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On the evolution of the lunar orbit
ICAl~us 30, 254-266 (1977)
On the Evolution of the Lunar Orbit ] ) . L. TURCOTTE, ,]. L. ('ISNE, AND ,L C. NORI)MANN
Department of Geological Sciences, Cornell Unh~ersily, Ithaca, N¥w York 1/~853 Received l)ecember 3, 1975; revised M a y 13, 1976 II is getmrally accepted t h a t t h e E a r t h -Moon separalion is al present increasing due to tidal dissipation. Values for the corresponding hmar deceleralion and the related slowing of (,he E a r t h ' s rot at;on are obtained from ~stronomical observations and by studies of ancient eclipses. t".xtrapolati(m of these wdues leads to a ch)se approach of the E a r t h and Moon 1 3 b,y. BP. ttowever, justification for such an extrapolation is required. It ha~ been hypothesized l h a t periodicities in the Precambrian stronmtoliies can be used to delermine t h e number of solar clays in it hmar re(ruth prior to 50(1 m.y. BP. These data combined with dynamic constrainls on the number of solar (lays in a h m a r m o n t h indieate a (:lose approach of the E a r t h and Moon at 2.85 :t: 0.25 b.y. BP. It is suggested that, the nmre volcanism on (he Moon and high-temperature Archean volcanism on the E a r t h prior lo this date were caused by tidal heating. I t is also suggested t h a t the strong tidal heating during a (qose approach could have e(mtribuled to the formati(m of ihe firsi living m'ganisms.
l NTR()I)(TCTION Darwin (1880) showed that the hmar orbit is receding from the Earth due t() tidal dissipati(m. Early astronomical studies (1;'otheringham, 1920 ; Spencer ,lent,s, 1939) confirmed this increase in the Earth-Moon separati(m and the eorresp(mtling (tecrease in l he rotatimml velocity ()f the Earth. Using these measurements, Gerstenkm'n (1955, 1957, 1967a) suggested that a close approach occurred at about. 1.9 b.y. BP. His conclusions were e(mfirmod by MacDonald (1964a, t), 1965, 1966, 1967) and l)y Lamar el al. (1970). Independent evidence on the (,w)lutim~ , f the E a r t h Mo,m system has t)c(,n obtained from studies of tim y(,~rly and m(mthly petit)die(ties in the size, ()f daily growth increments in the skol('tons -f corals, mollusks, and ()ther Phanerozoic organisms, and in Precambrian and Phanerozoic algal stromatolites. Tile growth ()f these marine organisms reflects both the tidal cycle, with a lunar monthly period,
"rod a daily cycle with a period that gent,rally approximates the, solar day (Pannella and MacClintock, 1968; Pannella el at., 1968). These, studies (Scrutt(m, 1967, 1970; Wells, 1970; Berry and Barker, 1968) showed that the number of days in both a year and a month were increasing through the Phanerozoic. (;erst(mkorn (1955) argued that the, Moon was originally in a retrograde orbit, that tidal friction decr(,ased the Earth,~l()on Sel)arati(m and increased the in(,linatiml of the lunar orbit until the ,\loon flipped into a pr()grade orbit at a sel)arati(,n n(,ar the (lethe limit for tidal disintegration, and that tidal friction th('n increased tim E a r t h Moon separation to its present value. (;oldreich (1966, 1968) showed that this sequence of (w(,nts was dynamically unacceptable (see also (b,rstenkorn, 19671), 1968). Also, many geologists argued that there was no evidence in the geological record for a close approach at about 2 b.y. BP. Although
254 Copyright ~) 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.
ISSN 0019- 1035
EVOLUTION OF THE LUNAR ORBIT Gerstenkorn (1969) and Alfven and Arrhenius (1969) proposed qualitative alternatives to the orbital flip, these alternatives have not been confirmed by detailed calculations. The evolution of the lunar orbit has many implications regarding both the origin of the Moon and its evolution. If the Moon has always been closer to the Earth than it is now, this places important constraints on any theory for the origin of the Moon. However, if the Moon was originally at a large distance from the Earth, was drawn to the Earth by tidal dissipation, and experienced a nonlinear close interaction prior to the present receding orbit, such constraints are not applicable. If the Moon was originally at a position closer to the Earth than it is now, capture is dynamically unlikely. However, if the Moon was originally at a large distance from the Earth, the probability of capture is enhanced. Virtually all studies of the thermal evolution of the Moon have neglected heating by tidal dissipation. The importance of tidal heating within the Moon has been suggested by Kaula (1963, 1966), Williams (1973), and Wones and Shaw (1975). Sjogren and Wollenhaupt (1976) have associated the figure of the lunar maria with tidal interactions. Recent studies of periodicities in Precambrian stromatolites by Pannella (1972) have important implications regarding a lunar close approach. Turcotte et al. (1974) hypothesized that these periodicities were consistent with a close approach of the Earth and Moon at 2.85 ~ 0.25 b.y. BF. EVOLUTION OF THE LUNAR ORBIT Many previous authors have utilized numerical calculations to study the evolution of the lunar orbit. However, an approximate analytic approach illustrates the important physical processes and the results are in excellent agreement with the numerical calculations. The essential simpli-
255
lying assumption is that the angular momentum vectors for the Earth's rotation and the motion of the Moon about ~he Earth are assumed to be parallel. The Moon is also assumed to be in a circular orbit about the Earth and the energy dissipation due to solar tides is neglected. With these assumptions, conservation of angular momentum in the Earth-Moon systems requires that M~t C~o + - - - R'coL = Ho, M + m
(1)
where C is the moment of inertia of the Earth about its axis of rotation, ~o is the rotational velocity of the Earth, M is the mass of the Earth, m the mass of the Moon, R is the mean Earth-Moon separation, ~L is the angular velocity of the Moon about the Earth, and H0 is the present angular momentum of the system. Kepler's third law requires that ~'~t~~ = G(M + m),
(2)
where G is the universal constant of gravity. The energy of the system is made up of the kinetic energy of the Earth's rotation plus the kinetic and potential energy of the Moon's orbital motion
l (___Mm_~ + -
2 \M+
GMm R % L 2 -- _ _
m/
R
(3)
The energy E is being reduced by tidal dissipation. We assume that the torque on the Earth, N, due to the lunar tide, is inversely proportional to the sixth power of the Earth-Moon separation (Goldreich and Soter, 1966) N = N o ( R o / R ) 4,
(4)
where No is the present value of the tidal torque and R0 is the present Earth-Moon separation. The torque on the Earth is related to the change in its angular ve-
25(i
TUt{COTTIq, CISNE AND NORI)MANN
locit,y b y
in a lunar month,
X = C(d,,.,/dt).
(5)
Combining (4) and (5) gives the dependenee of the change in angular velocity on separation
d,.o/dt = (d~/dt)o(I¢,,/l¢)';,
(6)
where (d%/dl)o is the present ac('.(,h,ratioil ()f the Earth's r(/(ati(m, C(nnbining (1), (2), and (6) w(! find thai
,.:
-
i/,;;R-i,'-;\J/0
,;
('b
= (%
\ d~/0 \-}}-/
(7)
hltegration gives
'~ [l:{(dR~,q2]13
([~ 2]13
where to is tile time when R -+ The number of solar days m o n t h and in q year will also Tilt' length of tile 3"(,at' is given
(s)
0. in a lun:/r be derived. by
Ty = 2~/'.q,
(9)
where ~ is the angular v(qocity of the Earth about the Sun. The h'ngth of the hmar mtmth is given by
TL.,, = 2 , ~ / ( ~ , ~ - ~a)
(lo)
and the length (ff the, solar day is given by Ts,,
= 2,~/(~
- - ~2).
(11)
C,(nnbining (9) "rod (11) with (1) and (2), the number of s.lar days in a year is given t)3"
Ty
llo
Mm (
R(; 3~
. . . . . . . . . . . . . .
1.
