The Moon and the Origin of Life on Earth
Jacques Laskar Laluneet l'origine April 1993∗ del'homme If the Moon did not exist, the orientation of the Earth’s Moon and the Sun. A similar precession of a solid body’s axis axisr JACQUES wouldTASKAR not be stable, and would be subject to large of rotation can easily be observed with an ordinary spinning chaotic variations over the ages. The resulting climatic top. One consequence of this phenomenon is that the Earth’s changesSi la Lune n'existait very likelypas, l'orientation would have de I'axe markedly de rotation disturbedde laTerre the de- rotational axis does not always point toward Polaris, but in- velopmentne seraitpas stable, of organizedet subirait delife. largesvariations chaotiques au cours stead describes a large circle in the celestial sphere. This desAges. Les changementsclimatiques engendrds par cesvariations auraientWe are alors all perturbd familiarfortement with lethe ddveloppement change ofde la seasons vie organisde. due to the fact sometimes disturbs the quibblings of astrologers, since inclination of the equator with respect to the plane of the the precession of the equinoxes has so greatly displaced the Earth’s orbit around the Sun. This inclination of 23◦270, zodiacal calendar from the apparent motion of the Sun that ous sommestous familiersdu lationspossibles de l'obliquit6, et qu'elle Une des cons6quencesde ce ph6no- calledrythme “obliquity” dessaisons, dont la suc- byagit astronomers, donc commeun r6gulateur alsoclimati- givesmdne est rise que toI'axethe de rotation polar de la presently, on the date corresponding to the sign of Aries, the cessionr6sulte de I'inclinaison que de la Terre. Terrene pointe pas toujours vers l'6toile circles,de l'6quateur par inside rapport au of plan which de En day720 avant and J.-C., night Hipparque maypolaire, eachmais d6crit lastun large severalcercle sur la Sun is in the constellation Pisces. I'orbite de la Terre autour du Soleil. d6couvreque la directionde I'axede vo0tec6leste. months.Cette inclinaison The de 23o27', distributionappel6e rotation deof la Terre solar n'est pas heat fixe. En overLa pr6cession the Earth’sdes 6quinoxes sur-consti- The precession of the equinoxes also affects the Earth’s cli- obliquit6par lesastronomes, est aussi la effet,ce dernier ddcrit un c6nedans I'es- tue d'ailleursune objectionimportante facecausede I'existencealso dependsdes cercles polaires, on thepace,avec obliquity,une p6rioded'environ making26 000 aux itarguties an essentialdes adeptes de I'astrologie. part mate. The Earth’s orbit is in fact not circular, but, as Kepler i I'int6rieurdesquels les jours et lesnuits ans.Ce mouvement,appel6 prdcession carelle a introduitun tel d6calaseentre ofpeuvent ourdurer understanding plusieursmois. Lar6par- des of6quinoxes, terresterialr6sulte de I'existence climate.du le calendrier Calculationset le mouvementapparent car- tition de la quantit6de chaleursolaire bourrelet6quatorial de la Terre,et du du Soleilqu'ir la datecorrespondant au showed in the early 17th century, is instead approximately el- reEued la surfacede la Terred6pend de couple exerc6sur ce bourrelet par la signedu B6lier,le Soleilse trouve main- riedson obliquit6, outqui at estI'un the des6l6ments BureauLune ofet par Longitudes le Soleil.On observe intrds Paristenant dans show la constellation thatdes the Pois- liptic with the Sun residing at one focus. The eccentricity of fondamentauxde la comprdhensiondu facilementce ph6nomdne de pr6cession SONS. Moonclimat.Les calculs stabilizesque nous avons oscillationseffec- de I'axe de rotation in the d'un Earth’scorps solide obliquity,Cettepr6cession atherefore un effet sur le cli- this ellipse (which measures its elongation) is small (0.017), tu6s au Bureau des Longitudes dansun champde pesanteurquand on mat de la Terre.En effet.l'orbite de la actingmontrent que as la Lune a stabilise climaticles oscil- regulatorfait tourner une toupie for sur the une table. Earth.Terren'est pas circulaire. mais approxi- but is enough to measurably change the quantity of solar heat reaching the Earth at perihelion, or point of closest ap- proach to the Sun, as compared to aphelion, its point of far- thest departure from the Sun. At present, the Earth passes through its perihelion January 4th, during the boreal winter. This diminishes seasonal contrasts in the northern hemish- pere, and accentuates them in the southern hemishpere. In 13,000 years, the situation will be reversed and seasonal con- 22 JUIN trasts will be more accentuated in the northern hemisphere. The precession of the equinoxes thus affects the distribution of insolation at a given location on the Earth in the course of 1. L'ALTERNANCE DES SAISONS d6pendde I'obliquit6 e de la la Terre est au point le plus prbs du Soleil (p6rih6lie), pendant l'6t6 Terre (a) et de la pr6cessiondes 6quinoxes (D). En 616,la quantit6 de de I'h6misphbre Nord ou pendant I'hiver, comme c'est le cas actuel- chaleur solaire regue dans I'h6misphbreNord est plus importante lement. Il en r6sulte une augmentation, ou une diminution du a year. In fact, it appears possible to trace more significant Figureque dansI'h6misphbre 1: TheSud. Selon changela valeur de I'angle of de seasons pr6cession, contraste depends des saisons. on the Earth’s obliq- climatic changes to variations in the Earth’s eccentricity and uity14 (a) and on the precession of the equinoxes (b). InO poun sum-LA sc ENCE obliquity. mer, the amount of solar heat received in the northern hemi- sphere is greater than that received in the southern hemi- sphere. Depending on the angle of precession, the Earth may be at its point nearest the Sun (perihelion) during the north- The Astronomical Theory of Climates ern hemisphere’s summer, or during its winter, as is currently In Kepler’s view, the Earth’s orbit was an