The Moon and the Origin of Life on Earth

Jacques Laskar

April 1993∗

If the Moon did not exist, the orientation of the Earth’saxis would not be stable, and would be subject to largechaotic variations over the ages. The resulting climaticchanges very likely would have markedly disturbed the de-velopment of organized life.

We are all familiar with the change of seasons due to theinclination of the equator with respect to the plane of theEarth’s orbit around the Sun. This inclination of 23◦27′,called “obliquity” by astronomers, also gives rise to the polarcircles, inside of which day and night may each last severalmonths. The distribution of solar heat over the Earth’s sur-face also depends on the obliquity, making it an essential partof our understanding of terresterial climate. Calculations car-ried out at the Bureau of Longitudes in Paris show that theMoon stabilizes oscillations in the Earth’s obliquity, thereforeacting as a climatic regulator for the Earth.

Lalune et l'originede l'hommer JACQUES TASKAR

Si la Lune n'existait pas, l'orientation de I'axe de rotation de laTerrene serait pas stable, et subirait de larges variations chaotiques au coursdes Ages. Les changements climatiques engendrds par ces variationsauraient alors perturbd fortement le ddveloppement de la vie organisde.

ous sommes tous familiers durythme des saisons, dont la suc-cession r6sulte de I'inclinaison

de l'6quateur par rapport au plan deI'orbite de la Terre autour du Soleil.Cette inclinaison de 23o27', appel6eobliquit6 par les astronomes, est aussi lacause de I'existence des cercles polaires,i I ' int6rieur desquels les jours et les nuitspeuvent durer plusieurs mois. Lar6par-tition de la quantit6 de chaleur solairereEue d la surface de la Terre d6pend deson obliquit6, qui est I 'un des 6l6mentsfondamentaux de la comprdhension duclimat. Les calculs que nous avons effec-tu6s au Bureau des Longi tudesmontrent que la Lune stabilise les oscil-

lations possibles de l 'obliquit6, et qu'elleagit donc comme un r6gulateur climati-que de la Terre.

En 720 avant J.-C., Hipparqued6couvre que la direction de I 'axe derotation de la Terre n'est pas fixe. Eneffet, ce dernier ddcrit un c6ne dans I'es-pace, avec une p6riode d'environ 26 000ans. Ce mouvement, appel6 prdcessiondes 6quinoxes, r6sulte de I 'existence dubourrelet 6quatorial de la Terre, et ducouple exerc6 sur ce bourrelet par laLune et par le Soleil. On observe trdsfacilement ce ph6nomdne de pr6cessionde I'axe de rotation d'un corps solidedans un champ de pesanteur quand onfait tourner une toupie sur une table.

Une des cons6quences de ce ph6no-mdne est que I 'axe de rotation de laTerre ne pointe pas toujours vers l '6toilepolaire, mais d6crit un large cercle sur lavo0te c6leste.

La pr6cession des 6quinoxes consti-tue d'ail leurs une objection importanteaux arguties des adeptes de I 'astrologie.car elle a introduit un tel d6calase entrele calendrier et le mouvement apparentdu Soleil qu'ir la date correspondant ausigne du B6l ier , le Solei lse t rouve main-tenant dans la constellation des Pois-SONS.

Cette pr6cession a un effet sur le cli-mat de la Terre. En effet. l'orbite de laTerre n'est pas circulaire. mais approxi-

22 JUIN

1. L'ALTERNANCE DES SAISONS d6pend de I'obliquit6 e de laTerre (a) et de la pr6cession des 6quinoxes (D). En 616, la quantit6 dechaleur solaire regue dans I'h6misphbre Nord est plus importanteque dans I'h6misphbre Sud. Selon la valeur de I'angle de pr6cession,

14

la Terre est au point le plus prbs du Soleil (p6rih6lie), pendant l'6t6de I'h6misphbre Nord ou pendant I'hiver, comme c'est le cas actuel-lement. Il en r6sulte une augmentation, ou une diminution ducontraste des saisons.

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Figure 1: The change of seasons depends on the Earth’s obliq-uity (a) and on the precession of the equinoxes (b). In sum-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 maybe at its point nearest the Sun (perihelion) during the north-ern hemisphere’s summer, or during its winter, as is currentlythe case. The hemispheres thus experience a correspondingaccentuation or dimunition of seasonal contrasts.

In 120 BC, Hipparcus discovered that the direction of theEarth’s rotational axis is not fixed with respect to the stars.In fact, it traces out a cone in space roughly once every 26,000years. This so-called precession of the equinoxes is the resultof the torque exerted on the Earth’s equatorial bulge by the

∗This text is a close translation (by H.S. Dumas) of the original paperLa Lune et l’origine de l’homme that was first published in the frenchversion of Scientific American, Pour la Science, 186, pp 34 - 41, April1993, shortly after the publication of the associated research papers inNature. This paper has since been reprinted in several foreign editionsof Scientific American (Italian, Arabic, Japanese, German, Polish), andin Portugese in Cincia Hoje. Up to now (september 2009), It was notavailable in English.

Moon and the Sun. A similar precession of a solid body’s axisof rotation can easily be observed with an ordinary spinningtop. One consequence of this phenomenon is that the Earth’srotational axis does not always point toward Polaris, but in-stead describes a large circle in the celestial sphere. Thisfact sometimes disturbs the quibblings of astrologers, sincethe precession of the equinoxes has so greatly displaced thezodiacal calendar from the apparent motion of the Sun thatpresently, on the date corresponding to the sign of Aries, theSun is in the constellation Pisces.

