitude of 0.00092 Ρ²( λ ) c m / s e c - - i . e . , m o r e

than a thousand t i m e s as l a r g e as the c u r r e n t e s t i m a t e s of the v e l o c i t y of c o n v e c t i o n c u r r e n t s i n s i d e the lunar g l o b e .

W i l l such m o t i o n e x e r t any influence on the lunar

e n e r g y balance as r e p r e s e n t e d by E q . 6? T h e a n s w e r depends e s s e n t i a l l y on w h e t h e r the m o o n ' s r e s p o n s e to the v a r y i n g f i e l d of t i d a l f o r c e i s e l a s t i c o r p l a s t i c - - i . e . , on the c o m p a r i - son of the M a x w e l l i a n r e l a x a t i o n t i m e t#, as defined by E q . 4, with the p e r i o d Ρ of the v a r y i n g t i d a l f o r c e w h i c h i s equal to 27. 32 d a y s .

T h e v a l u e of t* depends c r i t i c a l l y on the c o e f f i c i e n t of v i s c o s i t y of m a t t e r constituting the lunar g l o b e , and i t s e s t i - m a t e s a r e s t i l l highly u n c e r t a i n . T h e v e l o c i t i e s of t e c t o n i c m o t i o n s o b s e r v e d in the E a r t h ' s c r u s t a r e i n d i c a t i v e of the c o e f f i c i e n t μ of v i s c o s i t y as high as

1 02 2

in c g s units, w h i l e m e a s u r e m e n t s of the v i s c o s i t y of s p e c i f i c r o c k s c l u s t e r around the v a l u e of 10^^· ^Qr e v e n l e s s . T h e f o r m e r l e a d s to a v a l u e of t* c l o s e to 10*0 s e c o n d s o r s o m e 300 y e a r s ; the l a t t e r to 1θ6 s e c o n d s o r about 10 d a y s . If the f o r m e r a p p l i e s to the m o o n as a w h o l e , the r e s p o n s e of the lunar g l o b e to a monthly t i d a l w a v e should be e s s e n t i a l l y e l a s t i c - - a n d e l a s t i c o s c i l l a - tions entail no d i s s i p a t i o n of e n e r g y . On the o t h e r hand, a v i s c o s i t y c o e f f i c i e n t of 10*8 g / c m s e c l e a d s to a r e l a x a t i o n t i m e s h o r t enough to g i v e r i s e to v i s c o e l a s t i c f l o w , and cause a d i s s i p a t i o n of e n e r g y c h a r a c t e r i z e d by a function $ w h o s e a v e r a g e v a l u e ( p e r month) should be c l o s e to

**av 2 \ P / \ A / \ßl An insertion of this constant for $ on the right-hand

side of the e n e r g y Eq. 6 leads, in t i m e , to the generation of t e m p e r a t u r e s inside the lunar globe which, for μ = 1018 g / c m s e c , a r e of the o r d e r of 100°K; and f o r μ = 10*9 g / c m s e c , of the o r d e r of 1 0 0 0 ° K - - i . e . , c o m p a r a b l e w i t h i n t e r n a l t e m p e r a t u r e s e x p e c t e d by the g r a d u a l r e l e a s e of r a d i o g e n i c heat in the c o u r s e of 4. 5 b i l l i o n y e a r s . F o r μ < < 1θ18 g / c m s e c , the amount of heat p r o d u c e d by d i s s i p a t i o n of kinetic e n e r g y through v i s c o s i t y would be t o o s m a l l to be of c o s m o - g o n i e i m p o r t a n c e . On the o t h e r hand, f o r μ » 10*9 g / c m s e c the r e s p o n s e of the lunar g l o b e to a f o r c e d o s c i l l a t i o n of t i d a l o r i g i n in the p e r i o d of one month would b e c o m e e l a s t i c

and c e a s e , as such, to e n t a i l any d i s s i p a t i o n of e n e r g y o v e r a c y c l e . H o w e v e r , i f the v a l u e of the v i s c o s i t y happens to l i e within the l i m i t s 10l8 to 1 0^{1 9} g / c m s e c ( a s s u g g e s t e d by e x p e r i m e n t s w i t h i n d i v i d u a l s a m p l e s of t e r r e s t r i a l c o m m o n r o c k s ) the m e c h a n i c a l heating of the m o o n by b o d i l y t i d e s could have p r o d u c e d , throughout the long lunar past, i n t e r n a l t e m p e r a t u r e s c o m p a r a b l e w i t h , o r e v e n h i g h e r than, those due to the r a d i o g e n i c heating i t s e l f .