immutable el- the case. The hemispheres thus experience a corresponding lipse. Newton challenged this view by demonstrating that accentuation or dimunition of seasonal contrasts. the masses of the other planets perturbed the Earth’s orbit, so that it is only an ellipse to first approximation: neither its In 120 BC, Hipparcus discovered that the direction of the eccentricity nor its obliquity are fixed. LeVerrier (famed for Earth’s rotational axis is not fixed with respect to the stars. his discovery in 1846 of the planet Neptune based on pertur- In fact, it traces out a cone in space roughly once every 26,000 bations of Uranus’ orbit) was the first to calculate possible years. This so-called precession of the equinoxes is the result long-term (or “secular”) variations in the Earth’s eccentricity. of the torque exerted on the Earth’s equatorial bulge by the In doing so, he took up calculations of the Earth’s orbital mo- tion begun by Laplace shortly before the French Revolution. ∗This text is a close translation (by H.S. Dumas) of the original paper La Lune et l’origine de l’homme that was first published in the french It was LeVerrier’s Earth-orbit calculations that, in 1941, led version of Scientific American, Pour la Science, 186, pp 34 - 41, April the Yugoslavian astronomer Milutin Milankovich to hypoth- 1993, shortly after the publication of the associated research papers in esize that the ice ages were the result of high-lattitude vari- Nature. This paper has since been reprinted in several foreign editions ations in terrestrial insolation induced by secular variations of Scientific American (Italian, Arabic, Japanese, German, Polish), and in Portugese in Cincia Hoje. Up to now (september 2009), It was not in the Earth’s orbit and axial orientation. His theory did not available in English. win immediate acceptance, as the variations in insolation did
1 not seem adequate to account for glaciation. But the same as it melts ice accumulated over the winter and prevents the theory has gained wider acceptance over the last two decades. ice caps from extending their reach. Weak variations in the Measurements carried out by John Imbrie and coworkers of Earth’s obliquity are therefore a determining factor in regu- the relative concentration of the oxygen isotopes O18 and O16 lating the relatively moderate climate enjoyed by the Earth present in the carbonates of marine sedimentary layers can over the last several million years, and in allowing the ap- be related to the past thickness of the polar ice caps. From pearance of organized life as we understand it. The ice ages this it is possible to estimate mean ocean temperatures in the constitute significant climatic changes, but were not so se- distant past. Indeed, it provides some record of the Earth’s vere as to permanently change the conditions for life on the past climate up to more than three million years ago. Though Earth’s surface. mativementelliptique, comme l'a mon- diminue le contrastedes saisonsdans La theorieastronomique muchtrd Kepleren less 1609,le precise, Soleiloccupant un geologicalI'h6misphdre records reflect climatic condi- Nord, alors qu'elle despal6oclimats desfoyers de l'ellipse.L'excentricit6 de I'accentuedans I'h6misphdre Sud. Dans I'ellipse(qui mesureson aplatissement) 13 tions as far back as 200000million ans,I'effet sera years.contraire, et les Moreover,Pour Kepler, la improved Terre d6crivaitune estfaible (0,017),mais suffit pour chan- contrastesdes saisons seront plus accen- ellipseimmuable. Newton a boulevers6 ger la quantit6 de chaleur reEued la models of climatic responsetu6sdans I'h6misphdre to variationsNord. La pr6ces- incet the 6quilibre Earth’sen montrantque orbit la masse Variations in the Earth’s Obliquity surfacede la Terre, entre le p6rih6lie, sion des 6quinoxesmodifie donc la des autresplanbtes du Sys[dmesolaire positionoD la Terre est le plus prdsdu r6partition show that the effects of changesde I'insolation inen insolation un lieu de perturbait mayl'orbite be de laampli- Terre,qui n,est Soleil,et I'aph6lieoi elleest d son6loi- la Terreau coursde I'ann6e.En fait,des donc une ellipse qu'en premibre gnementmaximal. variations Perturbations exerted by other planets cause the Earth’s or- de climats beaucoupplus approximation: ni I'excentricit6de la fiedActuellement, throughle passage secondaryau p6rih6- importantes effects, such as growth of the ice caps semblentaussi rdsultef des Terre, ni son obliquitd ne sont fixes. lie a lieu le 4 janvier pendantI'hiver variations de l'excentricit6et de I'obli- LeVerrier (c6ldbrepour avoir d6cou- bit to turn in space with a motion that may be represented orbordal. changesCette diff6rence ind'6loisnement the make-up of the atmosphere. quit6 de I'orbite de la Terre. vert, par le calcul des perturbations approximately as the sum of several uniform rotations, each arising from the influence of a particular planet, with peri- ods ranging from 40,000 to several million years. It is the effect of this complicated motion on our terrestrial spinning top that gives rise to the small oscillations in its obliquity. If the excitation period produced by this motion of the Earth’s orbit is close to the period of precession of its axis, the clas- sical phenomenon of resonance may arise. Resonance occurs, for example, when a swing is pushed in the right way—each time it reaches its highest point. Even if each push is small, the swing’s oscillations will be amplified (especially in the absence of friction). But if the swing is instead pushed at random intervals, nothing special takes place in general. Instead of using the periods, we will consider the rotational speeds of these different motions. Since all the precessional motions we consider are very slow, they are expressed in units of arc seconds per year, abbreviated simply as seconds per year. A rotational speed of one second per year thus cor- responds to a period of 360 × 3, 600 = 1, 296, 000 years. I will introduce a slight abuse of terminology by calling these rotational speeds frequencies. With this convention, the fre- quency of precession of the Earth’s orbit is 50.47 seconds per year, while the principal frequencies of the motion of the Earth’s orbit range from 26.33 seconds per year down