The precession of the equinoxes also affects the Earth’s cli-mate. The Earth’s orbit is in fact not circular, but, as Keplershowed in the early 17th century, is instead approximately el-liptic with the Sun residing at one focus. The eccentricity ofthis ellipse (which measures its elongation) is small (0.017),but is enough to measurably change the quantity of solarheat 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 passesthrough its perihelion January 4th, during the boreal winter.This diminishes seasonal contrasts in the northern hemish-pere, and accentuates them in the southern hemishpere. In13,000 years, the situation will be reversed and seasonal con-trasts will be more accentuated in the northern hemisphere.The precession of the equinoxes thus affects the distributionof insolation at a given location on the Earth in the course ofa year. In fact, it appears possible to trace more significantclimatic changes to variations in the Earth’s eccentricity andobliquity.

The Astronomical Theory of Climates

In Kepler’s view, the Earth’s orbit was an immutable el-lipse. Newton challenged this view by demonstrating thatthe masses of the other planets perturbed the Earth’s orbit,so that it is only an ellipse to first approximation: neither itseccentricity nor its obliquity are fixed. LeVerrier (famed forhis discovery in 1846 of the planet Neptune based on pertur-bations of Uranus’ orbit) was the first to calculate possiblelong-term (or “secular”) variations in the Earth’s eccentricity.In doing so, he took up calculations of the Earth’s orbital mo-tion begun by Laplace shortly before the French Revolution.It was LeVerrier’s Earth-orbit calculations that, in 1941, ledthe Yugoslavian astronomer Milutin Milankovich to hypoth-esize that the ice ages were the result of high-lattitude vari-ations in terrestrial insolation induced by secular variationsin the Earth’s orbit and axial orientation. His theory did notwin immediate acceptance, as the variations in insolation did

1

not seem adequate to account for glaciation. But the sametheory has gained wider acceptance over the last two decades.Measurements carried out by John Imbrie and coworkers ofthe relative concentration of the oxygen isotopes O18 and O16

present in the carbonates of marine sedimentary layers canbe related to the past thickness of the polar ice caps. Fromthis it is possible to estimate mean ocean temperatures in thedistant past. Indeed, it provides some record of the Earth’spast climate up to more than three million years ago. Thoughmuch less precise, geological records reflect climatic condi-tions as far back as 200 million years. Moreover, improvedmodels of climatic response to variations in the Earth’s orbitshow that the effects of changes in insolation may be ampli-fied through secondary effects, such as growth of the ice capsor changes in the make-up of the atmosphere.

mativement ell iptique, comme l'a mon-trd Kepler en 1609, le Soleil occupant undes foyers de l'ellipse. L'excentricit6 deI'ellipse (qui mesure son aplatissement)est faible (0,017), mais suffit pour chan-ger la quantit6 de chaleur reEue d lasurface de la Terre, entre le p6rih6lie,position oD la Terre est le plus prds duSoleil, et I 'aph6lie oi elle est d son 6loi-gnement maximal.

Actuellement, le passage au p6rih6-lie a l ieu le 4 janvier pendant I 'hiverbordal. Cette diff6rence d'6loisnement

diminue le contraste des saisons dansI 'h6misphdre Nord, alors qu'el leI'accentue dans I 'h6misphdre Sud. Dans13 000 ans, I'effet sera contraire, et lescontrastes des saisons seront plus accen-tu6s dans I'h6misphdre Nord. La pr6ces-sion des 6quinoxes modif ie donc lar6partition de I'insolation en un lieu dela Terre au cours de I'ann6e. En fait, desvariations de climats beaucoup plusimportantes semblent aussi rdsultef desvariations de l'excentricit6 et de I'obli-quit6 de I'orbite de la Terre.

La theorie astronomiquedes pal6oclimats

Pour Kepler, la Terre d6crivait uneellipse immuable. Newton a boulevers6cet 6quilibre en montrant que la massedes autres planbtes du Sys[dme solaireperturbait l'orbite de la Terre, qui n,estdonc une el l ipse qu'en premibreapproximation : ni I'excentricit6 de laTerre, ni son obliquitd ne sont f ixes.LeVerrier (c6ldbre pour avoir d6cou-vert, par le calcul des perturbations

2.LAPRECESSION DES EQUINOXES. La Terre n'est pas parfai-tement spheriqud, mais ldgirement aplatie aux p6les e-t renfl6e il'6quateur. sous I'action gravitationnelle de ra Lune et du soleil, sonaxe de rotation d6crit un cdne, comme Ie fait une toupie. La direction

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de I'axe de la Terre trace un large cercle sur la vo0te c6leste en26 000 ans environ. Il y a 5 fi)O an1, ra direction du pOte Nord 6taitdonn6e par l'6toile alph_g du Dragon, et non p"r p".

^l'6toile polaire.

Dans 13 0(X) ans, cette direction sera ceUe ae V6ga

15

Figure 2: Precession of the equinoxes. The Earth is not per-fectly spherical, but slightly oblate, with flattened poles andan equatorial bulge. Under the gravitational action of theSun and Moon, its axis of rotation traces out a cone, muchlike a spinning top. The Earth’s rotation axis traces out alarge circle in the celestial sphere approximately once every26,000 years. 5000 years ago the North Pole was indicated bythe star Alpha, in Draco, rather than by Polaris. In 13,000years, this direction will be indicated by Vega.

An essential part of any study of variations in the Earth’sinsolation is the calculation of variations in its obliquity underthe influence of planetary perturbations. Over a one millionyear period, this variation is only ±1.3 degrees around themean value of 23.3 degrees. This may not seem like much,but it is enough to induce variations of nearly 20 percent inthe summer insolation received at 65 degrees north lattitude.The amount of additional heat received during the summerat high lattitudes is an important factor in climate studies,

as it melts ice accumulated over the winter and prevents theice caps from extending their reach. Weak variations in theEarth’s obliquity are therefore a determining factor in regu-lating the relatively moderate climate enjoyed by the Earthover the last several million years, and in allowing the ap-pearance of organized life as we understand it. The ice agesconstitute significant climatic changes, but were not so se-vere as to permanently change the conditions for life on theEarth’s surface.