(t2)
The number of solar days ut a year decreased monotonically in the past. Similarly, eombiifing (10) and (11) with (1) and (2) gives the number of solar days
tlo r,,,,
Mm ( RG )' (7,, d i 7 , 7 ,
-
(1:~)
5/'Sl) Rtt \
-]~
-
-
l
()he asp(,('( of (13) which has reeeiv(,d little a t t e n t i . n [although it was included in the calculations of MacDonald (19648, b) and L a m a r el al. (1970)] is th'tt the l~Um|)er of solar days in a lunar tllollth has a maximum. Since b o t h the h'ngth of the solar day and the length . f the lunar mo~dh are elmnghtg it is n(~t a priori evident how the ratio varies. ICr()m (13) the lnaxinmm number of solar clays in a lunar m o n t h is 31.5 and it ,mt'urs at R/Re = 0.85. These values will change wh(,n alh)wance is made for the Earth's obliquity and for solar tidal torques; however, the results . f MacDonald (19643, b) and I,amar ct al. (1970) indieate these changes are small. Similar results are obtained for the mmfl)(,r of lunar days in a lunar m, mlh. Fro' this ease the m'~ximum is 30.5 days/'m(mth, also at R;'Ro = 0 . 8 5 , STROMATOLITE PI:~RIODICITIE8 Although studies of periodicities in corals show t h a t Ill(> number of solar days in a [llIlar lIloilth alia a year arty decreasing, the seatter in the data and possible time w~riations ,,f tidM dissipation preclude ])aekward extrapolation. Of particular imp()l'ialH~(,, (bert,fore, are '{he illeasurelllellts of p(,riodieiti(,s in Precambrian strolllatolit(,s given by Pannella (1972). His (!mints of the peri()dieities are, given in Vig. 1. The older stronmtolit(,s seem to have better p(,riodicities t h a n the y()unger. This could 1)e due lo lhe larger tides caused by '~ n(,arer 5teen. If the maximum count is •(ssoeiat(!d with the fortnightly rid(; the number of solar clays in a hmar month is given in Fig. 2. The error bars (m lhe,
EVOLUTION OF THE LUNAR ORBIT
20
150 MYBP
0
o9 ;Z
257
~ ' ~ J ~ J ] - ~
~
'-~-
20
510 MYBP
0
0
20
,,
o
9 0 0 - 1 , 3 0 0 MYBP ~
-
~
~
~ , ~
o
>'(JZ 4020 r-'-r~'q-r-H~-~/L~,
1,600-1,900MYBP
"'
(21 0 t,
60
[
~
2 , 6 0 0 - 3,10 0 MYBP
40 20 o
0
I0
2 0
-
~
30
COUNTS
40
50
Fro. 1. Counts of periodicities in stromatolites as given by Pannella (1972). number of days are the standard deviations given b y Pammlla (•972). The error bars oil the dates are those given b y the author, who dated the rocks from which the fossils were obtained. Also given in Fig. 2 is a data point obtained b y M o h r (1975). Clearly this is not consistent with the data of Pannella (1972). Pannella (1975) has discussed this discrepancy and points out t h a t low points are often the result of incomplete counts. Although it is clear t h a t stromatolite periodicities must be used with caution, we will consider the implications of the data given b y Pannella (1972). In using the stronmtolite data to determine the evolution of the lunar orbit, the Bulawayan data at 2.85 ~: 0.25 b.y. BP. are critical. Although the counts of the Bulawayan growth patterns favor the 18.7day m o n t h because of the strong peak at 9 days corresponding to the fortnightly tides, Pannella (1972) did not rule ou~ the alternative interpretation of a 37.4-day month. However, our calculations show
t h a t this value is dynamically unacceptable since there is a maximum of 31.5 solar days in a lunar month.
30
+
1
20
,, ~
,o o
o Pannella (1972) o Mohr (1975)
I TIME
i
j
2
3
BYBP
FIG. 2. The data points were obtained from periodicities in stromatolites by Pannella (1972) and Mohr (1975). The solid curve is from Eqs. (8) and (13).
258
TURCOTTE, CISNE AND NORDMANN
-I" A.<[ i,i
40 0
(/)
Z 0 0
20
ir
Ltl 7" <[
t~ I~
0 0
L
L
I
I
2
3
TIME
BYBP
Fro. 3. I)ependence of the Earl h-Moon separation on lime from Eq. (8). On the basis of the stromatolite d a t a we assume t h a t R = R0 at t = 2.85 X 109 yr. F r o m (8) we find t h a t the c,)rresponding value for the increase in the E a r t h - M o o n separation is 2.08 c m / y r . And from (3) the present energy dissipation is 1.85 X 10 t9 ergs/sec. T h e predicted dependence of the Earth--Mo(m separation on t i m e is given in Fig. 3. Using (8) and (13), the predicted (t('pendence of the n u m b e r of solar days in a lunar m o n t h on time is c o m p a r e d with
the str()matolite d a t a in Fig. 2. Within the given errors, all the d a t a points obtained b y I'annella (1972) fall on the predicted curve. It should be emphasized t h a t the predicted close a p p r o a c h at 2.85 =t= 0.25 b.y. BP. is critically dependent on the B u l a w a y a n d a t a point. However, there is no reason to have less confidence in this d a t a point t h a n in the others, and it is seen that. all the d a t a points are in excellent agreement with the predicted dependence. I n Fig. 4, the predicted depend-
/
I000
)n~ uJ Q. 03 ),< a
500
rr
.¢ -I 0 u)
o
I
2 TIME
5
BYBP
FIG. 4. Dependence of the number of days in a year on time from Eq. (8) and (12).
EVOLUTION OF THE LUNAR ORBIT
259
fo~
jo~ __
SOLAR
_ =FLU~ . . . . . .
ENERGY DISSIPATION ERGS/SEC,
--
- -
ic.
I0 0 MEAN
- G ~ O - - T ~ E f f M Z C -F-L O
l
~0
x
l
EARTH*MOON
-
~
. . . . . . . .
4]
DISTANCE,
0 EARTH
l
l 60
RADII
F~G. 5. Dependence of the rate of energy dissipation in the Earth-Moon system on the EarthMoon separation. ence of the n u m b e r of days in a y e a r on t i m e from (8) and (12) is given. T h e rate of energy dissipation is given as a function of the E a r t h - M o o n separation in Fig. 5. Also included in this figure are the t o t a l geothermal heat flux f r o m the interior of the E a r t h at the present time and the present solar flux incident onto the Earth. Clearly the energy input into the E a r t h b y tidal dissipation played an i m p o r t a n t role in the terrestrial energy balance if the M o o n was at a n y time significantly closer to the Earth. Since the length of time the M o o n would spend in close proximity to the E a r t h m a y be quite limited, it is of interest to give the total energy in the E a r t h - M o o n system, from (3), as a function of the E a r t h - M o o n separation; this is done in Fig. 6. An a p p r o a c h to ten E a r t h radii would require the dissipation of 3.5 X 10 a7 ergs; this is sufficient energy to heat the entire E a r t h a b o u t 500°C.
I n each case, the measured acceleration of the M o o n or the deceleration of the E a r t h has been converted into a rate of energy dissipation assuming t h a t the angular m o m e n t u m of the E a r t h - M o o n s y s t e m is conserved and t h a t (3) is applicable. There is considerable discrepancy a m o n g the results. Explanations for these discrepancies include : (i) T h e angular m o m e n t u m of the E a r t h M o o n s y s t e m is not conserved. There ap-
2
ENERGY I037 ERGS !
HISTORICAL MEASUREMENTS The present rate of tidal dissipation can be inferred from studies of the orbital dynamics of the E a r t h - M o o n system. T h e m e a s u r e m e n t s are s u m m a r i z e d in Table I.
'
"MEAN
2'o
EARTH-MOON
'
DISTANCE
~o
'
EARTH
s'o
RADII
Fro. 6. Dependence of the energy in the EarthMoon system on the Earth-Moon separation.
