증산도에서 말하는 우주 계절 변화에 따른 지축정립은 아직 과학에서 받아들이지 않고 있습니다. 그러나 최근 몇몇 과학자들은 지금까지 생각했던 것과는 달리 지축 기울기가 크게 변할 수 있는지 조금씩 밝히고 있습니다. KORDIC에 실린 한글 자료와 Nature 지에 이번에 실린 논문을 소개합니다. 제 목 : 자전축이 고대 지구 기후에 미친 영향 1998/12/04 정보출처 : http://www.academicpress.com/inscight/12021998/graphb.htm
여름의 더위와 겨울의 추위는 지구의 자전축이 기울어진데서 비롯한다. 이것은 특정 지역에서 한 해를 통해 얼마나 많은 양의 태양빛이 지구에 도달하느냐를 결정한다. 몇몇 과학자들은 과거엔 이러한 기울어짐이 훨씬 심했었고 이것으로 적도 지방이 추웠던 시기를 설명할 수 있다고 생각하고 있다. 현재 연구자들은 지구가 어떻게 스스로 똑바로 설 수 있었는지에 대해 설명을 할 수 있다. Nature지 다음 호에 발표될 그들의 각본에 의하면 이것은 지구의 모양을 바꾸어 놓는 거대한 얼음층들의 증가와 감소에 달려 있다. 오늘날 지구의 자전축은 지구의 공전 궤도면에 23.5도 만큼 기울어져 있다. 이러한 자전축의 경사는 여름에는 극지방에 적도지방보다 더 적은 양의 햇빛이 도달하게 하고 겨울에는 전혀 도달하지 못하게 만든다. 그러나 지질학자들은 뒤섞인 암석들 속에 빙하가 열대 지방을 덮었던 흔적이 남아있는 6억 년 전을 생각해 보았다. 이것은 전체 행성이 빙하로 뒤덮였다는 것을 의미하는 것일까? 많은 연구자들은 이러한 "눈덩이의 지구"에 반대한다. 왜냐하면 그러한 조건하에서 생명체가 어떻게 살아남을 수 있었을까 하는 의문 때문이다. 대신에 그들은 지구의 자전축이 54도 이상으로 기울어졌었을 것이라고 주장한다. 그것은 많이 누워서 도는 팽이와도 비슷하다. 그러면 적도 지방은 모든 것이 얼어붙은 반면 극지방이 온난한 시기에 들어갔을 것이다. 그러나 문제는 어떻게 지구가 오늘날의 경사각도를 갖게 되었느냐 하는 것이다. 달, 태양, 그리고 다른 행성들에 의해서 생겨나는 조수의 힘은 지구의 모양에 의존하기 때문에 지구 물리학자들은 지구의 모양을 좀 더 둥글게 만들거나 덜 둥글게 만들 수 있는 빙하의 양에 대한 효과를 모형화했다. 만일 큰 얼음 덩어리가 적도로부터 극지방으로 흘러가면 지구는 그 모양이 서서히 변화된다. 연구자들은 이러한 변화가 지구 자전에 영향을 줘서 1억 년 이내에 수십 도정도의 기울어짐을 바로 잡을 수 있다는 것을 발견했다. "기후와 빙하와 경사 각도 사이의 상호 작용은 매우 복잡합니다. 우리는 특정한 환경 조건 안에서 그것이 효력을 갖게 만들 수 있다는 것을 보여주었습니다."라고 논문의 공저자 James Kasting은 말했다. 그는 University Park에 있는 펜실베니아 주립 대학교에서 일하고 있다. 메릴랜드 그린벨에 있는 나사의 고다드 우주비행센터 지구물리학자 Bruce Bills는 이 이론이 매우 그럴 듯하다고 말한다. "그러나 모든 사람이 경사각이 그렇게 컸다는 것을 확신하지는 않습니다. 그래서 이것은 존재하지 않았던 현상에 대한 하나의 설명이 될 수도 있습니다."라고 그는 덧붙였다. Bills와 Kasting은 둘 다 고대 지구에 있었던 빙하의 시기와 지리적인 패턴을 측정하기 위해 빙하 퇴적물에 대한 더 많은 연구를 계획하고 있다.
원문출판날짜 1998년 12월 02일 국가코드 미국 주제분야 지구물리 Copyright(c) 1998, KORDIC All right reserved Email comments to Webmaster === An oblique view of climate BRUCE G. BILLS Nature 396, 405 - 406 (1998) ⓒ Macmillan Publishers Ltd. 3 December 1998 One explanation for certain patterns of glaciation in the past invokes a large and comparatively swift decline in the tilt, or obliquity, of the Earth. A provocative hypothesis provides a mechanism by which such a decline could have occurred. How do variations in Earth's orbital and rotational geometry influence climate? Does the climate system, in turn, influence rotation? We all experience the radiative and thermal cycles of night and day, winter and summer. So we are familiar enough with the influence of Earth's rotational and orbital motions on the spatio-temporal pattern of light and temperature to make it easy to imagine how long-term variations in the orbit and rotation would affect climate. Much recent data and modelling help confirm that principle1,2. Somewhat further removed from human experience is the notion that climatic change itself could influence the rotational dynamics of the Earth. That, however, is the hypothesis advanced by Williams et al. on page 453 of this issue3. The basic idea is quite simple, and involves feedback between Earth's obliquity (the angular separation between the spin pole and orbit pole around the Sun, Fig. 1) and its oblateness (departure from spherical symmetry). Figure 1 Earth's obliquity. Full legend {{ }} Figure 1 Earth's obliquity. Williams and colleagues' work3 stems from the need to account for a 20-30° decline in obliquity, required by a hypothesis that explains the occurrence of low-latitude glacial deposits 750-550 Myr ago through an obliquity of more than 54° (a), when the equatorial regions would have been colder than the poles. b, Since about 430 Myr, obliquity is thought to have been around 23.5°. The authors propose that ice-sheet formation and configuration (not shown) was the driving force. First, however, it is useful to recall how orbital and rotational geometry influences climate. The main seasonal cycle is primarily determined by the orientation of the spin axis, and only secondarily by the eccentricity of the