Variations in the Earth’s Obliquity

Perturbations exerted by other planets cause the Earth’s or-bit to turn in space with a motion that may be representedapproximately as the sum of several uniform rotations, eacharising from the influence of a particular planet, with peri-ods ranging from 40,000 to several million years. It is theeffect of this complicated motion on our terrestrial spinningtop that gives rise to the small oscillations in its obliquity. Ifthe excitation period produced by this motion of the Earth’sorbit 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—eachtime it reaches its highest point. Even if each push is small,the swing’s oscillations will be amplified (especially in theabsence of friction). But if the swing is instead pushed atrandom intervals, nothing special takes place in general.

Instead of using the periods, we will consider the rotationalspeeds of these different motions. Since all the precessionalmotions we consider are very slow, they are expressed in unitsof arc seconds per year, abbreviated simply as seconds peryear. A rotational speed of one second per year thus cor-responds to a period of 360 × 3, 600 = 1, 296, 000 years. Iwill introduce a slight abuse of terminology by calling theserotational speeds frequencies. With this convention, the fre-quency of precession of the Earth’s orbit is 50.47 secondsper year, while the principal frequencies of the motion ofthe Earth’s orbit range from 26.33 seconds per year downto nearly 0.67 seconds per year, with the main frequenciesat 18.85 and 17.75 seconds per year. We are thus far fromresonance, which explains the relatively small variations ob-served in the Earth’s obliquity. This is not the case for Mars,whose frequency of precession is 7.5 seconds per year andwhose obliquity is presently 25.2 degrees. William Ward, ofthe Jet Propulsion Laboratory in California, has pointed outthat the proximity of secular orbital resonances causes Marsto undergo substantial variations in obliquity (on the orderof ±10 degrees).

What if the Moon Were Removed?

To answer this question, I do not propose anything so dras-tic as to physically remove the Moon, but rather to study,through numerical simulations on a computer, the Moon’seffect on the Earth’s dynamics. We know that the Moonaccounts for about two thirds of the torque acting on theEarth’s equatorial bulge, with the Sun accounting for the re-maining third. Without the Moon, the Earth’s frequency of

2

d'uranus, la plandte Neptune en 1846)a,le premier, calcul6 les variations d trdslong terme, appel6es variations s6cu-laires, de I'excentricit6 de la Terre. Ilpoursuivai t en cela les t ravaux deLaplace effectu6s un peu avant la R6vo-lution franEaise. C'est en utilisant lessolutions de LeVerrier pour le mouve-ment orbital de la Terre, que I'astro-nome yougoslave Milutin Milankovitch6mit, en 794I, I'hypothbse que lesgrandes p6riodes glaciaires du Quater-naire r6sultent des variations de I'inso-lation aux hautes latitudes induites parles variations s6culaires de I'orbite et deI'orientation de la Terre. Cette th6orien'a pas 6t€ accept6e imm6diatement. Enfait, ces variations d'insolation ne sem-blaient pas suffisantes pour engendrerdes variations de temp6rature pouvantentrainer une glaciation.

Cette th6orie a 6t6, lar gement conso-lid6e depuis environ deux d6cennies.Les mesures isgtopiques des taux d'oxy-gdne O'o/O'o ef fectu6es par John

Imbrie et ses collaborateurs fournissentdes indicateurs de l '6paisseur descalottes polaires qui ont permis d'obte-nir des estimations des temp6raturesmoyennes des mers dans les dpoquesrecul6es.

Actuellement, ces mesures effec-tu6es par I'analyse des carbonates pr6-sents dans les carottes de s6dimentsmarins permettent de retrouver les cli-mats du pass6 sur des dur6es d'environtrois millions d'ann6es. Il existe m6medes enregistrements gdologiques, beau-coup moins pr6cis, mais qui permettentde remonter jusqu'd 200 mill ionsd'ann6es. D'autre part, une meilleuremod6lisation de la r6ponse climatiqueaux variations de l'orbite terrestre mon-tre que I'effet des changements d'insola-t ionpeut 6tre ampl i f id par des ef fetssecondaires tels que I 'extension descalottes polaires ou le changement de lacomposition de I'atmosphdre.

Un des 6l6ments essent ie ls dansl'6tude des variations d'insolation de la

Terre est le calcul des variations de sonobliquit6 sous l'influence des perturba-t ions plandtaires. Sur un mi l l iond'ann6es, cette variation n'est que de+1,3 degr6 autour de la valeur moyennede 23,3 degr6s. Cela peut sembler trbspeu, mais entraine cependant des varia-tions de prbs de 20 pour cent dans I'in-solation reEue en 6t6, h 65 degr6s delatitude Nord. Or la quantitd de chaleursuppl6mentaire reEue pendant l'6td auxhautes latitudes est une donn6e impor-tante pour l'6tude des climats, car c'estelle qui fait fondre les glaces accumuldespendant I'hiver et empOche I'extensiondes calottes polaires.

Les faibles variations de I'obliquit6de la Terre sont ddterminantes pour luiassurer la relative 16gularit6 climatiquedont elle a b6n6fici6 depuis plusieursmi l l ions d 'ann6es, et qui a permisI'apparition de vie organis6e telle quenous la connaissons. Les pdriodes gla-ciaires constituent des changements cli-matiques importants, mais qui n'ont pas6t6 suffisants pour alt6rer de manidredurable les conditions de vie d la surfacede la Terre.

Les variations de I'obliquit6de la Terre

Les perturbations exerc6es par lesautres plandtes font tourner I'orbite dela Terre dans l'espace avec un mouve-ment qui peut se repr6senter, de manidreapproximative, comme la r6sultante deplusieurs rotat ions uni formes dep6riodes allant de 40 000 e plusieursmillions d'ann6es, chacune d'entre ellesprovenant plus particulidrement de I'in-fluence d'une des plandtes. C'est I'effetde ce mouvement compliqu6 sur notretoupie terrestre qui induit les petitesoscillations de son obliquit6.