260
TURCOTTE, CISNE ANI) NORI)MANN TAB1,E I Measurements of the Present Evolution of the ]Pmrth-Moon System Reference
Fotheringham (1920) Murray (1957) Newton (1970)
Muller and Stephenson (1975) Spencer Jones (1939) Newton (1968) Van Flandern (1970) Morrison (1973) Van Flandern (1975) Oesterwinter and Cohen (1972)
Loss of energy ~ ( 1(),9 ergs/sec) Ancient asl ronomical observalions, hlllar orbili Ancient ast,ronomical observations, Earth's rolalion Ancient astronomical obsexwations Ancient astrononfical observalions, -762 to 500, lunar orbit Ancient astronomical observations, -762 to 500, Earth's rotation Ancient a~tronomi(..al observat,ions, since 500, lunar orbit Ancient aslrononfical observations, since 500, l';art.h's rotalion Ancien( ~Lsi,ronomical ot)setwaiions Lun'~r "rod planelary observations since 1750 Orbits of near-Earth satellites Occultalions of stars by Moon versus atomic lime OcculIalions of stars by Moon versus atomic time Occull.adons of slars by Moon vel~us atomic lime Meridian observations from 1912 to 1968
3.42 2.65 5.54 4- 0.8 5.45 4- 0.56 3.63 4- 0.45 5.54 4- 0.80 2.(`)5 4- 0.13 4.9 l 4- 0.65 2.(,)4 4- 0.16 2.63 4- 0.34 6.81 4- 2.l 5.54 4- 0.8 8.58 4- 2.38 4,(,)8 4- 1.05
- To convert to lunar acceleration in arcsec/century ~-, nmltiply by --7.63. p e a r s t o b e a s y s t e m a t i c difference in tide r e s u l t s of F o t h e r i n g h a n ~ (1920) a n d N e w t o n (1970) b a s e d on l u n a r a c c e l e r a t i o n a n d Earth deceleration. Attempts have been m a d e t o cxt)lain t h e n o n c , m s e r v a t i ( m of a n g u l a r m o m e n t u m b y m e t e o r o h ) g i c a l effects a n d I)roccsses w i t h i n tide E a r t h , b u t no a d e q u a t e m e c h a n i s m h a s /)e(m f o u n d ( M u n k a n d M a c l ) o n a l d , 1960). (it) T h e g r a v i t a t i o n a l c o n s t a n t (; is c h a n g i n g . T h e r e a p p e a r s t() be a s y s t e m a t i c difference b e t w ( , e n m(,asuremen~s b a s e d on e p h e r m e r i s t i m e a n d on a t o m i c t i m e . T h i s difference ('all b e a t t r i b u t e d t,) a ('hange in U ( V a n F l a n d e r n , 1975). (iii) T h e r e a r e e r r o r s in stone or all ()f t h e o b s e r v a t i o n s whi('h r(,main t() 1)e resolved. The discrepancies between measuremenI s u s i n g t h e s a m e t e c h n i q u e a r e so l a r g e t h a t it is ditEeult a t t h i s t i m e t o Sllecify ( w i t h i n a b o u t a f a c t o r of 2) j u s t w h a t t h e p r e s e n t r a t e of t i d a l d i s s i p a t i o n is. T h e v a l u e ,)f 1.85 X 10 .9 e r g s / s e e i n f e r r e d f r o m t h e
s t r o m a t o l i t e d a t a is n e a r t h e l o w e r l i m i t of t i l e ()bservations. Aid o r b i t a l c a l c u l a t i o n u s i n g t i l e h i g h e r v a l u e s w o u l d r e s u l t ill a n E a r t h M o o n ch)se a p p r o a c h subsequ(,nt to 2,85 b.y. BI ). T h e a s s u m p t i o n t h a t t i d a l en(,rgy dissipation has a simple functional dependell(~e i)lt t h e t i d a l forces o v e r gcologi(',al t i m e is o p e n t() q u e s t i o n . T h e s o u r c e ()f tile tidal dissipation has not been establishe(1. S o m e a u t h o r s c o n c l u d e t h a t t h e p r i m a r y source ,)f t i d a l d i s s i p a t i o n is t h e s h a l l o w seas (l~ambeck, 1975). If t h i s is tide case, t h e t i d a l d i s s i p a t i ( m c o u l d c h a n g e b y at l e a s t a n o r d e r of m a g n i t u d e b e c a u s e of c h a n g e s in s(,a level a n d c o n t i n ( , n t a l drift. ( ) t h e r a u t h m ' s ('(intend t h a t t h e e n e r g y a s s o c i a t e d w i t h t i d a l d i s s i p a t i o n is diss i p a t e d w i t h i n t h e solid E a r t h ( M e l c h i o r , 1974) a n d m a y d r i v e t h e d y n a m o r e s p o n sible for t h e E a r t h ' s m a g n e t i c field. If t h i s is t h e case, a r e l a t i v e l y s i m p l e d e p e n d e n c e su('h as (4) m a y be valid.
EVOLUTION OF THE LUNAR ORBIT
261
THE GEOLOGICAL AND SELENOLOGICAL Earth and the Moon can explain the maria RECORD volcanism on the Moon and the highThere is evidence in the geological temperature Archean volcanism on the record that there was an important change Earth. Tidal heating during a close approach in the evolution of continents at about 2.7 b.y. BP. Burke and Dewey (1973) of the type proposed by Gerstenkorn give this date as the end of what they (1955) would not give the required heating. call the permobile phase of continental Significant tidal heating within the Moon evolution. They suggest that this may would appear to require the Moon to be have been due to a rapid decline in internal initially in a highly elliptical orbit. Pushheat generation at this time. Sutton (1973) pull tides on the Moon would reduce the recognizes a similar transition between 2.9 elliptical orbit to a near-circular orbit and 2.4 b.y. BP when widespread plutonic (Goldreich, 1963). Assuming that a paraactivity ceased to affect the entire crust bolic orbit is reduced to a circular orbit and was gradually restricted. The Archean with the same minimum Earth-Moon prior to 2.85 b.y. BP was characterized separation and assuming that the resultant by high-temperature ultramafic volcanism tidal heating occurs uniformly throughout (Naldrett, 1973) with komatiite volcanism the Moon, the temperature increase is at temperatures as high as 1650°C (Green, given in Fig. 7. It is seen that this mecha1975). nism can significantly heat the lunar inIt is interesting to note that this is the terior. Sinmltaneous tidal slowing of the same period during which mare volcanism Earth's rotation could have heated the was occurring on the Moon. Although con- Earth's interior. duction calculations can be carried out THE BIOLOGICALRECORD that give a period of near-surface heating on the Moon between 3.8 and 3.1 b.y. BP The thermal regime accompanying the (Solomon and Toks6z, 1973), these cal- close approach of the Earth and Moon culations require quite restrictive initial should have had a catastrophic effect on conditions. Tidal heating on both the life, if it existed at. that time. The large 3000
2000
AT °C
I000
0
20
MINIMUM
40
EARTH-MOON
60
SEPARATION,
I00
80
EARTH
RADII
Fro. 7. Change of temperature within the Moon when a highly eccentric orbit is reduced to a circular orbit as a function of the minimum Earth-Moon separation.