2.LAPRECESSION DES EQUINOXES. La Terre n'est pasparfai- de I'axe de la Terre trace un large cerclesur la vo0te c6lesteen to nearly 0.67 seconds per year, with the main frequencies tement spheriqud, mais ldgirement aplatie aux p6les e-t renfl6e i 26 000 ans environ. Il y a 5 fi)O an1, ra direction du pOteNord 6tait l'6quateur.sous I'action gravitationnellede ^l'6toile ra Lune et du soleil, son donn6epar l'6toile alph_gdu Dragon, et non p"r p". polaire. axeFigurede rotation d6crit 2: un Precession cdne,comme of the equinoxes. The Earth is not per- Ie fait une toupie.La direction Dans 13 0(X)ans, cette direction seraceUe ae V6ga at 18.85 and 17.75 seconds per year. We are thus far from
@fectly pounLA sctENcE spherical, but slightly oblate, with flattened poles and 15 resonance, which explains the relatively small variations ob- an equatorial bulge. Under the gravitational action of the served in the Earth’s obliquity. This is not the case for Mars, Sun and Moon, its axis of rotation traces out a cone, much whose frequency of precession is 7.5 seconds per year and like a spinning top. The Earth’s rotation axis traces out a whose obliquity is presently 25.2 degrees. William Ward, of large circle in the celestial sphere approximately once every the Jet Propulsion Laboratory in California, has pointed out 26,000 years. 5000 years ago the North Pole was indicated by that the proximity of secular orbital resonances causes Mars the star Alpha, in Draco, rather than by Polaris. In 13,000 to undergo substantial variations in obliquity (on the order years, this direction will be indicated by Vega. of ±10 degrees).
An essential part of any study of variations in the Earth’s What if the Moon Were Removed? insolation is the calculation of variations in its obliquity under the influence of planetary perturbations. Over a one million To answer this question, I do not propose anything so dras- year period, this variation is only ±1.3 degrees around the tic as to physically remove the Moon, but rather to study, mean value of 23.3 degrees. This may not seem like much, through numerical simulations on a computer, the Moon’s but it is enough to induce variations of nearly 20 percent in effect on the Earth’s dynamics. We know that the Moon the summer insolation received at 65 degrees north lattitude. accounts for about two thirds of the torque acting on the The amount of additional heat received during the summer Earth’s equatorial bulge, with the Sun accounting for the re- at high lattitudes is an important factor in climate studies, maining third. Without the Moon, the Earth’s frequency of
2 d'uranus, la plandteNeptune en 1846) Imbrie et sescollaborateurs fournissent Terre est le calcul desvariations de son a,le premier,calcul6 les variations d trds des indicateurs de l'6paisseurdes obliquit6 sousl'influence des perturba- long terme, appel6esvariations s6cu- calottespolaires qui ont permisd'obte- tions plandtaires. Sur un million laires,de I'excentricit6de la Terre. Il nir des estimationsdes temp6ratures d'ann6es,cette variation n'est que de poursuivait en cela les travaux de moyennesdes mers dans les dpoques +1,3degr6 autour de la valeurmoyenne Laplace effectu6sun peu avantla R6vo- recul6es. de 23,3degr6s. Cela peut semblertrbs lution franEaise.C'est en utilisant les Actuellement, ces mesures effec- peu,mais entraine cependant des varia- solutionsde LeVerrier pour le mouve- tu6espar I'analysedes carbonatespr6- tions de prbsde 20 pour cent dansI'in- ment orbital de la Terre, que I'astro- sentsdans les carottesde s6diments solation reEue en 6t6, h 65 degr6s de nome yougoslaveMilutin Milankovitch marins permettent de retrouver les cli- latitudeNord. Or la quantitdde chaleur 6mit, en 794I, I'hypothbse que les matsdu pass6sur desdur6es d'environ suppl6mentairereEue pendant l'6td aux grandesp6riodes glaciairesdu Quater- trois millions d'ann6es.Il existem6me hauteslatitudes est une donn6eimpor- naire r6sultentdes variations de I'inso- desenregistrements gdologiques, beau- tante pour l'6tudedes climats, car c'est lation aux hauteslatitudes induites par coup moinspr6cis, mais qui permettent ellequi fait fondreles glaces accumuldes lesvariations s6culaires de I'orbiteet de de remonter jusqu'd 200 millions pendantI'hiver et empOcheI'extension I'orientationde la Terre. Cette th6orie d'ann6es.D'autre part, une meilleure descalottes polaires. n'a pas6t€ accept6eimm6diatement. En mod6lisationde la r6ponseclimatique Les faiblesvariations de I'obliquit6 fait, cesvariations d'insolation ne sem- aux variationsde l'orbiteterrestre mon- de la Terre sont ddterminantespour lui blaient pas suffisantespour engendrer tre queI'effet des changements d'insola- assurerla relative16gularit6 climatique des variations de temp6raturepouvant tionpeut6tre amplifid par deseffets dont elle a b6n6fici6depuis plusieurs entrainer une glaciation. secondairestels que I'extensiondes millions d'ann6es,et qui a permis Cette th6orie a 6t6,lar gementconso- calottespolaires ou le changementde la I'apparition de vie organis6etelle que lid6e depuis environ deux d6cennies. compositionde I'atmosphdre. nous la connaissons.Les pdriodes gla- Lesmesures isgtopiques des taux d'oxy- Un des 6l6mentsessentiels dans ciairesconstituent des changements cli- gdne O'o/O'o effectu6espar John l'6tude desvariations d'insolation de la matiquesimportants, mais qui n'ont pas 6t6 suffisantspour alt6rer