Si la pdriode de I'excitation produitepar ce mouvement de I'orbite de la Terreest proche de la p6riode de pr6cessionde son axe, un ph6nombne classique enphysique intervient : la r6sonance. Il y a,par exemple, r6sonance si on pousse unebalanEoire au bon moment, i chaquefois qu'elle arrive d son point le plushaut. M0me si cette pouss6e est trdspetite, on verra s'amplifier les oscilla-tions de la balangoire (surtout s'il n'y apas de frottements). En revanche, si I'onpousse la balanEoire n'importe quand, ilne se passera rien de particulier.

Au lieu d'utiliser les p6riodes, nousconsid6rerons plut6t des vitesses derotation de ces diffdrents mouvements.Comme tous les mouvements de pr6ces-sion dont nous parlerons sont trds lents,l'unit6 employde est la seconde d'arc paran ou, en abr6g6, seconde par an. Unevitesse de rotation de une seconde oaran correspond alors d une p6riode de

ENSEMBLE TERRE.LUNE TERRE SEULE.rJ-l(rtr

(rF,lLJ

tsatr4

=z[!

z=Joct)z

{- l

TEMPS EN MtLLtoNs o'nruruEEs

3. SUR CETTE SIMULATION NUMfRIQUE, la Lune est supprim6e brutalement i la dated'aujourd'hui (r = 0). Sous I'action des perturbations plan6taires, et en pr6sence de la Lune,I'obliquit6 de la Terre subit de petites variations (+1J degr6) autour de sa valeur moyenne(23,3 degr6s) (a). Ces variations sont suffisantes pour induire les variations de prbs de 20 pourcent de I'insolation regue sur Terre ir 65 degr6s de latitude Nord (D) qui sont, selon la th6oriede M. Milankovitch, i I'origine des pdriodes glaciaires. Aprbs la suppression de la Lune,lesvariations sur un million d'ann6es de I'obliquit6 et de l'insolation deviennent beaucoup plusimportantes.

to

ENSEMBLE TERRE.LUNE TERRE SEULE

a.tll

crn

I.JJoztI|.ulFla=dl

20

I

TEMPS EN MILLIONS D'ANNEES

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Figure 3: In this numerical simulation, the Moon is removedabrubtly at our present date (t = 0). Under the influenceof planetary perturbations, and in the presence of the Moon,the Earth’s obliquity is not fixed, but undergoes small varia-tions (±1.3 degrees) about its mean value (23.3 degrees) (a).These small variations are enough to induce changes of nearly20 percent in the insolation received on Earth at 65 degreesnorth lattitude (b), and, according to Milankovich’s theory,are the cause of the ice ages. After removing the Moon, varia-tions in terrestrial obliquity over a period of one million yearsare significantly increased.

precession would decrease from its present value of 50.47 toaround 15.6 seconds per year, thus approaching the Earth’sorbital frequencies and their attending resonances. In 1982,W. Ward studied this problem using a simplified model, andconcluded that removing the Moon would induce variationsin terrestrial obliquity on the order of those of Mars. But theMoon’s absence would also mean a higher rotational speedfor the Earth, which would increase the size of its equato-rial bulge. According to Ward, the resulting increase in solartorque on the larger bulge would offset the absence of torquedue to the Moon, leading in the end to obliquity variationscomparable to those observed now.

At the Bureau of Longitudes in Paris, we recently studiedthis problem using a much more accurate model of terrestrialmotion. We made use of calculations of the orbital motionof the Earth and the other planets that I carried out earlierover a model time period of some 400 million years. It wasthese calculations that I used in 1989 to show that the orbitalmotion of the solar system, and more especially of the innerplanets (Mercury, Venus, Earth, and Mars), is chaotic. It wastherefore possible to study numerically, over very long time

periods, variations in the Earth’s orientation due to its orbitalvariations. We first of all simulated an abrupt disappearanceof the Moon, then observed the behavior of the Earth’s obliq-uity over one million years. This is a relatively short time, notlong enough, for example, for effects arising from the chaoticnature of the orbital motion to be detected. Nevertheless,variations on the order of ±15 degrees in the Earth’s obliq-uity were observed, and the resulting variations in insolationat 65 degrees north lattitude were much more significant thanbefore. If, as advanced in Milankovich’s theory, the variationsin insolation at high lattitudes are responsible for periods ofglaciation, it is very likely that the variations depicted in Fig-ure 3 would induce still more significant temperature changeson the Earth’s surface.

Our goal is however not to rid ourselves of the Moon, butto understand the possible evolution of the Earth had theMoon not existed, which naturally leads us to inquire aboutthe Moon’s origins.

The Origin of the Moon

The Moon confronts us with a number of astronomical prob-lems. Its mass, 1/81 that of the Earth, is very large for aplanetary satellite, and in that respect is unique in the solarsystem. Only Jupiter, Saturn, and Neptune possess satellitesof comparable mass, yet those planets are respectively 318,95, and 17 times as massive as the Earth. The formation ofthe Moon thus poses a distinct problem, for which a numberof different scenarios have been proposed.

In the fission scenario, centrifugal forces of a rapidly rotat-ing Earth (2–3 hours) tore off a large portion of its mantle toform the Moon. This model has been very nearly abandoned,in part because it is difficult to account for such a high initialrotation speed for the Earth, in part because of the Earth’sand Moon’s noticeably different chemical compositions, andespecially because the Moon does not lie close to the Earth’sequatorial plane, but instead only 5 degrees from its orbitalplane.

The Moon might have been formed at the same stage asthe Earth, through the accretion of material in orbit aroundit. This would explain the Moon’s nearness to the planeof the ecliptic, but not the marked difference in chemicalcomposition.

In the capture hypothesis, the Moon was formed in someneighboring part of space, then captured by the Earth’s grav-itational field. Two modes of capture have been proposed:“soft” capture, and “hard” capture. Hard capture entails aviolent collision between the Earth and some massive body,with the subsequent accretion of the resulting debris form-ing the Moon. The problem with these scenarios—the lattercurrently enjoying the most favor—is their low probabilityof occurrence. Skepticism concerning a capture scenario ad-heres to the “principle of mediocrity,” which requires thatobserved events be generic rather than exceptional.