262
TURCOTTE, CISNE AND NORDMANN
a m o u n t of energy dissipated through tidal heating quite conceivably could have vaporized the world ocean (Munk, 1968). About 3 X 10 a4 ergs would be required to vaporize the present world ocean. F r o m Fig. 6 this is seen to be a v e r y small fraction of the energy dissipated during the ch>se approach. In all likelihood, whatever living organisms m a y have been present at t h a t time were killed. The paleontological record is consistent with the view t h a t life originated at about the predicted time of close approach. Within the range of error in radiometrie age determination, the (,h)se approach coincides with the first records of life. Some confusion has existed concerning the age of the Swaziland system of southern Africa, which contains the first possible records of life. A minimmn age of 3000 =t= 30 m.y. has been established from R b S r ages ()f intrusives (Allsopp et al., 1968), and a nmximum age of 3 2 3 0 3290 ln.y. has been obtained from studies ()f the U-Th--Pb systematics of lavas and pilh)w basalts in the Onverwa(:ht series at the base of the Swaziland system (Sinha, 1972). Previously made Rb Sr whole rock age determinations, particularly those in excess of 3300 m.y., have been cited as indicating a more ancient age f.r the first records of life. More, recently it has t)een rexealed t h a t l i b - S t chemistry ,,f the ()nverwacht has been disturbed by metamorphism (Alls()pp et al., 1973; Jahn and Shih, 1973). Ages determined from mlmerous samph,s cover the range 3300 =k 500 m.y. (.lahn and Shih, 1973). The firs'~ reliable evidence ()f living organisms seems to be cells from the Fig Tree series, which overlies the Onverwacht series (Sehopf, 1975). However, toward the extremes in the nmrgin ()f dating error, the Bulawayan stromatolites may actually be older t h a n the Fig Tree cells by as nmch as 100 m.y. Earlier "cell-like objects" from ()nverwacht w)lcanic rocks (l,]ngel cl al., 1968) are lm)bably m)t cells (Sch()l)f,
1975) but m a y be fossil coaeervate droplets (Mueller, 1972). Carbon and organic con> pounds in Onverwacht rocks m a y or may not have been associated with biological activity (Scott et al., 1970; Oehler el al., 1972; Brooks el al., 1973; Schopf, 1975). ()therwise, extensive banded iron forlnation, indirect evidence of life (Cloud, 1968), has been reliably dated at no more t h a n 3000 m.y. (Goldich, 1973). Perhaps life originated twice, once before and once after the close approach of the E a r t h and Moon. lieliable evidence of living ()rganisms a significant period before the pr(,dicted time of close approach is lacking. It is conceivable that the close approach played a direct role in the origin of life. The close approach would have resulted in a large input of heat energy inh) evolving prebiologieal systems ~hat t . g e t h e r with ultraviolet radiation and other energy inputs could haw~ been important in driving syntheses ()f prel)iological c()mpounds. Since an '%rganic SOUl)" ()f pr(,bit)logical eomp(mnds in dilute aque()us solution has been synthesized under a variety . f possible early-Earth conditions t h a t do nl)t itlw)lvc' heat as the primary (,nergy source, there is no reason 1o b(,lieve t h a t a thermal event was nec(,ssary for the f r s t steps in prebioh)gical ev()luti(m. But the I)r('dicted thermal catastrot)h(' may lmv(, b(,(,n quite important at succeeding st(,ps. A world o('ean of "organic SOUl)" would have been heated, t)erhaps ('omplet(qy vaporized, and then r(,(;()ndens(,d in th(, e(mrse of the approach and recession ()f the Earth and Moon. The progression ()f gh)bal conditimts would res(,lllble tim r(@m(,n of experiments in which mixtures of amino acids and wat(,r haw~ be(,n vaporized and then rccondensed (l"-x, 1965, 1971). The result of these exp(¢iments was thermal t)olym(,rizatim~ of amino acids to form proteinoids and f.rmati(m of cell-like protein(rid ('oaeervates m~ rec(mdensati,m, l l l a S l n U C h 118 anlill() acid polymeriz'ttimt can take l)lace thrq)ugh
EVOLUTION OF THE LUNAR ORBIT catalysis at lower temperatures, a thermal event is not necessary to explain the formation of proteinoids. While the thermal catastrophe, in combination with other factors, may help in explaining the synthesis of prebiological compounds, its primary significance is perhaps as a means by which these compounds could be concentrated out of aqueous solution on a global scale. It has often been suggested that prebiological compounds were concentrated in intertidal pools and cavities from which water evaporated at low tide. Increased tidal amplitude during the time of close approach would obviously have facilitated this mechanism. However, vaporization of the entire world ocean during the time of close approach, followed by fractional recondensation as temperatures afterward returned to normal, would seem to provide a more dramatic, if not more effective, mechanism for the concentration of prebiological compounds and, eventually, the formation of coacervate droplets in aqueous solution. From this point, living cells may have arisen from selfreplicating coacervate droplets. Contrary to the idea that life was the product of a long period of prebiological evolution under relatively constant conditions, we suggest that life was perhaps the product of a geologically short period of singular conditions brought about by a close approach of the Earth and Moon. CONCLUSIONS Despite the substantial increase in our knowledge of the Moon which resulted from the Apollo Project, the origin of the Moon and the evolution of the lunar orbit remain an enigma. We favor the hypothesis put forward by Clark et al. (1975) that the Moon was captured during the final stages of accretion (approximately 4.6 b.y. BP). This capture placed the Moon in a retrograde orbit at a large distance from the Earth. Initially both the Earth and Moon were hot, tidal friction
263
was large, and tidal dissipation caused the Moon to approach the Earth. We further hypothesize that tidal interactions between the Earth and the Moon occurred over an extended period of time between about 3.8 and 2.8 b.y. BP and that the frictional heating due to these tidal interactions was responsible for the high-temperature Archean volcanism on the Earth and the maria volcanism on the Moon. A natural consequence of this hypothesis is that the surface deformation of the Moon due to tidal forces fractured the brittle outer shell of the Moon, allowing the magmas to fill the preexisting craters. Similar effects on the surface of the Earth could have initiated plate tectonics. The interaction of the Earth and Moon may also have played an important role in the initiation of life. Although it is far from obvious how nmjor tidal interactions between the Earth and the Moon could extend over a billion years, the dynamics of a close interaction are poorly understood. It is possible that a series of resonant interactions as proposed by Alfven and Arrhenius (1969) occurred during this time. At about 2.85 b.y. BP we hypothesize that the Moon entered a prograde orbit about the Earth. Since then the E a r t h Moon separation has been increasing and the tidal interaction decreasing. This orbital evolution is consistent with the measurements of periodicities in Precambrian stromatolites given by Pannella (1972). An extrapolation of the present Earth-Moon orbit requires a close approach; the orbital evolution which we hypothesize is in better agreement with the historical observations than alternative hypotheses which keep the Moon in a retrograde orbit since it was formed. ACKNOWLEDGMENTS The ~uthors acknowledgehelpful discussionswith D. R. Wones, P. M. Muller, and W. M. Kaula and would like to thank S. J. Weidmsclfillingfor
264
T U R C O T T E , C I S N E AND N O R I ) M A N N
a very helpful review of all earlier version of lhis paper, This research was supported by G r a n t N G R 33-010-108 from ~he National Aeronautics and Space Administration. C o n t r i h u l i , n of the l)cpar(men( of Geological Sciences No. 593.
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ALLSOPP, H. L., VILJOEN, ~[. d., AND VItA()EN, I2[. P. (1973). Stronlium isotopic studies ()f tim marie and felsie rocks of the Onverwacht group of the Swaziland sequence. Geol. Rundschau 62, (.t02 (.117. BI,;RIty, W. B. N., AND BAICK~.:Ib R. M. (196S). Fossil bivalve shells indicalc hmger mm~th and year Cretaceous than present. Nat~re (Loadort) 217, 938-939. B~mOKS, J., M u m , M. ])., AXO S~,.XxV, (L (197;'). Chemistry and morphohigy of Precambrian microorganisms. Nature (London,) 244, 215 217. BURKE, K., AND DI.:WFy, J. F. (1(.1731. An oulline of Precambrian plate developmm,~. In [replicalions of Conlinental Drift lo lhe Earlh Scienee,~ (I). lt. Tarling and S, K. Runcorn, Eds3, V.l. 2, pp. 1035-1045. Academic Press, Lon&m.
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l,~v.xl~, I). L., M(:(I ~xx-l,~x~xl{, a. V., x~xl~ Xl~.:url,'JJ:~,~), P. M. (19701. Age mid origin of lhe V:trth-Xh).n syslem, hi 1)alaeog(,ophysh'.s (S. K. Runcorn, ]':d.), pp. 41 52. Academic Press, New York. "L.~,xn~v:(:K, K. (19751. leA'feels of tidal dissipaii(m in lhe oee'ms on lhe Moon's orbit and the ]';arl,h's rolatiun. J. Geoph W. lies. 80, 2917-2(.125.
EVOLUTION OF THE LUNAR ORBIT hlAcDoNALD, G. J. F. (1964a). Earth and Moon: Past and future. Science 145, 881-890. MAcDoNALD, G. J. F. (1964b). Tidal friction. Rev. Geophys. 2, 467-541. MAcDoNALD, G. J. F. (1965). Origin of the Moon: Dynamical considerations. Ann. N. Y. Acad. Sci. 118, 739-782. ~IACI)ONALD, C~. J. F. (1966). Origin of the Moon: Dynamical considerations. In The Earth-hloon Syslem lB. G. Mamden and A. G. W. Cameron, Eds.), pp. 165-209. Plenum, New York. --~{AcDONALD, G. J. F. (1967). Evidence from the surface configuration of the Moon on its dynamical evolution. Proc. Roy. Soc. London A 296, 298-303. MFLCHIOR, P. (1974). Earth tides. Gcophys. Surveys I, 275-303. MOHR, R. E. (1975). Measured periodicities of the Biwabik (Precambrian) stromatolites and their geophysical significance. In Growth Rhythms and the History of the Earth's Rotation (G. D. Rosenberg and S. K. Runcorn, Eds.), pp. 43-55. Wiley, New York. MORRISON, L. V. (1973). Rolation of the Earth from A. I). 1663-1972 and the const'mcy of G. Nat~tre (London) 241, 519-520. MUV;LLm~, G. (1972). Hydrotherma]ly associated organic microspheres from S. W. Mrica and elsewhere. In Molecular Evolution: Prebiological and Biological (D. L. Rohlfing and A. I. Oparin, Eds.), pp. 379-397. Plemlm, New York. MULLI'Ht, P. M., A.ND STEPHENSON, F. R. (1975). The acceleralions of the Earth and Moon from early astronomical observations. In Growth Rhythms and the History of the Earth's Rotation (G. l). Rosenberg and S. K. Runcorn, Eds.), pp. 459-533. Wiley, New York. MI~NK, W. H. (1968). Once again--tidal friction. Quart. J. Roy. Astron. Soc. 9, 352-375. MUNK, W. H., .~ND MACDONALD, G. J. F. (1960). The Rotation of the Earth. Cambridge, London.