T h e s e c u l a r heating of the m o o n by r a d i o a c t i v e o r g r a v i t a t i o n a l p r o c e s s e s and c o o l i n g by the e s c a p e of heat through the s u r f a c e should e n t a i l , of c o u r s e , a t h e r m a l

expansion o r c o n t r a c t i o n of the m o o n as a w h o l e . S i m p l i f i e d c a l c u l a t i o n s of this e f f e c t c a r r i e d out in r e c e n t y e a r s by M a c Donald ( 2 1 ) i n d i c a t e that the p r e s e n t e x t e r n a l r a d i u s of the m o o n m a y e x c e e d by 3 to 5 k m the r a d i u s the m o o n w o u l d have had i n i t i a l l y as a c o l d body and that i t s p r e s e n t r a d i u s i s c l o s e to a m a x i m u m , o r p o s s i b l y c o m m e n c i n g to d i m i n i s h at a r a t e of about 1/2 m p e r m i l l i o n y e a r s .

T h i s change in s i z e of the m o o n , c a u s e d by the s l o w g e n e r a t i o n and t r a n s p o r t of heat i n s i d e i t s body, m a y s e e m to be i n s i g n i f i c a n t ; actually i t i s not. In o r d e r to a p p r e c i a t e i t s e f f e c t s , it should be r e c a l l e d that a change in e x t e r n a l r a d i u s of the m o o n by 1 km w o u l d r e s u l t in a change of 4. 5 χ 10^ km^

( o r about 0. 1%) of i t s p r e s e n t s u r f a c e a r e a . T h i s m i g h t p r o - duce o b s e r v a b l e e f f e c t s in the c o u r s e of t i m e . S t i l l m o r e s o , the s t e e p nonuniform t e m p e r a t u r e g r a d i e n t in the f i r s t 100 k m o r s o b e l o w the s u r f a c e (20) should p r o d u c e c r u s t a l s t r a i n s w h i c h m a y g i v e r i s e to a l i v e l y s e i s m i c a c t i v i t y and ( i f the s t r a i n s e x c e e d the e l a s t i c s t r e n g t h of the r o c k s ) p o s s i b l y to c r a c k s and f i s s u r e s . A t h e o r y of nonuniform t h e r m a l e x p a n - sion of s o l i d s p h e r e s r a d i o a c t i v e l y heated f r o m w i t h i n has b e e n d e v e l o p e d by L o w a n ( 2 2 ) , and i t s quantitative c o n s e q u - e n c e s w e r e e x h a u s t i v e l y i n v e s t i g a t e d by the author ( 1 5 , 2 0 ) . A m o r e s p e c i f i c and c r i t i c a l i n v e s t i g a t i o n of i t s b e a r i n g on the p r o l i f i c s u r f a c e m a r k i n g s of the m o o n r e m a i n s , h o w e v e r , s t i l l an a l m o s t e n t i r e l y v i r g i n f i e l d .

C O N V E C T I O N I N L U N A R I N T E R I O R

T h e r e l a t i v e l y high t e m p e r a t u r e s w h i c h t h e r e i s now r e a s o n to e x p e c t in the lunar i n t e r i o r m a y , in turn, e n t a i l a

number of o t h e r c o n s e q u e n c e s ; one of these should be at l e a s t a p a r t i a l m e l t i n g of the r o c k s e x p o s e d to t h e m f o r a s u f f i - c i e n t l y long t i m e . If s o , i t i s r e a s o n a b l e to ask w h e t h e r o r not the s t r a t i f i c a t i o n of such m a t e r i a l would be stable o v e r t i m e i n t e r v a l s c o m p a r a b l e with the a g e of the m o o n i f s u s - c e p t i b l e to actual h y d r o d y n a m i c a l f l o w , o r i f m o t i o n w o u l d be bound to a r i s e to s a f e g u a r d the c o n s e r v a t i o n of e n e r g y . B e f o r e an a n s w e r to this question i s a t t e m p t e d , a p o s s i b l e c a u s e of such m o t i o n should be sought.