Though the Moon’s origin remains enigmatic and subjectto varied speculation, it is nevertheless possible to retrace itshistory to a very distant past.

3

The Moon’s Past History

The Moon exerts a force of attraction on the Earth whichwe observe daily through the phenomenon of tides. Since theEarth rotates more rapidly on its axis (once daily) than theMoon revolves around the Earth (about once every 28 days),the tides move over the Earth’s surface, and this motion isaccompanied by a dissipation of energy.

This in turn leads to a slowing of the Earth’s rotationalspeed (a lengthening of the day by 0.002 seconds per century),and an increase of the Moon’s mean distance from the Earthof about 3.5 centimeters per year. Several million years ago,the Earth rotated noticeably more rapidly on its axis, andthe Moon was noticeably closer.

360 x 3600 =1.296000 ans. Je ferai mOmeun l6ger abus de langage en appelant cesvitesses angulaires de rotation des fr6-quences.

Dans ces nouvelles rotations, la fr6-quence de pr6cession de la Terre est de50,47 secondes par an, alors que les fr6-quences principales du mouvement deI 'orbi te de la Terre vont de 26,33secondes par an jusque pratiquement0,67 seconde par an,les principales 6tant18,85 secondes par an et l7 ,75 secondespar an. Nous sommes donc loin desr6sonances, ce qui explique les faiblesvariations de I'obliquit6 de la Terre. Iln'en est pas de m0me pour Mars, dont lafrdquence de prdcession est de 7,5secondes par an pour une obliquit6actuelle de25,2degr6s, et William Ward,du Jet Propulsion Laboratory, avaitremarqu6 que Mars pr6sentait desvariations d'obliquit6 importantes (+lQdegr6s), d cause de la proximit6 des16sonances s6culaires orbitales.

Et si I'on supprimait la Lune?Il est, bien entendu, hors de question

de faire ou d'inciter qui que ce soit hfaire une chose pareille, mais seulementde comprendre, i travers des simula-tions num6riques sur ordinateur, l'im-portance de I'action de la Lune sur ladynamique de la Terre. En effet,le cou-ple gravitationnel qui s'exerce sur lebourrelet 6quatorial de la Terre pro-vient aux deux tiers de I'action de laLune, pour environ un tiers du Soleil.Sans la Lune, la fr6quence de pr6cessionde la Terre passe de 50,47 secondes paran d environ 15,6 secondes par an,et elle s'approche alors des fr6quencesorbitales de la Terre, ce qui entraine lapossibil i t6 de rdsonance. En 1'982,W. Ward avait 6tudi6 ce probldme surun moddle simplifi6 et avait conclu quela suppression de la Lune entraineraitdes variations d'obliquit6 de la Terre deI'ordre de celles de Mars. Toutefois.en l'absence de la Lune,la Terre auraiteu une vitesse de rotation plus 6lev6e, cequi augmenterait I'importance de sonbourrelet 6quatorial. Selon W. Ward,I'effet accru du Soleil compenseraitI'absence du couple d0 d la Lune pourconduire finalement ir des variationsd'obliquit6 similaires h celles observ6esactuellement.

Au Bureau des Longitudes (Paris),nous avons 6tudi6 ce probldme en utili-sant un modBle beaucoup plus prdcis dumouvement de la Terre. Nous dispo-sions de la solution du mouvement orbi-tal de la Terre et des autres plandtes quej'avais calcul6 auparavant sur 400 mil-lions d'ann6es. Cette solution m'avaispermis de montrer, en L989, que le mou-vement orbital des planbtes internes

@ poun LA scrENcE

(Mercure, V6nus, Terre et Mars) estchaotique. Il 6tait donc possible d'6tu-dier num6riquement, sur de trds longuesdur6es.les variations de I'orientation dela Terre produites par ses variationsorbitales.

Dans un premier temps, nous avonssimul6 une disparition brutale de laLune et observ6 ce que devient I'obli-quit6 de la Terre pendant un milliond'ann6es, ce qui est relativement court,car, pour une telle dur6e, les effets pos-sibles provenant de la nature chaotiquedu mouvement orbital ne sont pasencore sensibles. Les variations d'obli-quit6 de la Terre qui en r6sultent sont deI'ordre de +15 degr6s, et les variationsinduites pour I'insolation i 65 degr6s delatitude Nord sont consid6rablementplus importantes qu'auparavant. Si lesvariations pass6es de I'insolation dansles hautes latitudes sont bien, commeI'avance la thdorie de M. Milankovitch,responsables des passages en pdriodeglaciaire, il est fort probable que lesvariations de la figure 3 induiront ir lasurface de la Terre des variations detemp6rature encore plus importantes.

Notre but n'est cependant pas desupprimer la Lune, mais de comprendrel'dvolution possible que la Terre auraitconnue si la Lune n'avait pas exist6 ; sepose alors le probldme de son origine.

L'origine de la Lune

La Lune pose de gros problbmes auxastronomes. Sa masse, L/8L de celle de laTerre, est trbs importante pour un satel-lite d'une plandte, ce qui est unique dansle Systbme solaire. Seuls Jupi ter ,Saturne et Neptune possddent des satel-lites de masse comparable, alors qu'ellessont respectivement 318, 95 et L7 foisplus massives que la Terre. Laformationde la Lune pose alors un probldme par-ticulier, et plusieurs sc6narios ont 6t6avanc6s pour expliquer la formation dela Lune.

Dans le sc6nario fission,la Terre, enrotation trds rapide (2-3 heures), ses6pare d'une partie de son manteau sousI'effet de la force centrifuge. Ce moddleest pratiquement abandonnl, car il estdifficile d'expliquer une rotation initialeaussi rapide de la Terre, la diff6rencenotable de composition chimique de laTerre et la Lune, et surtout le fait que laLune ne se trouve pas dans le plan del'6quateur, mais d cinq degr6s du plan deI'orbite de la Terre.