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OEHLER, O. Z.~ SCHOPF~J. W.~ AND KVENVOLDEN K. A. (1972). Carbon isotope studies on organic matter in Precamblian rocks. Science 175, 12461248. OESTERWlNTER, C., ANn COHEN, C. J. (1972). New orbital elemen(s for Moon and planets. Celestial 3[ech. 5, 317-395. PANNELLA, (]. (1972). Paleontological evidence on the Earth's rotational history since early Precambrian. Astrophys. Space Sci. 16, 212-237. PANNELLA, G. (1975). Palaeontological clocks and the history of the Earth's rotalion. In Growth Rhythms and the History of the Earth's Rotation (G. D. Rosenberg and S. K. Runcoru, Eds.), pp. 253-283. Wiley, New York. PANNFLLA, (~., AND ~IACCLINTOCK, C. (1968). Mollusk shells and Earth's history. Discovery 4, 3-12.
PANNELLA, G., .-~,IAcCLINTOCK~C., AN1) THOMPSON, M. N. (1968). Paleontological evidence of variations in length of synodic Inonth since late Cambrian. Science 152, 792-796. SCHOPF, J. W. (1975). Paleobiology of the Precambrian: The age of bhm green algae. Evol. Biology 7, 1-43.
SCOTT, W. ~ . , MO1)ZEL~.;SK~,V. ]~]., :kiD NAGY, B. (1970). Pyrolysis of early pre-Cambrian Onverwacht organic matter (>3>(10 ~ yearn old). Nature (London) 225, 1129 ll30. SCRUTTON, C. W. (1965). Periodicity in Dev(mian coral growth. Paleontology 7, 552-558. SCI~UTTON, C. T. (1970). Evidence h)r a monthly periodicity in the growth of some corals. In Palaeogeophysics (S. K. Runcorn, Ed.), pp. 1]-]6. Academic Press, New York.
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N,tLDm.~TT, A. J. (1973). Nickel sulphide deposits-their classification and genesis with special eraphasis oa deposits of volcanic association. Canad. Inst. 3lin. 3let. Trans. 76, 183-20l.
SPENCER JONES, H. (1939). The rotaii(m of lhe Earth, and the secular acceleralion of lhe Stub Moon, and planets. Mon. Not. Roy. Astron. Soc. 99, 541-558.
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266
T U R C O T T E , C I S N E AND N O R I ) M A N N
TURCOTTE, l). L., NORDMANN, J. C., AND (?[SNE, J. L. (1974). Evolution of the Moon's orbit and the origin of life. Nature (London) 251, 124-125. VAN FL.
Runcorn, Ed.), pp. 3-9. Academic Press, New York. WILLIAMS, (}. ]~. (1973). Geotectonic cycles, lunar evolution, and the dynamics of the Earth-Moon system. Mod. Geol. 4, 159-183. WONt:S, D. R., AND SHAW, H. R. (1975). Tidal dissipation: A possible heat source for mare basalt magmas (abstract). In Lunar Science VI, pp. 878-879. Lunar Science Institute, Houston, Tex.
On the Evolution of the Lunar Orbit ] ) . L. TURCOTTE, ,]. L. ('ISNE, AND ,L C. NORI)MANN
Department of Geological Sciences, Cornell Unh~ersily, Ithaca, N¥w York 1/~853 Received l)ecember 3, 1975; revised M a y 13, 1976 II is getmrally accepted t h a t t h e E a r t h -Moon separalion is al present increasing due to tidal dissipation. Values for the corresponding hmar deceleralion and the related slowing of (,he E a r t h ' s rot at;on are obtained from ~stronomical observations and by studies of ancient eclipses. t".xtrapolati(m of these wdues leads to a ch)se approach of the E a r t h and Moon 1 3 b,y. BP. ttowever, justification for such an extrapolation is required. It ha~ been hypothesized l h a t periodicities in the Precambrian stronmtoliies can be used to delermine t h e number of solar clays in it hmar re(ruth prior to 50(1 m.y. BP. These data combined with dynamic constrainls on the number of solar (lays in a h m a r m o n t h indieate a (:lose approach of the E a r t h and Moon at 2.85 :t: 0.25 b.y. BP. It is suggested that, the nmre volcanism on (he Moon and high-temperature Archean volcanism on the E a r t h prior lo this date were caused by tidal heating. I t is also suggested t h a t the strong tidal heating during a (qose approach could have e(mtribuled to the formati(m of ihe firsi living m'ganisms.
l NTR()I)(TCTION Darwin (1880) showed that the hmar orbit is receding from the Earth due t() tidal dissipati(m. Early astronomical studies (1;'otheringham, 1920 ; Spencer ,lent,s, 1939) confirmed this increase in the Earth-Moon separati(m and the eorresp(mtling (tecrease in l he rotatimml velocity ()f the Earth. Using these measurements, Gerstenkm'n (1955, 1957, 1967a) suggested that a close approach occurred at about. 1.9 b.y. BP. His conclusions were e(mfirmod by MacDonald (1964a, t), 1965, 1966, 1967) and l)y Lamar el al. (1970). Independent evidence on the (,w)lutim~ , f the E a r t h Mo,m system has t)c(,n obtained from studies of tim y(,~rly and m(mthly petit)die(ties in the size, ()f daily growth increments in the skol('tons -f corals, mollusks, and ()ther Phanerozoic organisms, and in Precambrian and Phanerozoic algal stromatolites. Tile growth ()f these marine organisms reflects both the tidal cycle, with a lunar monthly period,
"rod a daily cycle with a period that gent,rally approximates the, solar day (Pannella and MacClintock, 1968; Pannella el at., 1968). These, studies (Scrutt(m, 1967, 1970; Wells, 1970; Berry and Barker, 1968) showed that the number of days in both a year and a month were increasing through the Phanerozoic. (;erst(mkorn (1955) argued that the, Moon was originally in a retrograde orbit, that tidal friction decr(,ased the Earth,~l()on Sel)arati(m and increased the in(,linatiml of the lunar orbit until the ,\loon flipped into a pr()grade orbit at a sel)arati(,n n(,ar the (lethe limit for tidal disintegration, and that tidal friction th('n increased tim E a r t h Moon separation to its present value. (;oldreich (1966, 1968) showed that this sequence of (w(,nts was dynamically unacceptable (see also (b,rstenkorn, 19671), 1968). Also, many geologists argued that there was no evidence in the geological record for a close approach at about 2 b.y. BP. Although
254 Copyright ~) 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.
ISSN 0019- 1035
EVOLUTION OF THE LUNAR ORBIT Gerstenkorn (1969) and Alfven and Arrhenius (1969) proposed qualitative alternatives to the orbital flip, these alternatives have not been confirmed by detailed calculations. The evolution of the lunar orbit has many implications regarding both the origin of the Moon and its evolution. If the Moon has always been closer to the Earth than it is now, this places important constraints on any theory for the origin of the Moon. However, if the Moon was originally at a large distance from the Earth, was drawn to the Earth by tidal dissipation, and experienced a nonlinear close interaction prior to the present receding orbit, such constraints are not applicable. If the Moon was originally at a position closer to the Earth than it is now, capture is dynamically unlikely. However, if the Moon was originally at a large distance from the Earth, the probability of capture is enhanced. Virtually all studies of the thermal evolution of the Moon have neglected heating by tidal dissipation. The importance of tidal heating within the Moon has been suggested by Kaula (1963, 1966), Williams (1973), and Wones and Shaw (1975). Sjogren and Wollenhaupt (1976) have associated the figure of the lunar maria with tidal interactions. Recent studies of periodicities in Precambrian stromatolites by Pannella (1972) have important implications regarding a lunar close approach. Turcotte et al. (1974) hypothesized that these periodicities were consistent with a close approach of the Earth and Moon at 2.85 ~ 0.25 b.y. BF. EVOLUTION OF THE LUNAR ORBIT Many previous authors have utilized numerical calculations to study the evolution of the lunar orbit. However, an approximate analytic approach illustrates the important physical processes and the results are in excellent agreement with the numerical calculations. The essential simpli-
255
lying assumption is that the angular momentum vectors for the Earth's rotation and the motion of the Moon about ~he Earth are assumed to be parallel. The Moon is also assumed to be in a circular orbit about the Earth and the energy dissipation due to solar tides is neglected. With these assumptions, conservation of angular momentum in the Earth-Moon systems requires that M~t C~o + - - - R'coL = Ho, M + m
(1)
where C is the moment of inertia of the Earth about its axis of rotation, ~o is the rotational velocity of the Earth, M is the mass of the Earth, m the mass of the Moon, R is the mean Earth-Moon separation, ~L is the angular velocity of the Moon about the Earth, and H0 is the present angular momentum of the system. Kepler's third law requires that ~'~t~~ = G(M + m),
(2)
where G is the universal constant of gravity. The energy of the system is made up of the kinetic energy of the Earth's rotation plus the kinetic and potential energy of the Moon's orbital motion
l (___Mm_~ + -
2 \M+
GMm R % L 2 -- _ _
m/
R
(3)
The energy E is being reduced by tidal dissipation. We assume that the torque on the Earth, N, due to the lunar tide, is inversely proportional to the sixth power of the Earth-Moon separation (Goldreich and Soter, 1966) N = N o ( R o / R ) 4,
(4)
where No is the present value of the tidal torque and R0 is the present Earth-Moon separation. The torque on the Earth is related to the change in its angular ve-
25(i
TUt{COTTIq, CISNE AND NORI)MANN
locit,y b y
in a lunar month,
X = C(d,,.,/dt).