A s the m o o n finds i t s e l f in v e r y n e a r l y m e c h a n i c a l e q u i l i b r i u m (within the l i m i t s m e n t i o n e d under " P r o b l e m s of H y d r o s t a t i c E q u i l i b r i u m , " the only c a u s e of m o t i o n w o u l d be the t h e r m a l i n s t a b i l i t y of i t s m a s s . T h e n e c e s s a r y condition f o r this to set in i s the r e q u i r e m e n t that the l o c a l t e m p e r a - ture g r a d i e n t be s u p e r a d i a b a t i c . N o w , as i s w e l l known ( 2 3 ) , the adiabatic t e m p e r a t u r e g r a d i e n t should be g i v e n by the equation

d T / d r = - < * g T / C p [ 1 0 ] w h e r e a denotes the c o e f f i c i e n t of v o l u m e t h e r m a l expansion,

C p the s p e c i f i c heat at constant p r e s s u r e , and g the g r a v i t a - t i o n a l a c c e l e r a t i o n w h i c h f o r a h o m o g e n e o u s body of density ρ i s c l e a r l y g i v e n by

g = | * G p r [ 1 1 ] A c c o r d i n g l y ,

( d ? )^{a d} •

- l - 3 c ^ '

^{r T}

^{l » 3}

N o w , f o r s i l i c a t e r o c k s , ûf- 2 χ 1 0 "⁵ deg~* and C p = 7 χ 1 0⁶ e r g / g deg ( 1 2 ) , w h i l e G = 6. 68 χ 1 0 "⁸ c m³/ g s e c and, f o r the m o o n , "p = 3.34 g / c m³. I f s o , then

(f)^ad = - < 2 . 7 x l 0 -⁸) r T [ 1 3 ]

w h e r e r i s e x p r e s s e d in k m and Τ in d e g r e e s . A t Τ = 1500°K and r = 100 k m f r o m the c e n t e r of the m o o n , the lunar

adiabatic t e m p e r a t u r e g r a d i e n t p r o v e s to be - 0 ° 0 0 4 / k m ; at r = 1000 k m , the v a l u e of this g r a d i e n t i n c r e a s e s t e n f o l d . On the other hand, the c o n d u c t i v e t e m p e r a t u r e g r a d i e n t as e s t a b - l i s h e d by U r e y and o t h e r s in i n v e s t i g a t i o n s a l r e a d y r e f e r r e d to (17 - 20) i s , on the a v e r a g e , of the o r d e r of - l ° / k m - - i . e . , ten to a hundred t i m e s l a r g e r .

So g r e a t a d i s p a r i t y b e t w e e n the adiabatic and c o n d u c - t i v e t e m p e r a t u r e g r a d i e n t s l e a v e s no r o o m f o r doubt that if, as a r e s u l t of m e c h a n i c a l o r r a d i o g e n i c heating, any part of the lunar i n t e r i o r b e c o m e s m o l t e n , c o n v e c t i v e c u r r e n t s a r e bound to a r i s e w h i c h w i l l t r a n s p o r t heat in addition to c o n d u c - tion o r r a d i a t i o n . M o r e o v e r , in o r d e r that this be t r u e , i t i s not n e c e s s a r y f o r actual m e l t i n g of the r o c k s to take p l a c e b e c a u s e c o n v e c t i o n can l i k e w i s e a r i s e in a v i s c o e l a s t i c m e d i u m c h a r a c t e r i z e d by a finite v i s c o s i t y , no m a t t e r how l a r g e , p r o - v i d e d only that

( d T / d r ) ^{a d}« ( d T / d r ) c o n d ft 4 ] r e m a i n s a s t r o n g i n e q u a l i t y and that the t i m e s c a l e of the flow i s s u f f i c i e n t l y long in c o m p a r i s o n w i t h the c o r r e s p o n d i n g M a x w e l l i a n r e l a x a t i o n t i m e ( w h i c h w e a l r e a d y found in the p r e c e d i n g s e c t i o n to be a m p l y the c a s e ) .