La Lune aurait pu se former enm€me temps que la Terre, par accrdtionde mat6riaux en orbite autour de celle-ci. Ce sc6nario explique la pr6sence dela Lune proche du plan de l'6cliptique,mais il n'explique pas la sensible diff6-

4. CES COUCHES SEUUENTAIRES AUSTRALIENNES,6tudi6es par G. Williams, sontAg6es de 650 millions d'ann6es (a). Elles sont produites parles d6p6ts successifs de boue fonc6eet de sable clair dans un estuaire, au rythme des mar6es. En supposant constante la dur6e del'ann6e, on retrouve la dur6e du jour et la distance Terre-Lune i ces 6poques recul6es. Datantde2r5 milliards d'ann6es,les couches (b) tdmoignent aussi des effets de mar6es lunaires.

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Figure 4: Sedimentary layers studied in Australia by G.Williams. (a) 650 million years ago, these layers were formedthrough successive deposits in an estuary of dark clay andlight sand by the tides. Assuming the length of the year hasremained constant, it is possible to deduce from these recordsthe length of the day and the distance between the Earth andMoon in the distant past. (b) Dating back 2.5 billion years,these layers probably also reflect the tidal effects of the Moon.

The rate of slowing is not constant, and evidence of itsvariation may be found in records of past tidal cycles, suchas coral reefs and certain shell fossils. But it was by ana-lyzing sedimentary deposits that the Australian geologist G.Williams found that the length of the day 2.5 billion years agowas about 20 hours, while the Moon was some 348,000 kmfrom Earth (compared with 384,000 km currently). To findthese values, Williams analyzed deposits that were succes-sively brought into an estuary by the sea through the actionof tides. The annual cycle of these tides allowed him to es-timate the time scale of these deposits, under the reasonableassumption that the length of the year has not appreciablychanged over time. The Moon was thus present at this earlyepoch. More tenuous fossil records seem to indicate that the

Moon was present still earlier, as far back as 3.8 billion yearsago. If the Moon was indeed captured, its capture appar-ently occurred during an early phase of the solar system’sdevelopment.

The Moonless Earth

As we saw earlier, if the Moon were not present, the Earth’srotational speed would be somewhat higher, since it wouldnot have been slowed through the dissipative effects of lu-nar tides. By extrapolating the values found previously byWilliams, the Earth’s primordial rotational speed may be es-timated at about 1.6 times its present value, correspondingto a day of about 15 hours in length. At the Bureau of Lon-gitudes, Frédéric Joutel, Philippe Robutel and I began withthis hypothesis and studied possible variations in the Earth’sobliquity. To do this, we used a new method for analyzingthe stability of motion: the method of frequency analysis.

Ordinarily, for each value of the Earth’s initial obliquity,we obtain a speed of precession of its axis of rotation. If themotion is stable, this precession speed changes continuouslywith the initial obliquity. On the other hand, if the motionis chaotic, or unstable, the speed of precession is no longeruniquely defined, and depends strongly on minor differencesin the initial conditions. A graph of the speed of precessionas a function of the initial obliquity therefore indicates thestability of subsequent obliquities (see Figure 5). This analy-sis shows a vast chaotic zone extending from 0 up to about 85degrees initial obliquity. Whatever the Earth’s initial obliq-uity in this range, in the absence of the Moon, the Earth’ssubsequent obliquity would be subject to strong oscillations,nearly ranging over the whole chaotic zone in the space of afew million years.

In Figure 5, we present the minimum, mean, and max-imum values attained by the Earth’s obliquity over an 18million year period, for various initial obliquity values. Onsuch a short time interval, the obliquity does not range overthe entire chaotic zone in the examples considered, but ouranalysis shows that the full extent of the chaotic zone maybe attained over longer time periods. In the absence of theMoon, the Earth would undergo variations in its obliquityof sufficient magnitude so as to drastically alter its surfaceclimate. It should be pointed out that with an obliquity of85 degrees, the Earth’s axis of rotation would very nearly liein its orbital plane, as is the case with Uranus. The wholeplanet would then be subject, as the polar zones are now, todays and nights of several months duration. At the poles,the Sun would remain high in the sky for long periods, and,although no climate simulations have yet been carried outfor the Earth in this tilted configuration, it is likely that sucha drastic redistribution of insolation would cause significantchanges in the Earth’s atmosphere.

Of course, in choosing a primordial rotational speed of 15hours for the Earth, we made what seemed to be the most rea-sonable choice, but other scenarios of lunar formation couldlead to different primordial rotational speeds. Since all ofthese are highly speculative, we also chose to study the sta-bility of the Earth’s obliquity in the absence of the Moon

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rence de composition chimique entre laTerre et la Lune.

Dans I 'hypothbse de la capture, laLune, form6e dans une r6gion voisine deI'espace, est captur€e par le champ gra-vitationnel de la Terre. Deux modes decapture sont actuellement proposes.Une capture ..douce> et une capture, oi un corps massif vient per-cuter la Terre. les d6bris r6sultant decette coll ision s'accr6tant ensuite pourformer la Lune. Le probldme posd parces hypothdses, la dernibre 6tant le plussouvent retenue actuellement. r6sidedans la faible probabil it6 qu'un tel 6v6-nement puisse se produire. Cela n'estgudre satisfaisant car le principe de

"m6diocrit6> voudrait que les 6v6ne-ments observ6s soient des 6v6nementsg6n6r iques, et non des 6v6nementsexceptionnels.

Si I'origine de la Lune reste 6nigma-t ique, et est I 'objet de spdculat ions

vari6es, i l est en revanche possible deretracer son histoire jusqu'd une 6poquetrbs recul6e.