de manidre durableles conditions de vie d la surface de la Terre. ENSEMBLETERRE.LUNE TERRESEULE periods, variations in the Earth’s orientation due to its orbital variations.Lesvariations Wede I'obliquit6 first of all simulated an abrupt disappearance a .tll ofde thela Terre Moon, then observed the behavior of the Earth’s obliq- c rn Les perturbations par I.JJ uity over one millionexerc6es years. les This is a relatively short time, not o autresplandtes font tourner I'orbite de z long enough, for example, for effects arising from the chaotic tI| la Terre dans l'espaceavec un mouve- .ul F naturement qui peut of setherepr6senter, orbitalde motion manidre to be detected. Nevertheless, l a variationsapproximative, oncomme the la order r6sultante of ±de 15 degrees in the Earth’s obliq- = 20 plusieurs dl rotations uniformes de uityp6riodes were allant observed, de 40 000 and e plusieurs the resulting variations in insolation atmillions 65 degreesd'ann6es, northchacune lattituded'entre elles were much more significant than provenantplus particulidrementde I'in- before.fluence d'une If, asdes advancedplandtes. C'est in I'effet Milankovich’s theory, the variations
I inde ce insolation mouvement atcompliqu6 high lattitudes sur notre are responsible for periods of TEMPSEN MILLIONSD'ANNEES glaciation,toupie terrestre it qui is veryinduit likely les petites that the variations depicted in Fig- oscillationsde sonobliquit6. ENSEMBLETERRE.LUNE TERRESEULE ureSi 3la wouldpdriodede induce I'excitation stillproduite more significant temperature changes .rJ-l (r onpar ce themouvement Earth’sde surface. I'orbite de la Terre tr est proche de la p6riode de pr6cession de sonOur axe, goalun ph6nombne is howeverclassique not toen rid ourselves of the Moon, but (r F physiqueintervient : la r6sonance.Il y a, ,lLJ to understand the possible evolution of the Earth had the par exemple,r6sonance si on pousseune t MoonbalanEoire notau existed,bon moment, which i chaque naturally leads us to inquire about s qu'elle a thefois Moon’sarrive origins. d son point le plus tr haut. M0me pouss6e 4 si cette est trds = petite, on verra s'amplifier les oscilla- z [! tions de la balangoire(surtout s'il n'y a z pasde frottements).En revanche,si I'on = poussela balanEoiren'importe quand, il J The Origin of the Moon o { ne sepassera rien de particulier. ct) -l z TEMPSEN MtLLtoNs o'nruruEEs Au lieu d'utiliserles p6riodes,nous Theconsid6rerons Moon confrontsplut6t des vitesses us withde a number of astronomical prob- 3. SUR CETTE SIMULATION NUMfRIQUE, la Lune estsupprim6e brutalement i la date rotation de cesdiffdrents mouvements. d'aujourd'hui (r = 0). SousI'action desperturbations plan6taires, et en pr6sencede la Lune, lems.Commetous Its les mass,mouvements 1/81de that pr6ces- of the Earth, is very large for a FigureI'obliquit6 3:la In Terre this subit numerical de petites variations simulation, (+1J degr6) the autour Moon isvaleur removed moyenne de de sa siondont nousparlerons sont trds lents, (23,3degr6s) (a). Cesvariations sont suffisantespour induire les variations de prbs de 20 pour planetary satellite, and in that respect is unique in the solar abrubtly at our present date (t = 0). Under the influence l'unit6employde est la seconded'arc par cent de I'insolation reguesur Terre ir 65 degr6sde latitude Nord (D) qui sont, selonla th6orie system. Only Jupiter, Saturn, and Neptune possess satellites ofde M. planetary Milankovitch, perturbations, i I'origine despdriodes andglaciaires. in theAprbs presence la suppression of thede la Moon, Lune,les an ou, en abr6g6,seconde par an. Une variations sur un million d'ann6esde I'obliquit6 et de l'insolation deviennentbeaucoup plus ofvitesse comparablede rotation de mass, une seconde yet thoseoar planets are respectively 318, the Earth’s obliquity is not fixed, but undergoes small varia- importantes. 95,an correspond and 17 timesalors d une as massivep6riode de as the Earth. The formation of tions (±1.3 degrees) about its mean value (23.3 degrees) (a). to the Moon thus posespoun a distinct problem, for which a number These small variations are enough to induce changes of nearly @ LAscrENcE of different scenarios have been proposed. 20 percent in the insolation received on Earth at 65 degrees north lattitude (b), and, according to Milankovich’s theory, In the fission scenario, centrifugal forces of a rapidly rotat- are the cause of the ice ages. After removing the Moon, varia- ing Earth (2–3 hours) tore off a large portion of its mantle to tions in terrestrial obliquity over a period of one million years form the Moon. This model has been very nearly abandoned, are significantly increased. in part because it is difficult to account for such a high initial rotation speed for the Earth, in part because of the Earth’s and Moon’s noticeably different chemical compositions, and especially because the Moon does not lie close to the Earth’s precession would decrease from its present value of 50.47 to equatorial plane, but instead only 5 degrees from its orbital around 15.6 seconds per year, thus approaching the Earth’s plane. orbital frequencies and their attending resonances. In 1982, The Moon might have been formed at the same stage as W. Ward studied this problem using a simplified model, and the Earth, through the accretion of material in orbit around concluded that removing the Moon would induce variations it. This would explain the Moon’s nearness to the plane in terrestrial obliquity on the order of those of Mars. But the of the ecliptic, but not the marked difference in chemical Moon’s absence would also mean a higher rotational speed composition. for the Earth, which would increase the size of its equato- In the capture hypothesis, the Moon was formed in some rial bulge. According to Ward, the resulting increase in solar neighboring part of