orbit. Currently, perihelion (Earth's closest approach to the Sun) occurs several weeks after winter solstice in the Northern Hemisphere (shortest daylight). However, neither the orbit nor the spin axis is fixed in space. Gravitational interaction with other planets (principally Venus) causes the shape and orientation of the orbit to change on a variety of timescales4, with the dominant period near 70,000 years (70 kyr) and subsidiary oscillations at periods ranging from 50 kyr to 1.9 million years (Myr). Gravitational torques exerted by the Moon and Sun on the oblate figure of the Earth cause the spin axis to precess with a period of 25.8 kyr. If the orbit plane were fixed, the path of the spin pole would be a circle centred on the orbit pole, keeping the obliquity fixed. However, because the orbit is also precessing, the obliquity oscillates by 1° about its present value of 23.5°, with a period of 41 kyr. These obliquity oscillations modulate the seasonal and latitudinal pattern of incident radiation, and thus affect climatic variations. How then does climate change influence rotation? One way is to change the spin precession rate by changing the oblateness of the Earth's mass distribution. During major glacial cycles, mass transport between the oceans and ice sheets is sufficient to change the precession rate by about 1%. The net change includes accumulation of continental ice and partially compensating subsidence of the Earth's surface. If the obliquity and oblateness oscillations are exactly in phase, there is no long-term net effect. But if the oblateness lags behind the obliquity, there will be a secular change in obliquity, with a rate that depends on the amplitude and phase of the oblateness variations5-7. The long-term stability of Earth's climate system is an important question, but one that remains elusive. Despite progress in short-term weather prediction (based on improved quality and quantity of observations, faster computers and better understanding of the system dynamics), our understanding of long-term climate dynamics is still quite primitive. Part of the problem, of course, is that the further back into the past we go, the more difficult it is to reconstruct which path the climate system has followed. When we still don't know what has happened, how can we reconstruct why? In this situation, the role of theoretical models such as that of Williams et al.3 is not so much to explain what actually happened as to broaden our perspectives on the types of behaviours that might have occurred. The principal novelty of the new work by Williams et al. concerns the rate and direction of the obliquity change they seek to explain (Fig. 1). They are invoking an obliquity-oblateness feedback to decrease Earth's obliquity, rather than increase it, and the obliquity change they seek is 20-30° in less than 100 Myr. They propose that such a change could have been caused by the very large ice sheets that might have built up during periods when the continents were clustered near to the poles.The motivation for that particular scheme comes from a suggestion that Earth's obliquity has been large throughout much of its history8 (in excess of 54°, the value at which the annual average incident radiation at the Equator equals that at the poles; at greater obliquities, the equatorial regions become colder than the poles). That suggestion was made in an attempt to explain evidence for low-latitude glacial deposits from the Neoproterozoic (750-550 Myr ago), while avoiding a 'snowball Earth', in which the entire surface of the Earth would be covered by ice9-12. As always, more work is needed. In this case, distinguishing between the two competing climatic possibilities (equatorial versus global glaciation) should be easily resolvable by searching for contemporaneous high-latitude and low-latitude glacial deposits13. Reconstructing an unambiguous obliquity history will be more of a challenge. Bruce G. Bills, currently at the Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, is in the Geodynamics Branch, NASA Goddard Space Flight Center, Mailstop 921.0, Greenbelt, Maryland 20771, USA. e-mail: bills@denali.gsfc.nasa.gov References Hilgen, F. J. Earth Planet. Sci. Lett. 107, 349-368 (1991). Links Imbrie, J. et al. Paleoceanography 7, 701-738 (1992). Links Williams, D. M., Kasting, J. F. & Frakes, L. A. Nature 396, 453-455(1998). Links Laskar, J. Astron. Astrophys. 