Histoire dc la LuneLa Lune exerce sur la Terre une force

d'attraction que nous observons quoti-diennement ir travers le ph6nomdne desmar6es. Comme la Terre tourne plusrapidement sur elle-m6me (en un jour)que la Lune autour de la Terre (en28 jours), les mar6es se d6placent d lasurface de la Terre, et ce d6placements'accompagne d'une dissipation d'6ner-gie.

Il en r6sulte un ralentissement de lavitesse de rotation de la Terre (donc unallongement de la dur6e du jour de0,002 seconde par s idcle), et l '6 lo igne-ment de la Lune d'environ 3.5 centimd-tres par an. I ly a plusieurs mill ions d'an-n6es, la Terre tournait donc plus

rapidement sur elle-mOme, et la Lune6tait plus prds.

Ce ralentissement n'est pas constant,et l 'on peut en retrouver une trace dansdiffdrents indicateurs qui varient sui-vant les cycles des mar6es oc6aniques,telle la croissance des coraux et de certainscoquil lages fossiles. Toutefois, c'est enanalysant des d6p6ts s6dimentaires quele g6ologue australien G. Will iams estremontd le plus loin dans le temps pourretrouver que la dur6e du jour, i ly a2,5mill iards d'ann6es. 6tait d'environ 20heures, alors que la Lune se trouvait ir348 000 kilomdtres de la Terre (384 000kilomdtres actuellement ).

Pour retrouver ces valeurs, i l a analy-s6 les ddpdts successivement apport6sdans un estuaire au rythme des marees.Le cycle annuelde ces mardes permet deretrouver l 'dchelle de temps. en suppo-sant, ce qui semble raisonnable, que ladur6e de I 'ann6e n'a pas sensiblementvari6 depuis ce temps. La Lune existaitdonc ddje d cette 6poque. D'autrestraces fossiles plus t6nues permettent depenser que la Lune 6tait pr6sente )r des6poques encore plus recul6es, de I 'ordrede 3.8 mill iards d'ann6es. Si la Lune a 6t6capturde, elle I 'a donc 6t6 dans unephase trds pr6coce du Systdme Solaire.

La Terre sans LuneSi la Lune n'avait pas 6t6 pr6sente, la

vitesse de rotation de la Terre serait,nous I 'avons vu. plus 6lev6e, car ellen'aurait pas 6t6 ralentie par I 'effet demar6e d0 d la Lune. En extrapolant lesvaleurs trouv6es par G. Will iams, onpeut estimer une vitesse de rotation pri-mordiale de la Terre de I 'ordre de1.6 fois sa vitesse actuelle. soit une du-rde du jour de 15 heures. Avec Fr6d6ricJoutel et Phil ippe Robutel, nous avons6tudi6, au Bureau des Longitudes, lesvariations possibles de I 'obliquit6 de laTerre sous cette hypothdse. Pour cefaire. nous avons uti l isd une nouvellem6thode d'analyse de la stabil it6 d'unmouvement : l 'analyse en frdquence.Pour chaque valeur de l 'obliquit6 ini-t iale de la Terre. on obtient une vitessede pr6cession de son axe de rotation. Sile mouvement est stable. cette vitesse deprdcession varie contin0ment quand onchange I'obliquit6 init iale.

En revanche. si le mouvement estchaotique ou instable, la vitesse de pr6-cession n'est plus d6finie de manidreunique, et d6pend fortement deminuscules diff6rences dans les condi-tions init iales. Le graphe de la vitesse depr6cession en fonction de l 'obliquit6 ini-t iale permet alors de statuer sur la stabi-lit6 de l'obliquitd de la Terre (voir lafigtre 5). Cette analyse montre I 'exis-tence d'une vaste zone chaotique qui va

5. CHAQUE POINT de ces figures correspond i une simulation du mouvement de la Terresur 18 millions d'annt{es, avec la Lune (a-b) et sans Lune (c-d). Les valeurs minimales,

moyennes et maximales atteintes par I'obliquit6 sont port6es en (b) et (d) en fonction deI'obliquit6 initiale. Si le mouvement est stable, la fr6quence de pr6cession (p) varie contin0-ment en fonction de I'obliquit6 initiale (eo). Dans cette zone r6gulibre (incluant les conditionsactuelles de la Terre), les variations d'obliquit6 de la Terre sont trbs faibles comme dans les

zones bleues des figures (a) et(c). En revanche, dans la zone rouge de la figure (a),la fr6quencede pr6cession n'est pas d6finie : I'obliquit6 est chaotique, et peut varier de 60 h 90 degr6s enquelques millions d'ann6es. Sans la Lune, et pour une p6riode de rotation de la Terre de 15heures, la zone chaotique (en rouge) s'6tend de 0 h prbs de 90 degr6s (c). Sur 18 millions

d'ann6es, I'obliquit6 ne parcourt pas int6gralement cette zone (d), mais aucune barribre neI'emp6che de le faire sur une dur6e plus longue.

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?1r)0

position.Mars is far from the Sun, and its satellites Phobos and

Deimos have masses far too small to slow its rotation, so thatits present rotational period of 24 hours 37 minutes is close toits primordial rotational period. Mars’ equator is inclined 25degrees with respect to its orbital plane, and its speed of pre-cession, 7.26 seconds per year, is close to certain frequenciesof motion of its orbit. Moreover, variations in the inclinationof Mars’ orbit are considerably stronger than those of theEarth. It follows that variations in its obliquity over a periodof one million years are also much stronger than the Earth’s,and G. Ward has found obliquity variations on the order of±10 degrees about a mean value of 25 degrees. These vari-ations bring about strong climatic changes on Mars’ surface,and certain surface structures seem to bear witness to thesechanges.

Our recent computations provide also evidence that themotion of Mars’ rotational axis is chaotic. This has two con-sequences. First, as is also the case for the orbital motion ofthe inner planets, it is not possible to predict the orientationof Mars’ axis for periods longer than a few million years.