In o r d e r to e s t i m a t e the r e l a t i v e i m p o r t a n c e of c o n - v e c t i o n f o r the e n e r g y t r a n s p o r t , r e t u r n to E q . 6 and e s t i m a t e the n u m e r i c a l magnitudes of the t e r m s I I I and I V on i t s r i g h t - hand s i d e in c o m p a r i s o n w i t h the t e r m s I and I I . In o r d e r to do s o , l e t us adopt ( c o n s i s t e n t w i t h l a b o r a t o r y e v i d e n c e ) the constants K — 10^ e r g / c m s e c deg and β d 1 0 ~⁸ e r g / g / s e c . T h e magnitude of the t e r m I c l e a r l y should be of the o r d e r of K T / R² o r 1 0 "⁸ e r g / c m³ s e c f o r Τ = 1 0³ deg and the s c a l e length R of 1000 k m = 1 0⁸ c m . T h e product p € constituting the t e r m I I i s then of the s a m e o r d e r of m a g n i t u d e .

T h e t e r m I I I r e p r e s e n t i n g the heat t r a n s p o r t by c o n - v e c t i o n o b v i o u s l y should be of the o r d e r of U P / R , w h e r e U denotes the ( a v e r a g e ) v e l o c i t y of the c o n v e c t i v e m o t i o n . U n d e r which conditions a r e t e r m s I o r I I and I I I l i k e l y to be c o m - p a r a b l e in the lunar i n t e r i o r ? I f K T / R² i s equated w i t h U P / R , for a p r e s s u r e Ρ of 10^ a t m o r 10*0 d y n e s / c m³ ( c f . E q . 1 ) , i t i s found that this i s the c a s e f o r U ^ K T / P R 1 0 "^{1 0} c m / s e c

o r about a c e n t i m e t e r p e r e v e r y thousand y e a r s . A v e l o c i t y s o low a l r e a d y can r e n d e r c o n v e c t i o n and conduction of c o m - p a r a b l e i m p o r t a n c e f o r heat t r a n s p o r t in lunar i n t e r i o r ; f o r h i g h e r v e l o c i t i e s it i s the c o n v e c t i o n w h i c h should p r e d o m i n a t e .

S e v e r a l g e o l o g i c a l phenomena (continental drift, p o s t - g l a c i a l uplift, e t c . ) on E a r t h i n d i c a t e c r u s t a l v e l o c i t i e s , p o s s i b l y of c o n v e c t i v e o r i g i n , of the o r d e r of 1 c m / y r ( 2 4 ) . If such v e l o c i t i e s w e r e p r e s e n t in the m o o n - - a n d only a f u l l - d r e s s solution of the N a v i e r - S t o k e s equations subject to

a p p r o p r i a t e boundary conditions can furnish the a n s w e r - - t h e n not only w i l l the t e r m I I I dominate the r i g h t - h a n d s i d e of the e n e r g y E q . 6, being about 1000 t i m e s l a r g e r than I and I I c o m b i n e d , but e v e n the v i s c o u s d i s s i p a t i o n t e r m I V , of the o r d e r of μ ( U / R )², should b e c o m e at l e a s t as i m p o r t a n t as I o r I I .

A s i m p l i f i e d p r o b l e m of v i s c o u s c o n v e c t i o n in h o m o - g e n e o u s liquid g l o b e s r e c e n t l y has been i n v e s t i g a t e d in l i n e a r ( B o u s s i n e s q ) a p p r o x i m a t i o n by C h a n d r a s e k h a r ( 2 5 ) . F r o m his w o r k it i s i n f e r r e d that steady c o n v e c t i o n flow c h a r a c t e r i z e d by a g i v e n s p h e r i c a l - h a r m o n i c s y m m e t r y η i s m a r g i n a l l y stable f o r c e r t a i n d i s c r e t e v a l u e s of the n o n d i m e n s i o n a l R a y l e i g h n u m b e r .