198, 341-362 (1986). Links Rubincam, D. P. J. Geophys. Res. 98, 10827-10832 (1993). Links Bills, B. G. Geophys. Res. Lett. 21, 177-180 (1994). Links Ito, T., Masuda, K., Hamano, Y. & Matsui, T. J. Geophys. Res. 100, 15147-15161 (1995). Links Williams, G. E. Earth Sci. Rev. 34, 1-45 (1993). Links Harland, W. B. Geol. Rundsh. 54, 45-55 (1964). Links Caldeira, K. & Kasting, J. F. Nature 359, 226-228 (1992). Links Evans, D. A., Beukes, N. J. & Kirschvink, J. L. Nature 386, 262-266 (1997). Links Hoffman, P. F., Kaufman, A. J., Halverson, G. P. & Schrag, D. P. Science 281, 1342-1346 (1998). Links Kennedy, M. J. et al. Geology 26, 1059-1063 (1998). Links Nature ⓒ Macmillan Publishers Ltd 1998 Registered No. 785998 England. 98-12-7 오후 11:00 정석근 internet: jung@cbl.umces.edu http://cbl.umces.edu/~jung 계속하시겠습니까? (Y/n) >> Y 정석근 (fishery ) [과학] 지축정립관련 아래 관련 논문 1998-12-08 13:07 468 line 아래 Nature 지 News & View에서 인용했던 지축 기울기 변화에 관한 논문 두 개입니다. ===================================== HISTORY OF THE EARTHS OBLIQUITY WILLIAMS, GE EARTH-SCIENCE REVIEWS 34: (1) 1-45 MAR 1993 Document type: Review Language: English Abstract: The evolution of the obliquity of the ecliptic (epsilon), the Earth's axial tilt of 23.5-degrees, may have greatly influenced the Earth's dynamical, climatic and biotic development. For epsilon > 54-degrees, climatic zonation and zonal surface winds would be reversed, low to equatorial latitudes would be glaciated in preference to high latitudes, and the global seasonal cycle would be greatly amplified. Phanerozoic palaeoclimates were essentially uniformitarian in regard to obliquity, with normal climatic zonation and zonal surface winds, circum-polar glaciation and little seasonal change in low latitudes. Milankovitch-band periodicity in early Palaeozoic evaporites implies epsilonBAR almost-equal-to 26.4 +/- 2.1-degrees at approximately 430 Ma, suggesting that the obliquity during most of Phanerozoic time was comparable to the present value. By contrast, the paradoxical Late Proterozoic (approximately 800-600 Ma) glacial environment-frigid, strongly seasonal climates, with permafrost and grounded ice-sheets near sea level preferentially in low to equatorial palaeolatitudes-implies glaciation with epsilon > 54-degrees (assuming a geocentric axial dipolar magnetic field). Palaeotidal data accord with a large obliquity in Late Proterozoic time. Indeed, Proterozoic palaeoclimates in general appear non-uniformitarian with respect to climatic zonation, consistent with epsilon > 54-degrees. The primordial Earth's obliquity is unconstrained by the widely-accepted single-giant-impact hypothesis for the origin of the Moon; an impact-induced obliquity greater than or similar to 70-degrees is possible, depending on the impact parameters. Subsequent evolution of epsilon depends on the relative magnitudes of the rate of obliquity-increase epsilon(t) caused by tidal friction, and the rate of decrease epsilon(p) due to dissipative core-mantle torques during precession (epsilon < 90-degrees is required for precessional torques to move epsilon toward 0-degrees). Proterozoic palaeotidal data indicate epsilon(t) = 0.0003-0.0006''/cy (seconds of arc per century) during most of Earth history, only half the rate estimated using the modern, large value for tidal dissipation. The value of epsilon(p) resulting from the combined effects of