space, then captured by the Earth’s grav- torque on the larger bulge would offset the absence of torque itational field. Two modes of capture have been proposed: due to the Moon, leading in the end to obliquity variations “soft” capture, and “hard” capture. Hard capture entails a comparable to those observed now. violent collision between the Earth and some massive body, At the Bureau of Longitudes in Paris, we recently studied with the subsequent accretion of the resulting debris form- this problem using a much more accurate model of terrestrial ing the Moon. The problem with these scenarios—the latter motion. We made use of calculations of the orbital motion currently enjoying the most favor—is their low probability of the Earth and the other planets that I carried out earlier of occurrence. Skepticism concerning a capture scenario ad- over a model time period of some 400 million years. It was heres to the “principle of mediocrity,” which requires that these calculations that I used in 1989 to show that the orbital observed events be generic rather than exceptional. motion of the solar system, and more especially of the inner Though the Moon’s origin remains enigmatic and subject planets (Mercury, Venus, Earth, and Mars), is chaotic. It was to varied speculation, it is nevertheless possible to retrace its therefore possible to study numerically, over very long time history to a very distant past.
3 360x 3600=1.296000 ans. Je ferai mOme (Mercure, V6nus, Terre et Mars) est L'originede la Lune un l6gerabus de langageen appelantces chaotique.Il 6tait donc possibled'6tu- vitessesangulaires de rotation des fr6- dier num6riquement,sur de trdslongues La Lune posede grosproblbmes aux quences. dur6es.lesvariations de I'orientationde astronomes.Sa masse, L/8L de cellede la Dans cesnouvelles rotations, la fr6- la Terre produites par ses variations Terre,est trbs importantepour un satel- quencede pr6cessionde la Terre est de orbitales. lite d'une plandte,ce qui estunique dans 50,47secondes par an, alorsque les fr6- Dans un premier temps,nous avons le Systbme solaire. Seuls Jupiter, quencesprincipales du mouvement de simul6 une disparition brutale de la Saturneet Neptunepossddent des satel- I'orbite de la Terre vont de 26,33 Lune et observ6ce que devient I'obli- litesde massecomparable, alors qu'elles secondespar an jusque pratiquement quit6 de la Terre pendant un million sont respectivement318, 95 et L7 fois 0,67seconde par an,lesprincipales 6tant d'ann6es,ce qui est relativementcourt, plusmassives que la Terre.Laformation 18,85secondes par an et l7 ,75secondes car,pour une telle dur6e,les effetspos- de la Lune posealors un probldme par- par an. Nous sommes donc loin des siblesprovenant de la nature chaotique ticulier, et plusieurs sc6nariosont 6t6 r6sonances,ce qui explique les faibles Thedu mouvement Moon’s orbital ne Past sont pas Historyavanc6spour expliquer la formation de Moon was present still earlier, as far back as 3.8 billion years variations de I'obliquit6 de la Terre. Il encore sensibles.Les variationsd'obli- la Lune. n'en estpas de m0mepour Mars,dont la quit6 de la Terre qui en r6sultentsont de Dans le sc6nariofission,la Terre, en ago. If the Moon was indeed captured, its capture appar- frdquence de prdcessionest de 7,5 TheI'ordre Moon de +15 degr6s, exertset ales force variations of attractionrotation trds on rapide the (2-3 Earth heures), whichse ently occurred during an early phase of the solar system’s secondespar an pour une obliquit6 weinduites observepour I'insolation daily throughi 65 degr6s thede phenomenons6pared'une partie oftides.de sonmanteau Sincesous the actuellede25,2degr6s, et William Ward, latitude Nord sont consid6rablement I'effet de la force centrifuge.Ce moddle development. du Jet Propulsion Laboratory, avait Earthplus importantes rotates qu'auparavant. more rapidlySi les on itsest pratiquement axis (once abandonnl, daily) than car il theest remarqu6 que Mars pr6sentait des Moonvariations revolves pass6esde around I'insolation the dans Earthdifficile (about d'expliquer once everyune rotation 28 days), initiale variations d'obliquit6 importantes(+lQ les hautes latitudes sont bien, comme aussirapide de la Terre, la diff6rence degr6s), d cause de la proximit6 des theI'avance tidesla thdorie move de over M. Milankovitch, the Earth’snotable surface, de composition and thischimique motion de la is The Moonless Earth 16sonancess6culaires orbitales. accompaniedresponsablesdes bypassages a dissipationen pdriode ofTerre energy. et la Lune, et surtout le fait que la glaciaire,il est fort probable que les Lune ne se trouve pas dans le plan de This in turn leads to a slowing of the Earth’s rotationalplan Et siI'on supprimait la Lune? variations de la figure 3 induiront ir la l'6quateur,mais d cinq degr6sdu de As we saw earlier, if the Moon were not present, the Earth’s speedsurface (a de lengtheningla Terre des variations of the dayde byI'orbite 0.002 de la seconds Terre. per century), Il est,bien entendu,hors de question temp6ratureencore plus importantes. La Lune aurait pu se former en rotational speed would be somewhat higher, since it would de faire ou d'inciter qui que ce soit h andNotre an increasebut n'est cependant of the Moon’s pas de meanm€metemps distanceque la fromTerre,par the accrdtion Earth not have been slowed through the dissipative effects of lu- autour de celle- faire une chosepareille, mais seulement ofsupprimer aboutla 3.5 Lune, centimeters maisde comprendre per year.de mat6riaux Severalen million orbite years ago, nar tides. By extrapolating the values found previously by de comprendre, i travers des simula- thel'dvolution Earth possible rotatedque la noticeably Terre aurait moreci. Ce sc6nario rapidlyexplique on its la axis,pr6sence andde tions num6riques sur ordinateur, l'im- connuesi la Lune