Cn • ^W ° ^{£ R 6 C y} [15J 9 Κ²μ

w h i c h f o r the moon ( R = 1. 738 χ 1 0⁸ c m and ρ = 3. 3 g / c m³) and f o r the p r e v i o u s l y adopted v a l u e s of the p h y s i c a l p a r a m e - t e r s a y e , Κ , μ, and C^v l e a d s to

Cⁿ^ 1 0 ⁶ [16]

So l a r g e a v a l u e of the R a y l e i g h number (in the light of the data c o m p i l e d by C h a n d r a s e k h a r in T a b l e s 1 and 2 of R e f . 25) can c o r r e s p o n d only to i n c i p i e n t c o n v e c t i o n c h a r a c t e r i z e d only by a v e r y high o r d e r of s p h e r i c a l - h a r m o n i c s y m m e t r y (n > . 2 2 ) , r e g a r d l e s s of w h e t h e r the bounding s u r f a c e i s r e g a r d e d as f r e e o r r i g i d . T h e z e r o s u r f a c e s of s p h e r i c a l h a r m o n i c s f o r η ^ 22 a r e , in turn, so c l o s e l y packed that the e n t i r e flow pattern would s p l i t up in i n d i v i d u a l c e l l s w h o s e tops would d e l i m i t , on the lunar s u r f a c e , a r e a s c o m p a r a b l e

with those of s m a l l e r c i r c u l a r m a r i a (such as M a r e C r i s i u m o r H u m o r u m ) o r of l a r g e c r a t e r s ( o f the C l a v i u s o r S c h i c k a r d t y p e ) . W h e t h e r o r not t h e r e i s i n d e e d a c a u s a l r e l a t i o n

b e t w e e n t h e s e phenomena s t i l l r e m a i n s an open p r o b l e m . T h e c i r c u m s t a n t i a l e v i d e n c e b e a r i n g on it w a s ably d i s c u s s e d in r e c e n t y e a r s by W a s i u t y n s k i ( 2 6 ) ; the p r e s e n t a r g u m e n t c a n - not but s t r e n g t h e n the c a s e f o r g i v i n g this p r o b l e m further c o n s i d e r a t i o n .

A n o t h e r p i e c e of e v i d e n c e b e a r i n g p o s s i b l y on lunar c o n v e c t i o n i s the unequal distribution of m a r i a o v e r the e n t i r e g l o b e of the m o o n . It has been noted long a g o that the d i s t r i - bution of continental land m a s s e s and o c e a n f l o w s on E a r t h i s d i s t i n c t l y a n t i s y m m e t r i c . A h a r m o n i c a n a l y s i s of the d e p a r - t u r e s of the actual t e r r e s t r i a l s u r f a c e f r o m a m e a n g e o i d e x h i b i t s a p r e p o n d e r a n c e of odd h a r m o n i c s of r e l a t i v e l y l o w o r d e r s ( 2 7 ) , a fact w h i c h w a s i n t e r p r e t e d by V e n i n g M e i n e s z (28) o r R u n c o r n (29) as an i n d i c a t i o n of c o n v e c t i v e flow in E a r t h ' s m a n t l e . A f t e r the f i r s t photographs of the f a r s i d e of the m o o n w e r e obtained by the R u s s i a n i n v e s t i g a t o r s ( 3 0 ) , it b e c a m e i m m e d i a t e l y o b v i o u s that the s a m e type of a n t i s y m - m e t r y a p p e a r s to p r e v a i l on the m o o n , as w e l l , to an e v e n g r e a t e r d e g r e e s i n c e v i r t u a l l y a l l lunar m a r i a a r e c o n c e n - t r a t e d on one (the v i s i b l e ) h e m i s p h e r e . N o w i f the t e r r e s t r i a l c o n t i n e n t - o c e a n a s y m m e t r y i s i n d e e d due to c o n v e c t i o n in E a r t h ' s m a n t l e , the s a m e i s l i k e l y to be t r u e on the moon as w e l l , f o r analogous r e a s o n s . M o r e o v e r , the f l o o r s of the s m a l l c i r c u l a r m a r i a ( o r of c r a t e r - l i k e w a l l e d p l a i n s ) m i g h t p o s s i b l y r e p r e s e n t the tops of subsurface c o n v e c t i v e c e l l s r e a c h i n g deep in the i n t e r i o r . M u c h m o r e w o r k r e m a i n s to be done, of c o u r s e , b e f o r e this t e n t a t i v e s u g g e s t i o n can be p l a c e d on a m o r e s e c u r e b a s i s .