viscous, electromagnetic and topographic core-mantle torques cannot be accurately determined because of uncertainties in estimating, at present and for the geological past, the effective viscosity of the outer core, the nature of magnetic fields at the core-mantle boundary (CMB) and within the lower mantle, and the topography of the CMB. However, several estimates of epsilon(p) approximate, or exceed by several orders of magnitude, the indicated value of epsilon(t). If epsilon(p) did indeed exceed epsilon(t) in the past, then the obliquity would have decreased during Earth history. It is postulated here that the primordial Earth acquired an obliquity of approximately 70-degrees (54-degrees < epsilon < 90-degrees) from the Moon-producing single giant impact at approximately 4500 Ma (approach velocity almost-equal-to 5-20 km/s, impactor/Earth mass-ratio almost-equal-to 0.08-0.14). Secular decrease in epsilonBAR subsequently occurred under the dominant influence of dissipative core-mantle torques. From 4500-650 Ma, epsilonBAR slowly decreased to approximately 60-degrees ([epsilon] = -0.0009''/cy). EpsilonBAR then decreased relatively rapidly from approximately 60-degrees to approximately 26-degrees between 650 and 430 Ma ([epsilon] = -0.0556''/cy); climatic zonation changed from reverse to normal when epsilonBAR = 54-degrees at approximately 610 Ma, and [epsilon] and the rate of amelioration of global seasonality were maxima for epsilonBAR = 45-degrees at approximately 550 Ma (the precessional rate OMEGA is maximum when epsilon = 45-degrees, and epsilon(p) varies as OMEGA2). Since 430 Ma, [epsilon] has been less than or similar to -0.0025''/cy and epsilonBAR has remained near its Quaternary range. The postulated relatively rapid decrease in epsilonBAR between 650 and 430 Ma may partly reflect special conditions at the CMB which caused significant increase in dissipative core-mantle torques at that time. This inflection in the curve of epsilonBAR versus time centred at epsilonBAR = 45-degrees also may be partly explained by the function epsilon(p) is-proportional-to (OMEGA2/omega)(sin 2epsilon), where omega is the Earth's rate of rotation, and other dynamical effects on epsilon(p). The Proterozoic-Phanerozoic transition may record profound change in global state caused by reduction in epsilonBAR through the critical values of 54-degrees and 45-degrees. The postulated flip-over of climatic zonation at approximately 610 Ma (epsilonBAR = 54-degrees) coincides with the widespread appearance of the Ediacaran metazoans at approximately 620-590 Ma, and the interval of most rapid reduction of obliquity and seasonality at approximately 550 Ma (epsilonBAR = 45-degrees) with the ''Cambrian explosion'' of biota at 550 +/- 20 Ma. These two most spectacular radiations in the history of life thus may mark the passage from an inhospitable global state of reverse climatic zonation and extreme seasonality (the Earth's Precambrian ''Uranian'' obliquity state) to a relatively benign state of normal climatic zonation and moderate seasonality. Further geological, palaeomagnetic and geochronological studies of Precambrian glaciogenic and aeolian deposits can test the predictions of a large obliquity (epsilon > 54-degrees) and reverse climatic zonation and zonal surface winds during the pre-Ediacaran Precambrian. Copyright ⓒ 1996, Institute for Scientific Information ==== Low-latitude glaciation and rapid changes in the Earth's obliquity explained by obliquity-oblateness feedback Nature 396, 453 - 455 (1998) 3 December 1998 DARREN M. WILLIAMS*, JAMES F. KASTING† & LAWRENCE A. FRAKES‡ * School of Science, Penn State Erie, The Behrend College, Station Road, Erie, Pennsylvania 16563-0203, USA † Department of Geosciences, The Pennsylvania State University, 443 Deike Building, University Park, Pennsylvania 16802, USA ‡ Department of Geology and Geophysics, University