(5)
Combining (4) and (5) gives the dependenee of the change in angular velocity on separation
d,.o/dt = (d~/dt)o(I¢,,/l¢)';,
(6)
where (d%/dl)o is the present ac('.(,h,ratioil ()f the Earth's r(/(ati(m, C(nnbining (1), (2), and (6) w(! find thai
,.:
-
i/,;;R-i,'-;\J/0
,;
('b
= (%
\ d~/0 \-}}-/
(7)
hltegration gives
'~ [l:{(dR~,q2]13
([~ 2]13
where to is tile time when R -+ The number of solar days m o n t h and in q year will also Tilt' length of tile 3"(,at' is given
(s)
0. in a lun:/r be derived. by
Ty = 2~/'.q,
(9)
where ~ is the angular v(qocity of the Earth about the Sun. The h'ngth of the hmar mtmth is given by
TL.,, = 2 , ~ / ( ~ , ~ - ~a)
(lo)
and the length (ff the, solar day is given by Ts,,
= 2,~/(~
- - ~2).
(11)
C,(nnbining (9) "rod (11) with (1) and (2), the number of s.lar days in a year is given t)3"
Ty
llo
Mm (
R(; 3~
. . . . . . . . . . . . . .
1.
(t2)
The number of solar days ut a year decreased monotonically in the past. Similarly, eombiifing (10) and (11) with (1) and (2) gives the number of solar days
tlo r,,,,
Mm ( RG )' (7,, d i 7 , 7 ,
-
(1:~)
5/'Sl) Rtt \
-]~
-
-
l
()he asp(,('( of (13) which has reeeiv(,d little a t t e n t i . n [although it was included in the calculations of MacDonald (19648, b) and L a m a r el al. (1970)] is th'tt the l~Um|)er of solar days in a lunar tllollth has a maximum. Since b o t h the h'ngth of the solar day and the length . f the lunar mo~dh are elmnghtg it is n(~t a priori evident how the ratio varies. ICr()m (13) the lnaxinmm number of solar clays in a lunar m o n t h is 31.5 and it ,mt'urs at R/Re = 0.85. These values will change wh(,n alh)wance is made for the Earth's obliquity and for solar tidal torques; however, the results . f MacDonald (19643, b) and I,amar ct al. (1970) indieate these changes are small. Similar results are obtained for the mmfl)(,r of lunar days in a lunar m, mlh. Fro' this ease the m'~ximum is 30.5 days/'m(mth, also at R;'Ro = 0 . 8 5 , STROMATOLITE PI:~RIODICITIE8 Although studies of periodicities in corals show t h a t Ill(> number of solar days in a [llIlar lIloilth alia a year arty decreasing, the seatter in the data and possible time w~riations ,,f tidM dissipation preclude ])aekward extrapolation. Of particular imp()l'ialH~(,, (bert,fore, are '{he illeasurelllellts of p(,riodieiti(,s in Precambrian strolllatolit(,s given by Pannella (1972). His (!mints of the peri()dieities are, given in Vig. 1. The older stronmtolit(,s seem to have better p(,riodicities t h a n the y()unger. This could 1)e due lo lhe larger tides caused by '~ n(,arer 5teen. If the maximum count is •(ssoeiat(!d with the fortnightly rid(; the number of solar clays in a hmar month is given in Fig. 2. The error bars (m lhe,
EVOLUTION OF THE LUNAR ORBIT
20
150 MYBP
0
o9 ;Z
257
~ ' ~ J ~ J ] - ~
~
'-~-
20
510 MYBP
0
0
20
,,
o
9 0 0 - 1 , 3 0 0 MYBP ~
-
~
~
~ , ~
o
>'(JZ 4020 r-'-r~'q-r-H~-~/L~,
1,600-1,900MYBP
"'
(21 0 t,
60
[
~
2 , 6 0 0 - 3,10 0 MYBP
40 20 o
0
I0
2 0
-
~
30
COUNTS
40
50
Fro. 1. Counts of periodicities in stromatolites as given by Pannella (1972). number of days are the standard deviations given b y Pammlla (•972). The error bars oil the dates are those given b y the author, who dated the rocks from which the fossils were obtained. Also given in Fig. 2 is a data point obtained b y M o h r (1975). Clearly this is not consistent with the data of Pannella (1972). Pannella (1975) has discussed this discrepancy and points out t h a t low points are often the result of incomplete counts. Although it is clear t h a t stromatolite periodicities must be used with caution, we will consider the implications of the data given b y Pannella (1972). In using the stronmtolite data to determine the evolution of the lunar orbit, the Bulawayan data at 2.85 ~: 0.25 b.y. BP. are critical. Although the counts of the Bulawayan growth patterns favor the 18.7day m o n t h because of the strong peak at 9 days corresponding to the fortnightly tides, Pannella (1972) did not rule ou~ the alternative interpretation of a 37.4-day month. However, our calculations show
t h a t this value is dynamically unacceptable since there is a maximum of 31.5 solar days in a lunar month.
30
+
1
20
,, ~
,o o
o Pannella (1972) o Mohr (1975)
I TIME
i
j
2
3
BYBP
FIG. 2. The data points were obtained from periodicities in stromatolites by Pannella (1972) and Mohr (1975). The solid curve is from Eqs. (8) and (13).
258
TURCOTTE, CISNE AND NORDMANN
-I" A.<[ i,i
40 0
(/)
Z 0 0
20
ir
Ltl 7" <[
t~ I~
0 0
L
L
I
I
2
3
TIME
BYBP
Fro. 3. I)ependence of the Earl h-Moon separation on lime from Eq. (8). On the basis of the stromatolite d a t a we assume t h a t R = R0 at t = 2.85 X 109 yr. F r o m (8) we find t h a t the c,)rresponding value for the increase in the E a r t h - M o o n separation is 2.08 c m / y r . And from (3) the present energy dissipation is 1.85 X 10 t9 ergs/sec. T h e predicted dependence of the Earth--Mo(m separation on t i m e is given in Fig. 3. Using (8) and (13), the predicted (t('pendence of the n u m b e r of solar days in a lunar m o n t h on time is c o m p a r e d with
the str()matolite d a t a in Fig. 2. Within the given errors, all the d a t a points obtained b y I'annella (1972) fall on the predicted curve. It should be emphasized t h a t the predicted close a p p r o a c h at 2.85 =t= 0.25 b.y. BP. is critically dependent on the B u l a w a y a n d a t a point. However, there is no reason to have less confidence in this d a t a point t h a n in the others, and it is seen that. all the d a t a points are in excellent agreement with the predicted dependence. I n Fig. 4, the predicted depend-
/
I000
)n~ uJ Q. 03 ),< a
500
rr
.¢ -I 0 u)
o
I
2 TIME
5
BYBP
FIG. 4. Dependence of the number of days in a year on time from Eq. (8) and (12).
EVOLUTION OF THE LUNAR ORBIT
259
fo~
jo~ __
SOLAR
_ =FLU~ . . . . . .