S P E C I A L P R O B L E M S ; E S C A P E O F V O L A T I L E S

A t p r e s e n t , t h e r e f o r e , w e s u s p e c t c o n v e c t i o n c u r r e n t s to be o p e r a t i n g in lunar i n t e r i o r in a m e d i u m of high v i s c o s i t y at an e x c e e d i n g l y s l o w r a t e . I s it c o m p l e t e l y r u l e d out, h o w - e v e r , that, at s o m e t i m e in the past, the situation c o u l d have been d i f f e r e n t and the m o o n c o m p l e t e l y m o l t e n ? T h e d e f i n i - t i v e a n s w e r cannot be g i v e n until m o r e i s known about the p o s s i b l e r o l e , in the lunar past, of c e r t a i n s h o r t - l i v e d r a d i o - a c t i v e i s o t o p e s of c o m m o n e l e m e n t s - - s u c h as i o d i n e I^{1 2} 9,

p a l l a d i u m P d^{1 0 7}, and, in p a r t i c u l a r , aluminum A l^{2 6}. T h e h a l f - l i v e s of t h e s e r a d i o a c t i v e e l e m e n t s a r e of the o r d e r of ΙΟ** to 10? y r only, and t h e r e f o r e , i f any of these had been p r e s e n t in the i n i t i a l m a s s of the m o o n , they would now be v i r t u a l l y e x t i n c t . T h e i r d e c a y products (such as X e ^ -²^ o r A g l O ? ) a p p e a r , h o w e v e r , to o c c u r in m e t e o r i t i c m a t t e r in abundances w h i c h r a i s e s s e r i o u s l y the question of f o r m e r r a d i o a c t i v i t y of t h e i r m o t h e r substances (31 to 3 3 ) . A r e a s o n - able abundance of t h e m in the p r i m o r d i a l m a s s of the m o o n m i g h t i n d e e d have been c a p a b l e of m e l t i n g i t s m a s s c o m p l e t e l y in the f i r s t few m i l l i o n y e a r s of i t s e x i s t e n c e , b e f o r e such l o n g - l i v e d r a d i o a c t i v e e l e m e n t s as K^{4 0}, T h^{2 3 2}, o r the t w o i s o t o p e s of u r a n i u m had t i m e to e x e r t any e f f e c t .

U r e y (34) a r g u e d against such a p o s s i b i l i t y s o m e t i m e ago by the fact that i f the m o o n w a s e v e r c o m p l e t e l y m o l t e n , 4 - 1 / 2 thousand m i l l i o n y e a r s would not have been long enough f o r it to s o l i d i f y to its p r e s e n t s t a t e . T h i s i n d e e d would be t r u e i f the c o o l i n g w e r e to take p l a c e by conduction of heat o n l y . In actual fact, h o w e v e r , a m o o n c o m p l e t e l y m o l t e n by the action of r a d i o g e n i c heat s o u r c e s a l m o s t c e r t a i n l y w o u l d have been r a t h e r v i o l e n t l y c o n v e c t i v e ; and c o n v e c t i o n c u r - r e n t s w o u l d drain off i n t e r n a l heat much m o r e e f f e c t i v e l y than conduction alone would have been able to a c c o m p l i s h . In other w o r d s , e v e n i f the m o o n m e l t e d c o m p l e t e l y at s o m e i n i t i a l s t a g e of i t s e v o l u t i o n by the action of s h o r t - l i v e d r a d i o a c t i v e e l e m e n t s l i k e I ^²^ , P d l O ? , o r A l²^ , c o n v e c t i v e c o o l i n g should have enabled it to s o l i d i f y again in a t i m e span c o m p a r a b l e with the p e r i o d of heating so that, at any r a t e , the s u r f a c e of the m o o n must have been s o l i d throughout m o s t of i t s a s t r o - n o m i c a l past, w h i l e the i n t e r n a l t e m p e r a t u r e has been s l o w l y r i s i n g as a r e s u l t of spontaneous d i s i n t e g r a t i o n of the l o n g - l i v e d e l e m e n t s l i k e Κ 4 0 , T h^{2 3 2},