n'avait pas exist6; se la Lune proche du plan de l'6cliptique, Williams, the Earth’s primordial rotational speed may be es- portance de I'action de la Lune sur la thepose Moonalors le probldme was noticeablyde son origine. closer.mais il n'explique pas la sensiblediff6- timated at about 1.6 times its present value, corresponding dynamiquede la Terre.En effet,le cou- ple gravitationnel qui s'exerce sur le to a day of about 15 hours in length. At the Bureau of Lon- bourrelet 6quatorial de la Terre pro- gitudes, Fr´ed´ericJoutel, Philippe Robutel and I began with vient aux deux tiers de I'action de la Lune, pour environ un tiers du Soleil. this hypothesis and studied possible variations in the Earth’s Sansla Lune, la fr6quencede pr6cession obliquity. To do this, we used a new method for analyzing de la Terre passede 50,47secondes par an d environ 15,6 secondespar an, the stability of motion: the method of frequency analysis. et elle s'approchealors des fr6quences Ordinarily, for each value of the Earth’s initial obliquity, orbitales de la Terre, ce qui entraine la possibilit6 de rdsonance.En 1'982, we obtain a speed of precession of its axis of rotation. If the W. Ward avait 6tudi6 ce probldme sur motion is stable, this precession speed changes continuously un moddle simplifi6 et avait conclu que la suppressionde la Lune entrainerait with the initial obliquity. On the other hand, if the motion desvariations d'obliquit6 de la Terre de is chaotic, or unstable, the speed of precession is no longer I'ordrede celles de Mars. Toutefois. uniquely defined, and depends strongly on minor differences en l'absencede la Lune,la Terreaurait eu une vitessede rotation plus6lev6e, ce in the initial conditions. A graph of the speed of precession qui augmenterait I'importance de son as a function of the initial obliquity therefore indicates the bourrelet 6quatorial. Selon W. Ward, I'effet accru du Soleil compenserait stability of subsequent obliquities (see Figure 5). This analy- I'absencedu couple d0 d la Lune pour sis shows a vast chaotic zone extending from 0 up to about 85 conduire finalement ir des variations d'obliquit6 similairesh cellesobserv6es degrees initial obliquity. Whatever the Earth’s initial obliq- actuellement. uity in this range, in the absence of the Moon, the Earth’s Au Bureau des Longitudes (Paris), nous avons6tudi6 ce probldme en utili- subsequent obliquity would be subject to strong oscillations, santun modBlebeaucoup plus prdcisdu nearly ranging over the whole chaotic zone in the space of a mouvement de la Terre. Nous dispo- few million years. sionsde la solution du mouvementorbi- tal de la Terre et desautres plandtes que 4. CES COUCHES SEUUENTAIRES AUSTRALIENNES,6tudi6es par G. Williams, sont In Figure 5, we present the minimum, mean, and max- j'avais calcul6 auparavantsur 400 mil- Ag6esde 650millions d'ann6es(a). Elles sont produites parles d6p6tssuccessifs de boue fonc6e imum values attained by the Earth’s obliquity over an 18 lions d'ann6es.Cette solution m'avais Figureet de sable 4:clair dans Sedimentary un estuaire,au rythme layers des mar6es.studiedEn supposant in Australiaconstante la by dur6e G. de permisde montrer,en L989,que le mou- Williams.l'ann6e, on retrouve (a) la 650 dur6e million du jour etyears la distance ago,Terre-Lune these i layersces6poques wererecul6es. formedDatant million year period, for various initial obliquity values. On vement orbital des planbtes internes de2r5 milliards d'ann6es,les couches(b) tdmoignent aussi des effets de mar6eslunaires. through successive deposits in an estuary of dark clay and such a short time interval, the obliquity does not range over @ pounLA scrENcE light sand by the tides. Assuming the length of the year has17 the entire chaotic zone in the examples considered, but our remained constant, it is possible to deduce from these records analysis shows that the full extent of the chaotic zone may the length of the day and the distance between the Earth and be attained over longer time periods. In the absence of the Moon in the distant past. (b) Dating back 2.5 billion years, Moon, the Earth would undergo variations in its obliquity these layers probably also reflect the tidal effects of the Moon. of sufficient magnitude so as to drastically alter its surface climate. It should be pointed out that with an obliquity of 85 degrees, the Earth’s axis of rotation would very nearly lie The rate of slowing is not constant, and evidence of its in its orbital plane, as is the case with Uranus. The whole variation may be found in records of past tidal cycles, such planet would then be subject, as the polar zones are now, to as coral reefs and certain shell fossils. But it was by ana- days and nights of several months duration. At the poles, lyzing sedimentary deposits that the Australian geologist G. the Sun would remain high in the sky for long periods, and, Williams found that the length of the day 2.5 billion years ago although no climate simulations have yet been carried out was about 20 hours, while the Moon was some 348,000 km for the Earth in this tilted configuration, it is likely that such from Earth (compared with 384,000 km currently). To find a drastic redistribution of insolation would cause significant these values, Williams analyzed deposits that were succes- changes in the Earth’s atmosphere. sively brought into an estuary by the sea through the action Of course, in choosing a primordial rotational speed of 15 of tides. The annual cycle of these tides allowed him to es- hours for the Earth, we made what seemed to be the most rea- timate the time scale of these deposits, under the reasonable sonable choice, but other scenarios of lunar formation could assumption that the length of the year has not appreciably lead to different primordial rotational speeds. Since all of changed over time. The Moon was thus present at this early these are highly speculative, we also chose to study the sta- epoch. More tenuous fossil records seem to indicate that the bility of the Earth’s obliquity in the absence of the Moon