ENERGY DISSIPATION ERGS/SEC,
--
- -
ic.
I0 0 MEAN
- G ~ O - - T ~ E f f M Z C -F-L O
l
~0
x
l
EARTH*MOON
-
~
. . . . . . . .
4]
DISTANCE,
0 EARTH
l
l 60
RADII
F~G. 5. Dependence of the rate of energy dissipation in the Earth-Moon system on the EarthMoon separation. ence of the n u m b e r of days in a y e a r on t i m e from (8) and (12) is given. T h e rate of energy dissipation is given as a function of the E a r t h - M o o n separation in Fig. 5. Also included in this figure are the t o t a l geothermal heat flux f r o m the interior of the E a r t h at the present time and the present solar flux incident onto the Earth. Clearly the energy input into the E a r t h b y tidal dissipation played an i m p o r t a n t role in the terrestrial energy balance if the M o o n was at a n y time significantly closer to the Earth. Since the length of time the M o o n would spend in close proximity to the E a r t h m a y be quite limited, it is of interest to give the total energy in the E a r t h - M o o n system, from (3), as a function of the E a r t h - M o o n separation; this is done in Fig. 6. An a p p r o a c h to ten E a r t h radii would require the dissipation of 3.5 X 10 a7 ergs; this is sufficient energy to heat the entire E a r t h a b o u t 500°C.
I n each case, the measured acceleration of the M o o n or the deceleration of the E a r t h has been converted into a rate of energy dissipation assuming t h a t the angular m o m e n t u m of the E a r t h - M o o n s y s t e m is conserved and t h a t (3) is applicable. There is considerable discrepancy a m o n g the results. Explanations for these discrepancies include : (i) T h e angular m o m e n t u m of the E a r t h M o o n s y s t e m is not conserved. There ap-
2
ENERGY I037 ERGS !
HISTORICAL MEASUREMENTS The present rate of tidal dissipation can be inferred from studies of the orbital dynamics of the E a r t h - M o o n system. T h e m e a s u r e m e n t s are s u m m a r i z e d in Table I.
'
"MEAN
2'o
EARTH-MOON
'
DISTANCE
~o
'
EARTH
s'o
RADII
Fro. 6. Dependence of the energy in the EarthMoon system on the Earth-Moon separation.
260
TURCOTTE, CISNE ANI) NORI)MANN TAB1,E I Measurements of the Present Evolution of the ]Pmrth-Moon System Reference
Fotheringham (1920) Murray (1957) Newton (1970)
Muller and Stephenson (1975) Spencer Jones (1939) Newton (1968) Van Flandern (1970) Morrison (1973) Van Flandern (1975) Oesterwinter and Cohen (1972)
Loss of energy ~ ( 1(),9 ergs/sec) Ancient asl ronomical observalions, hlllar orbili Ancient ast,ronomical observations, Earth's rolalion Ancient astronomical obsexwations Ancient astrononfical observalions, -762 to 500, lunar orbit Ancient astronomical observations, -762 to 500, Earth's rotation Ancient a~tronomi(..al observat,ions, since 500, lunar orbit Ancient aslrononfical observations, since 500, l';art.h's rotalion Ancien( ~Lsi,ronomical ot)setwaiions Lun'~r "rod planelary observations since 1750 Orbits of near-Earth satellites Occultalions of stars by Moon versus atomic lime OcculIalions of stars by Moon versus atomic time Occull.adons of slars by Moon vel~us atomic lime Meridian observations from 1912 to 1968
3.42 2.65 5.54 4- 0.8 5.45 4- 0.56 3.63 4- 0.45 5.54 4- 0.80 2.(`)5 4- 0.13 4.9 l 4- 0.65 2.(,)4 4- 0.16 2.63 4- 0.34 6.81 4- 2.l 5.54 4- 0.8 8.58 4- 2.38 4,(,)8 4- 1.05
- To convert to lunar acceleration in arcsec/century ~-, nmltiply by --7.63. p e a r s t o b e a s y s t e m a t i c difference in tide r e s u l t s of F o t h e r i n g h a n ~ (1920) a n d N e w t o n (1970) b a s e d on l u n a r a c c e l e r a t i o n a n d Earth deceleration. Attempts have been m a d e t o cxt)lain t h e n o n c , m s e r v a t i ( m of a n g u l a r m o m e n t u m b y m e t e o r o h ) g i c a l effects a n d I)roccsses w i t h i n tide E a r t h , b u t no a d e q u a t e m e c h a n i s m h a s /)e(m f o u n d ( M u n k a n d M a c l ) o n a l d , 1960). (it) T h e g r a v i t a t i o n a l c o n s t a n t (; is c h a n g i n g . T h e r e a p p e a r s t() be a s y s t e m a t i c difference b e t w ( , e n m(,asuremen~s b a s e d on e p h e r m e r i s t i m e a n d on a t o m i c t i m e . T h i s difference ('all b e a t t r i b u t e d t,) a ('hange in U ( V a n F l a n d e r n , 1975). (iii) T h e r e a r e e r r o r s in stone or all ()f t h e o b s e r v a t i o n s whi('h r(,main t() 1)e resolved. The discrepancies between measuremenI s u s i n g t h e s a m e t e c h n i q u e a r e so l a r g e t h a t it is ditEeult a t t h i s t i m e t o Sllecify ( w i t h i n a b o u t a f a c t o r of 2) j u s t w h a t t h e p r e s e n t r a t e of t i d a l d i s s i p a t i o n is. T h e v a l u e ,)f 1.85 X 10 .9 e r g s / s e e i n f e r r e d f r o m t h e
s t r o m a t o l i t e d a t a is n e a r t h e l o w e r l i m i t of t i l e ()bservations. Aid o r b i t a l c a l c u l a t i o n u s i n g t i l e h i g h e r v a l u e s w o u l d r e s u l t ill a n E a r t h M o o n ch)se a p p r o a c h subsequ(,nt to 2,85 b.y. BI ). T h e a s s u m p t i o n t h a t t i d a l en(,rgy dissipation has a simple functional dependell(~e i)lt t h e t i d a l forces o v e r gcologi(',al t i m e is o p e n t() q u e s t i o n . T h e s o u r c e ()f tile tidal dissipation has not been establishe(1. S o m e a u t h o r s c o n c l u d e t h a t t h e p r i m a r y source ,)f t i d a l d i s s i p a t i o n is t h e s h a l l o w seas (l~ambeck, 1975). If t h i s is tide case, t h e t i d a l d i s s i p a t i ( m c o u l d c h a n g e b y at l e a s t a n o r d e r of m a g n i t u d e b e c a u s e of c h a n g e s in s(,a level a n d c o n t i n ( , n t a l drift. ( ) t h e r a u t h m ' s ('(intend t h a t t h e e n e r g y a s s o c i a t e d w i t h t i d a l d i s s i p a t i o n is diss i p a t e d w i t h i n t h e solid E a r t h ( M e l c h i o r , 1974) a n d m a y d r i v e t h e d y n a m o r e s p o n sible for t h e E a r t h ' s m a g n e t i c field. If t h i s is t h e case, a r e l a t i v e l y s i m p l e d e p e n d e n c e su('h as (4) m a y be valid.
EVOLUTION OF THE LUNAR ORBIT
261
THE GEOLOGICAL AND SELENOLOGICAL Earth and the Moon can explain the maria RECORD volcanism on the Moon and the highThere is evidence in the geological temperature Archean volcanism on the record that there was an important change Earth. Tidal heating during a close approach in the evolution of continents at about 2.7 b.y. BP. Burke and Dewey (1973) of the type proposed by Gerstenkorn give this date as the end of what they (1955) would not give the required heating. call the permobile phase of continental Significant tidal heating within the Moon evolution. They suggest that this may would appear to require the Moon to be have been due to a rapid decline in internal initially in a highly elliptical orbit. Pushheat generation at this time. Sutton (1973) pull tides on the Moon would reduce the recognizes a similar transition between 2.9 elliptical orbit to a near-circular orbit and 2.4 b.y. BP when widespread plutonic (Goldreich, 1963). Assuming that a paraactivity ceased to affect the entire crust bolic orbit is reduced to a circular orbit and was gradually restricted. The Archean with the same minimum Earth-Moon prior to 2.85 b.y. BP was characterized separation and assuming that the resultant by high-temperature ultramafic volcanism tidal heating occurs uniformly throughout (Naldrett, 1973) with komatiite volcanism the Moon, the temperature increase is at temperatures as high as 1650°C (Green, given in Fig. 7. It is seen that this mecha1975). nism can significantly heat the lunar inIt is interesting to note that this is the terior. Sinmltaneous tidal slowing of the same period during which mare volcanism Earth's rotation could have heated the was occurring on the Moon. Although con- Earth's interior. duction calculations can be carried out THE BIOLOGICALRECORD that give a period of near-surface heating on the Moon between 3.8 and 3.1 b.y. BP The thermal regime accompanying the (Solomon and Toks6z, 1973), these cal- close approach of the Earth and Moon culations require quite restrictive initial should have had a catastrophic effect on conditions. Tidal heating on both the life, if it existed at. that time. The large 3000
2000
AT °C
I000
0
20
MINIMUM
40
EARTH-MOON
60
SEPARATION,
I00
80
EARTH
RADII
Fro. 7. Change of temperature within the Moon when a highly eccentric orbit is reduced to a circular orbit as a function of the minimum Earth-Moon separation.