u

^{2 3 5}

,

^{and U23 8.}

T h i s g r a d u a l i n c r e a s e of lunar i n t e r n a l t e m p e r a t u r e s throughout the long a s t r o n o m i c a l past of the m o o n should entail s e v e r a l i n t e r e s t i n g c o n s e q u e n c e s , and one of t h e m should be a d e s i c c a t i o n and d e g a s s i n g of i t s i n t e r i o r . I f the moon o r i g i n a t e d , as i s now b e l i e v e d , by an a c c u m u l a t i o n of e s s e n t i a l l y c o l d m a t t e r , i t s m a s s w a s bound to contain a l s o a finite c o n c e n t r a t i o n of c e r t a i n v o l a t i l e compounds (such as H 2 O , S O 2 , e t c . ) which could have been a b s o r b e d , at l o w t e m - p e r a t u r e s , in the c r y s t a l l a t t i c e of many m i n e r a l s and thus be

p r e s e n t in the i n i t i a l m o o n in the s o l i d s t a t e . A s e c u l a r i n c r e a s e in t e m p e r a t u r e , h o w e v e r , w o u l d in t i m e be bound to disrupt the s o l i d - s t a t e bonds and b r i n g about a l i b e r a t i o n of v o l a t i l e compounds f r o m the c r y s t a l s t r u c t u r e in which they w e r e i n i t i a l l y i m b e d d e d .

T h e c a s e of w a t e r i s p a r t i c u l a r l y a r r e s t i n g b e c a u s e of i t s r e l a t i v e l y high p r o p o r t i o n (up to 0. 1% by w e i g h t ) in stony m e t e o r i t e s and b e c a u s e of the high c o s m i c abundance of i t s constituent e l e m e n t s as w e l l as the g r e a t s t a b i l i t y of its m o l e - c u l e . In o r d e r to e s t i m a t e the p r o b a b l e amount of j u v e n i l e w a t e r in the m a s s of the m o o n , the m o r e e x t r e m e h y p o t h e t i c a l e s t i m a t e of its lunar abundance, as m e n t i o n e d e a r l i e r under

"Fundamental Data and C h e m i c a l C o m p o s i t i o n , " in connection with the d i s c u s s i o n of the m e a n density of the lunar g l o b e , w i l l be i g n o r e d , the f o l l o w i n g s a f e r analogy with E a r t h w i l l be u s e d . T h e p r e s e n t t o t a l amount of w a t e r in a l l the oceans of E a r t h i s such as to c o v e r its e n t i r e g l o b e with a u n i f o r m l a y e r a p p r o x i m a t e l y 1800 m in depth; if a l l this w a t e r w e r e p r o - duced by d e s i c c a t i o n of the w h o l e m a s s of E a r t h ( e q u a l to 5. 98 χ 10^7 g ) , each g r a m of this m a s s would have had to contribute 1. 54 χ 10~4 of j u v e n i l e w a t e r . If the s a m e p r o p o r - tion w e r e to hold for the m o o n as w e l l , i t s s m a l l e r m a s s of

7. 35 χ 10^5 g should contain an amount of j u v e n i l e w a t e r w h i c h , if s q u e e z e d out c o m p l e t e l y to the s u r f a c e , would have b e e n enough to c o v e r the lunar g l o b e w i t h an o c e a n of s o m e 300 m in depth.

W e know f r o m p h y s i c a l c h e m i s t r y that, at t e m p e r a - t u r e s in e x c e s s of 1000°K, w a t e r should have b e e n e x p e l l e d f r o m a l m o s t a l l s o l i d h y d r a t e s to f o r m s u p e r h e a t e d s t e a m . Just what this s t e a m could do i n s i d e the m o o n i s another m a t t e r . It m a n i f e s t l y could not f o r m " b u b b l e s " b e c a u s e , in m o s t p a r t s of the lunar i n t e r i o r , l o c a l h y d r o s t a t i c p r e s s u r e e x c e e d s the p a r t i a l p r e s s u r e of w a t e r v a p o r at 1000-2000°K by a w i d e m a r g i n . A l o n g any c a v i t y o r c r a c k t e m p o r a r i l y f o r m e d in the c r u s t it should be a b l e , h o w e v e r , to e s c a p e under i t s own p r e s s u r e t o w a r d s the o u t e r and c o o l e r l a y e r s , w h e r e it should condense into l i q u i d phase and e v e n t u a l l y f r e e z e in the subsurface l a y e r ( b e y o n d the r e a c h of the diurnal heat w a v e ) w h e r e a constant t e m p e r a t u r e of s o m e -40°C p r e - v a i l s ( 3 5 ) . A l o n g c r u s t a l f i s s u r e s , w h i c h could s e r v e as ducts f o r m o r e r a p i d e s c a p e , the f o r m a t i o n of i c e m a y , in