4 d'une obliquit6 nulle jusqu'i 85 degr6s V6nussont particulidres,car, sans doute Pour Mercure,la situationest un peu environ : si, quelle que soit I'obliquit6 h cause des effets de mar6e avec le diff6rente.Comme dans le casde V6nus, initiale de la Terre comprise entre ces Soleil, leurs vitesse de rotation sont nous ne connaissonspas la p6riode de deuxvaleurs, la Lune n'estpas pr6sente, actuellement trds faibles. V6nus pos- rotation primordialede Mercure,mais il I'obliquit6 de la Terre pourra subir de sbdeaussi une particularit6qui intrigue suffit de supposer qu'elle 6tait plus trds fortes oscillationset parcourir pra- depuis longtemps : elle ne tourne pas courte que 300 heures pour assurer, rencede compositionchimique entre la tiquementvari6es,il touteest en cette revanchezone enpossible quelquesde rapidementdans le m€mesur sens elle-mOme,que les etautres la Lune pla- qu'au cours de son histoire, Mercure a jusqu'd Terreet la Lune. millionsretracer sond'ann6es. histoire une6poque 6taitnbtes,plus ouprds. en d'autres termes, elle a la connuun 6pisodetrds fortement chaoti- Dans I'hypothbsede la capture,la trbsSurrecul6e. la figure 5, on a repr6sent6les t€teCe en ralentissement bas. n'est pas constant, que, avec des variations d'obliquit6 Lune,form6e dans une r6gion voisine de valeurs minimales,moyennes et maxi- et l'onJusqu'd peutpr6sent,la en retrouverplupart une trace desastro- dans allant de 0 degr6d 90degrds en quelques I'espace,est captur€e par le champgra- males,Histoire atteintesdc la Lune par l'obliquit6 de la diffdrentsnomes quiindicateurs s'6taient pench6squi varientsur cette sui- millions d'ann6es.Ensuite, comme la vant vitationnelde la Terre.Deux modesde Terre en L8 millions d'ann6es,pour les questionles cycles en avaientdes mar6es concluoc6aniques, que V6nus plandtecontinue de ralentir i causedes La Lune exercesur la Terreune force tellela croissance des coraux et decertains capture sont actuellement proposes. diff6rentes valeurs de I'obliquit6 ini- 6tait n6e de cette manibre, ou tout au effetsde mar6edus au Soleil,elle pourra ..douce> d'attractionque nousobservons quoti- coquillagesfossiles. Toutefois, c'est en Une capture et une capture tiale. Sur une dur6e aussicourte, I'obli- moins couch6e,car alors les effets dissi- se redresserpour finir dans sa position diennementir travers le ph6nomdnedes que 5 position. of the solar system formation, in the context of Safronov’s Mars is far from the Sun, and its satellites Phobos and hypothesis of a massive primordial solar system. Deimos have masses far too small to slow its rotation, so that its present rotational period of 24 hours 37 minutes is close to its primordial rotational period. Mars’ equator is inclined 25 degrees with respect to its orbital plane, and its speed of pre- Possibility of Extraterrestrial Life cession, 7.26 seconds per year, is close to certain frequencies of motion of its orbit. Moreover, variations in the inclination On October 12, 1992, NASA inaugurated a vast program of Mars’ orbit are considerably stronger than those of the called SETI (Search for Extra Terrestrial Intelligence) to Earth. It follows that variations in its obliquity over a period search for signals arriving from possible advanced civiliza- of one million years are also much stronger than the Earth’s, tions. Over the next ten years this program will use radio and G. Ward has found obliquity variations on the order of telescopes to search over a large portion of the radio frequency ±10 degrees about a mean value of 25 degrees. These vari- spectrum for signals of extraterrestrial origin. Because the ations bring about strong climatic changes on Mars’ surface, sky is so vast, some 800 stars of solar type at distances less and certain surface structures seem to bear witness to these than 80 light years from Earth have been singled out for changes. special attention. These will each be watched for about 20 Our recent computations provide also evidence that the hours, the seemingly minimum time during which something motion of Mars’ rotational axis is chaotic. This has two con- is likely to be detected, at least from a strong source of the sequences. First, as is also the case for the orbital motion of type that might be anticipated to come from one of these the inner planets, it is not possible to predict the orientation possible extra-solar systems. of Mars’ axis for periods longer than a few million years. A fundamental principle underlies any such project: our But more important, the obliquity of Mars is subject to situation on Earth is not extraordinary, and should therefore much larger variations than those predicted by Ward, rang- be repeated many times in our galaxy, in any number of var- ing between about 0 and 60 degrees in less than 50 million ied forms. Yet, for a given star in our galaxy, we are unable years. Models of the past climates of Mars should be re- to quantify the likelihood of the appearance of organized life viewed in light of these new results. The existence of this similar to that on our planet. large chaotic zone in the orientation motion of Mars also re- Even without reference to the appearance of life itself, nor moves a constraint from models of solar system formation, to the conditions that could lead to the development of a civ- since Mars’ obliquity cannot be considered primordial. ilization that might wish to communicate using radio waves, we presently have no idea of the probability of a Sun-like star possessing a planetary entourage. In spite of frequent an- The Formation of the Solar System nouncements of the discovery of