But more important, the obliquity of Mars is subject tomuch larger variations than those predicted by Ward, rang-ing between about 0 and 60 degrees in less than 50 millionyears. Models of the past climates of Mars should be re-viewed in light of these new results. The existence of thislarge chaotic zone in the orientation motion of Mars also re-moves a constraint from models of solar system formation,since Mars’ obliquity cannot be considered primordial.

The Formation of the Solar System

Since the work of Safronov in 1960, models of solar systemformation admit the existence of a very massive initial so-lar nebula. Because of gravitational instabilities, part of thisnebula condensed to form the Sun. The rest of the nebulacondensed into small bodies, or planetoids. The planets werethen formed out of the larger planetoids by way of collisionalaccretion of smaller planetoids. A large part of the remain-ing planetoid mass was then ejected from the solar system.Safronov showed that if accretion took place in the presence ofmany small planetesimals, the planets would all rotate in thesame direction with very nearly zero obliquity. To accountfor the considerable variation in the observed obliquities ofthe planets, Safronov was required to introduce a so-called“stochastic component” in the accretion mechanism; this en-tails a final phase in which planets suffer a number of ran-dom collisions with planetoids large enough to account forthe observed obliquities. Our recent results show that all theobliquities of the inner planets may be accounted for by theaction of secular perturbations of the planets, complemented,in the case of Mercury and Venus, by the dissipative effectsdescribed earlier.

We also show that the obliquities of the outer planets areessentially stable, as are their orbital motions. We are unableto account in this way for the large obliquity of Uranus (98degrees). It is however possible to envisage for Uranus ascenario similar to that proposed for Venus, in an early stage

of the solar system formation, in the context of Safronov’shypothesis of a massive primordial solar system.

Possibility of Extraterrestrial Life

On October 12, 1992, NASA inaugurated a vast programcalled SETI (Search for Extra Terrestrial Intelligence) tosearch for signals arriving from possible advanced civiliza-tions. Over the next ten years this program will use radiotelescopes to search over a large portion of the radio frequencyspectrum for signals of extraterrestrial origin. Because thesky is so vast, some 800 stars of solar type at distances lessthan 80 light years from Earth have been singled out forspecial attention. These will each be watched for about 20hours, the seemingly minimum time during which somethingis likely to be detected, at least from a strong source of thetype that might be anticipated to come from one of thesepossible extra-solar systems.

A fundamental principle underlies any such project: oursituation on Earth is not extraordinary, and should thereforebe repeated many times in our galaxy, in any number of var-ied forms. Yet, for a given star in our galaxy, we are unableto quantify the likelihood of the appearance of organized lifesimilar to that on our planet.

Even without reference to the appearance of life itself, norto the conditions that could lead to the development of a civ-ilization that might wish to communicate using radio waves,we presently have no idea of the probability of a Sun-like starpossessing a planetary entourage. In spite of frequent an-nouncements of the discovery of extra-solar planets, no suchobject has yet been observed directly, and only the obser-vations of (likely) proto-planetary disks of the Beta-Pictoristype are convincing.

However, almost all estimates of the probability of extrater-restrial life seem to agree on one point: in any planetary sys-tem, the planet located neither too close nor too far from itssun may allow the development of organized life as we know iton Earth. In fact, simulations carried out by Michael Hart in1978 showed that outside a thin “zone of habitability,” run-away greenhouse effect of the atmosphere could lead to situ-ations of the type observed on Venus if the Earth were only 5percent closer to the sun, while if the Earth were somewhatfurther from the sun, it would experience runaway glaciation.

Our calculations show that this is not the case, that theevolution of life on Earth is probably intimately linked withan event that seems unlikely in current models of the forma-tion of planetary systems: a planet located in the zone ofhabitability is able to sufficiently stabilize its long-term inso-lation variations through the presence of a massive Moon-likesatellite. Of course, it should be possible to find other partic-ular circumstances leading to long-term climatic stability fora planet, but it should be stressed that these situations areprobably uncommon. The probability of the existence, in aplanetary system, of planets with stable climates comparableto our own must no doubt be reexamined and reduced byseveral orders of magnitude, as is the case for the probabilityof success of NASA’s SETI project.

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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 pointedout that if our existence is intimately tied to that of theMoon, it is possible to accept a scenario for the formationof the Moon of such small probability of occurrence that wewould ordinarily reject it in confining ourselves to generic sit-uations. Theories of the formation of the Moon would thenneed to be reconsidered in this light.

In addition, the orbital motion of the planets and of theEarth itself is chaotic. This does not seem to induce majorchanges in its orbital parameters over a few hundred mil-lion years, but in other planetary systems, this may not bethe case, and orbital instabilities alone may induce strong cli-matic changes, or even the ejection from the planetary systemof the one planet initially residing in the zone of habitabil-ity. Only a deeper understanding of the global dynamics ofplanetary systems will allow us to respond, at least partly, tosuch questions.

We are also far from understanding the mechanisms of for-mation of planetary systems. One of the great difficultiesconfronting us is that we possess only one example of a plan-etary system, namely our own. The discovery of anotherwould be a boon to understanding the history of our solarsystem, even if no form of life existed in the other system.

Finally, the climatic changes on the surface of a planetarising from significant changes in its orbit or orientation arestill not well understood, and it can only be hoped that anincreased understanding of atmospheric dynamics will allowthese changes to be successfully simulated by computers.

These various problems, though encompassing disparatesubfields of astronomy, together make up a vast research pro-gram; but efforts toward their resolution will doubtless leadus to a better understanding of the origins of the solar systemand 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, September1989.

J. Laskar: La stabilité du système solaire, in “Chaos etDéterminisme”, 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 theEarth’s obliquity by the Moon, Nature, 361, 615–617, Febru-ary 18, 1993.

J. Laskar: A numerical experiment on the chaotic behaviorof the solar system, Nature, 338, 237–238, March 16, 1989.

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