262
TURCOTTE, CISNE AND NORDMANN
a m o u n t of energy dissipated through tidal heating quite conceivably could have vaporized the world ocean (Munk, 1968). About 3 X 10 a4 ergs would be required to vaporize the present world ocean. F r o m Fig. 6 this is seen to be a v e r y small fraction of the energy dissipated during the ch>se approach. In all likelihood, whatever living organisms m a y have been present at t h a t time were killed. The paleontological record is consistent with the view t h a t life originated at about the predicted time of close approach. Within the range of error in radiometrie age determination, the (,h)se approach coincides with the first records of life. Some confusion has existed concerning the age of the Swaziland system of southern Africa, which contains the first possible records of life. A minimmn age of 3000 =t= 30 m.y. has been established from R b S r ages ()f intrusives (Allsopp et al., 1968), and a nmximum age of 3 2 3 0 3290 ln.y. has been obtained from studies ()f the U-Th--Pb systematics of lavas and pilh)w basalts in the Onverwa(:ht series at the base of the Swaziland system (Sinha, 1972). Previously made Rb Sr whole rock age determinations, particularly those in excess of 3300 m.y., have been cited as indicating a more ancient age f.r the first records of life. More, recently it has t)een rexealed t h a t l i b - S t chemistry ,,f the ()nverwacht has been disturbed by metamorphism (Alls()pp et al., 1973; Jahn and Shih, 1973). Ages determined from mlmerous samph,s cover the range 3300 =k 500 m.y. (.lahn and Shih, 1973). The firs'~ reliable evidence ()f living organisms seems to be cells from the Fig Tree series, which overlies the Onverwacht series (Sehopf, 1975). However, toward the extremes in the nmrgin ()f dating error, the Bulawayan stromatolites may actually be older t h a n the Fig Tree cells by as nmch as 100 m.y. Earlier "cell-like objects" from ()nverwacht w)lcanic rocks (l,]ngel cl al., 1968) are lm)bably m)t cells (Sch()l)f,
1975) but m a y be fossil coaeervate droplets (Mueller, 1972). Carbon and organic con> pounds in Onverwacht rocks m a y or may not have been associated with biological activity (Scott et al., 1970; Oehler el al., 1972; Brooks el al., 1973; Schopf, 1975). ()therwise, extensive banded iron forlnation, indirect evidence of life (Cloud, 1968), has been reliably dated at no more t h a n 3000 m.y. (Goldich, 1973). Perhaps life originated twice, once before and once after the close approach of the E a r t h and Moon. lieliable evidence of living ()rganisms a significant period before the pr(,dicted time of close approach is lacking. It is conceivable that the close approach played a direct role in the origin of life. The close approach would have resulted in a large input of heat energy inh) evolving prebiologieal systems ~hat t . g e t h e r with ultraviolet radiation and other energy inputs could haw~ been important in driving syntheses ()f prel)iological c()mpounds. Since an '%rganic SOUl)" ()f pr(,bit)logical eomp(mnds in dilute aque()us solution has been synthesized under a variety . f possible early-Earth conditions t h a t do nl)t itlw)lvc' heat as the primary (,nergy source, there is no reason 1o b(,lieve t h a t a thermal event was nec(,ssary for the f r s t steps in prebioh)gical ev()luti(m. But the I)r('dicted thermal catastrot)h(' may lmv(, b(,(,n quite important at succeeding st(,ps. A world o('ean of "organic SOUl)" would have been heated, t)erhaps ('omplet(qy vaporized, and then r(,(;()ndens(,d in th(, e(mrse of the approach and recession ()f the Earth and Moon. The progression ()f gh)bal conditimts would res(,lllble tim r(@m(,n of experiments in which mixtures of amino acids and wat(,r haw~ be(,n vaporized and then rccondensed (l"-x, 1965, 1971). The result of these exp(¢iments was thermal t)olym(,rizatim~ of amino acids to form proteinoids and f.rmati(m of cell-like protein(rid ('oaeervates m~ rec(mdensati,m, l l l a S l n U C h 118 anlill() acid polymeriz'ttimt can take l)lace thrq)ugh
EVOLUTION OF THE LUNAR ORBIT catalysis at lower temperatures, a thermal event is not necessary to explain the formation of proteinoids. While the thermal catastrophe, in combination with other factors, may help in explaining the synthesis of prebiological compounds, its primary significance is perhaps as a means by which these compounds could be concentrated out of aqueous solution on a global scale. It has often been suggested that prebiological compounds were concentrated in intertidal pools and cavities from which water evaporated at low tide. Increased tidal amplitude during the time of close approach would obviously have facilitated this mechanism. However, vaporization of the entire world ocean during the time of close approach, followed by fractional recondensation as temperatures afterward returned to normal, would seem to provide a more dramatic, if not more effective, mechanism for the concentration of prebiological compounds and, eventually, the formation of coacervate droplets in aqueous solution. From this point, living cells may have arisen from selfreplicating coacervate droplets. Contrary to the idea that life was the product of a long period of prebiological evolution under relatively constant conditions, we suggest that life was perhaps the product of a geologically short period of singular conditions brought about by a close approach of the Earth and Moon. CONCLUSIONS Despite the substantial increase in our knowledge of the Moon which resulted from the Apollo Project, the origin of the Moon and the evolution of the lunar orbit remain an enigma. We favor the hypothesis put forward by Clark et al. (1975) that the Moon was captured during the final stages of accretion (approximately 4.6 b.y. BP). This capture placed the Moon in a retrograde orbit at a large distance from the Earth. Initially both the Earth and Moon were hot, tidal friction
263
was large, and tidal dissipation caused the Moon to approach the Earth. We further hypothesize that tidal interactions between the Earth and the Moon occurred over an extended period of time between about 3.8 and 2.8 b.y. BP and that the frictional heating due to these tidal interactions was responsible for the high-temperature Archean volcanism on the Earth and the maria volcanism on the Moon. A natural consequence of this hypothesis is that the surface deformation of the Moon due to tidal forces fractured the brittle outer shell of the Moon, allowing the magmas to fill the preexisting craters. Similar effects on the surface of the Earth could have initiated plate tectonics. The interaction of the Earth and Moon may also have played an important role in the initiation of life. Although it is far from obvious how nmjor tidal interactions between the Earth and the Moon could extend over a billion years, the dynamics of a close interaction are poorly understood. It is possible that a series of resonant interactions as proposed by Alfven and Arrhenius (1969) occurred during this time. At about 2.85 b.y. BP we hypothesize that the Moon entered a prograde orbit about the Earth. Since then the E a r t h Moon separation has been increasing and the tidal interaction decreasing. This orbital evolution is consistent with the measurements of periodicities in Precambrian stromatolites given by Pannella (1972). An extrapolation of the present Earth-Moon orbit requires a close approach; the orbital evolution which we hypothesize is in better agreement with the historical observations than alternative hypotheses which keep the Moon in a retrograde orbit since it was formed. ACKNOWLEDGMENTS The ~uthors acknowledgehelpful discussionswith D. R. Wones, P. M. Muller, and W. M. Kaula and would like to thank S. J. Weidmsclfillingfor
264
T U R C O T T E , C I S N E AND N O R I ) M A N N
a very helpful review of all earlier version of lhis paper, This research was supported by G r a n t N G R 33-010-108 from ~he National Aeronautics and Space Administration. C o n t r i h u l i , n of the l)cpar(men( of Geological Sciences No. 593.
REFERENCI,;S
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