extra-solar planets, no such object has yet been observed directly, and only the obser- Since the work of Safronov in 1960, models of solar system vations of (likely) proto-planetary disks of the Beta-Pictoris formation admit the existence of a very massive initial so- type are convincing. lar nebula. Because of gravitational instabilities, part of this However, almost all estimates of the probability of extrater- nebula condensed to form the Sun. The rest of the nebula restrial life seem to agree on one point: in any planetary sys- condensed into small bodies, or planetoids. The planets were tem, the planet located neither too close nor too far from its then formed out of the larger planetoids by way of collisional sun may allow the development of organized life as we know it accretion of smaller planetoids. A large part of the remain- on Earth. In fact, simulations carried out by Michael Hart in ing planetoid mass was then ejected from the solar system. 1978 showed that outside a thin “zone of habitability,” run- Safronov showed that if accretion took place in the presence of away greenhouse effect of the atmosphere could lead to situ- many small planetesimals, the planets would all rotate in the ations of the type observed on Venus if the Earth were only 5 same direction with very nearly zero obliquity. To account percent closer to the sun, while if the Earth were somewhat for the considerable variation in the observed obliquities of further from the sun, it would experience runaway glaciation. the planets, Safronov was required to introduce a so-called Our calculations show that this is not the case, that the “stochastic component” in the accretion mechanism; this en- evolution of life on Earth is probably intimately linked with tails a final phase in which planets suffer a number of ran- an event that seems unlikely in current models of the forma- dom collisions with planetoids large enough to account for tion of planetary systems: a planet located in the zone of the observed obliquities. Our recent results show that all the habitability is able to sufficiently stabilize its long-term inso- obliquities of the inner planets may be accounted for by the lation variations through the presence of a massive Moon-like action of secular perturbations of the planets, complemented, satellite. Of course, it should be possible to find other partic- in the case of Mercury and Venus, by the dissipative effects ular circumstances leading to long-term climatic stability for described earlier. a planet, but it should be stressed that these situations are We also show that the obliquities of the outer planets are probably uncommon. The probability of the existence, in a essentially stable, as are their orbital motions. We are unable planetary system, of planets with stable climates comparable to account in this way for the large obliquity of Uranus (98 to our own must no doubt be reexamined and reduced by degrees). It is however possible to envisage for Uranus a several orders of magnitude, as is the case for the probability scenario similar to that proposed for Venus, in an early stage of success of NASA’s SETI project. 6 Remaining Questions Using the orbital motions of the planets of the solar system, we have shown that the Earth very likely owes its climatic sta- bility to the presence of the Moon. It should also be pointed out that if our existence is intimately tied to that of the Moon, it is possible to accept a scenario for the formation of the Moon of such small probability of occurrence that we would ordinarily reject it in confining ourselves to generic sit- uations. Theories of the formation of the Moon would then need to be reconsidered in this light. In addition, the orbital motion of the planets and of the Earth itself is chaotic. This does not seem to induce major changes in its orbital parameters over a few hundred mil- lion years, but in other planetary systems, this may not be the case, and orbital instabilities alone may induce strong cli- matic changes, or even the ejection from the planetary system of the one planet initially residing in the zone of habitabil- ity. Only a deeper understanding of the global dynamics of planetary systems will allow us to respond, at least partly, to such questions. We are also far from understanding the mechanisms of for- mation of planetary systems. One of the great difficulties confronting us is that we possess only one example of a plan- etary system, namely our own. The discovery of another would be a boon to understanding the history of our solar system, even if no form of life existed in the other system. Finally, the climatic changes on the surface of a planet arising from significant changes in its orbit or orientation are still not well understood, and it can only be hoped that an increased understanding of atmospheric dynamics will allow these changes to be successfully simulated by computers. These various problems, though encompassing disparate subfields of astronomy, together make up a vast research pro- gram; but efforts toward their resolution will doubtless lead us to a better understanding of the origins of the solar system and of the appearance of life on Earth. Translated by H.S. Dumas References G. Willams, Tidal Rythmites: Geochronometers for the an- cient Earth-Moon System, in Episodes, Vol. 12, 3, September 1989. J. Laskar: La stabilit´edu syst`eme solaire, in “Chaos et D´eterminisme”, A. Dahan et al. Eds., Point Seuil, 1992. J. Laskar, P. Robutel: The chaotic obliquity of the planets, Nature, 361, 608–612, February 18, 1993. J. Laskar, F. Joutel, P. Robutel: Stabilization of the Earth’s obliquity by the Moon, Nature, 361, 615–617, Febru- ary 18, 1993. J. Laskar: A numerical experiment on the chaotic behavior of the solar system, Nature, 338, 237–238, March 16, 1989. 7