fact, take p l a c e v e r y c l o s e to the actual s u r f a c e and g i v e r i s e to m o r p h o l o g i c a l phenomena w h i c h s u g g e s t the p r e s e n c e of subsurface g l a c i e r s on the m o o n ( c f . F i g . 1 ) .

It r e c e n t l y has been s u g g e s t e d by Gold ( 3 6 ) , S a l i s b u r y (3 7), and o t h e r s that such subsurface lunar g l a c i e r s ( c o v e r e d by dust and other d e b r i s ) a r e o b s e r v e d as the " d o m e s^M- - i . e. , m i n o r bulges found in c o n s i d e r a b l e n u m b e r s in c e r t a i n r e g i o n s of the lunar s u r f a c e and o c c u r r i n g usually in c l u s t e r s . T h e R u m k e r f o r m a t i o n shown in F i g . 1 m a y be the l a r g e s t known lunar s p e c i m e n of this s p e c i e s . Other l a r g e d o m e s ( o v e r 20 k m a c r o s s ) o c c u r in the n e i g h b o r h o o d of the c r a t e r C o p e r n i c u s ( F i g . 2 ) , but a m a j o r i t y of t h e m attain d i m e n s i o n s of 3-6 k m and a m e a g e r height of s o m e 100-300 m (which m a k e s t h e m v i s i b l e only f o r a s h o r t t i m e during lunar s u n r i s e and s u n s e t ) . A t y p i c a l c l u s t e r of such d o m e s (containing at l e a s t 35 f o r m a - tions of this type o v e r an a r e a of a few hundred s q u a r e k i l o - m e t e r s ) can be s e e n in F i g . 3 i n s i d e the g r e a t w a l l e d plain east of the c r a t e r R e g i o m o n t a n u s . T h e s e f o r m a t i o n s p e r h a p s b e a r m o r e than a s u p e r f i c i a l r e s e m b l a n c e to the " p i n g o e s "

found in A l a s k a o r n o r t h e r n Canada, which m a y i n d e e d r e p r e - sent t h e i r t e r r e s t r i a l h o m o l o g u e s . C l o s e r e x a m i n a t i o n again w i l l be n e c e s s a r y b e f o r e such a s u g g e s t i o n can be p l a c e d on a m o r e s e c u r e b a s i s .

Other lunar s u r f a c e f o r m a t i o n s w h i c h m a y be i n d i c a - t i v e of the p r e s e n c e of subsurface m o i s t u r e a r e the w r i n k l e r i d g e s ( F i g . 4) w h i c h r e s e m b l e , when v i e w e d f r o m a b o v e , flat sand dunes of the t e r r e s t r i a l d e s e r t s . S a l i s b u r y (3 7) s u g g e s t e d r e c e n t l y that this w r i n k l i n g of r i d g e s o r d o m e s m a y have been caused by the hydration of subsurface beds of anhy- d r i d m i n e r a l s (such as the s e r p e n t i n i z a t i o n of o l i v i n e s ) , a p r o c e s s which i s g e n e r a l l y a c c o m p a n i e d by an i n c r e a s e in s p e c i f i c v o l u m e r o u g h l y adequate to p r o d u c e the o b s e r v e d bulging. But this v i e w r e m a i n s again s o far but a hypothesis w h i c h i s not y e t g e n e r a l l y a c c e p t e d ; and m o r e w o r k r e m a i n s to be done b e f o r e s c i e n c e can pronounce i t s final v e r d i c t .

C o m i n g back to the w a t e r making its w a y f r o m the lunar i n t e r i o r to the s u r f a c e - - s u p p o s e that, in an e x t r e m e c a s e , it m a y erupt in o c c a s i o n a l spurts as a g e y s e r . N o such phenomenon actually has been o b s e r v e d so f a r on the m o o n , though it would be v e r y difficult to detect ( v i r t u a l l y the only