of Adelaide, Adelaide, South Australia 5005, Australia Palaeomagnetic data suggest that the Earth was glaciated at low latitudes during the Palaeoproterozoic 1,2 (about 2.4-2.2 Gyr ago) and Neoproterozoic 3,4,5,6,7,8 (about 820-550 Myr ago) eras, although some of the Neoproterozoic data are disputed9,10. If the Earth's magnetic field was aligned more or less with its spin axis, as it is today, then either the polar ice caps must have extended well down into the tropics--the 'snowball Earth' hypothesis8--or the present zonation of climate with respect to latitude must have been reversed. Williams11 has suggested that the Earth's obliquity may have been greater than 54° during most of its history, which would have made the Equator the coldest part of the planet12. But this would require a mechanism to bring the obliquity down to its present value of 23.5°. Here we propose that obliquity-oblateness feedback 13 could have reduced the Earth's obliquity by tens of degrees in less than 100 Myr if the continents were situated so as to promote the formation of large polar ice sheets. A high obliquity for the early Earth may also provide a natural explanation for the present inclination of the lunar orbit with respect to the ecliptic (5°), which is otherwise difficult to explain. --- The most straightforward explanation for low-latitude glaciation is simply that the climate was very cold in Precambrian times as a consequence of reduced solar luminosity 14, uncompensated by high levels of greenhouse gases. It is difficult to explain, however, how the ice caps could have extended to low latitudes without causing the extinction of most or all surface life. Energy-balance climate models 14,15 suggest that runaway glaciation should occur if the ice line extends equatorwards of 25-30° latitude. At least some of the ancient glaciations appear to have occurred at latitudes much lower than this 8. Had the ice line moved down below the critical latitude for stability, the Earth should have switched into a globally glaciated state in which even the oceans would have frozen down to a depth of 1 km, provided that the thickness was limited by the efficiency of heat flow through the ice. If this had occurred during the Neoproterozoic era, the Earth could eventually have escaped from this state by atmospheric build-up of volcanically released CO2, which would have warmed the surface and melted the ice15. However, this process would have required 106-107 years, during which time the ocean and all marine organisms would have been deprived of sunlight. This is in apparent conflict with evidence for the continuous presence of photosynthetic marine organisms in the geological record, although some authors8 believe that this is exactly what happened. The high-obliquity hypothesis11 of Williams can resolve this climate paradox because high latitudes could have remained ice-free while the tropics were glaciated. A potentially damaging counter-argument has been presented by Vanyo and Awramik16, based on the sinsusoidal growth pattern of an 850-Myr-old stromatolite which suggests a planetary obliquity of 26.5° at that time. This argument presumes that the stromatolite growth face remained perpendicular to the Sun's noontime rays throughout the course of the year. Heliotropism has indeed been seen in modern columnar stromatolites in Australia and Yellowstone17, but in no case has it been shown that the growth pattern accurately tracks the minimum daily solar zenith angle over the year. Hence the main argument for a low obliquity during the late Proterozoic seems inconclusive. For the high-obliquity hypothesis to be viable, one needs to identify a mechanism that could have caused the Earth's obliquity to decrease by several tens of degrees between 600 Myr ago--the age of the youngest low-latitude glacial deposits3,4,5--and 430 Myr ago, when palaeotidal data suggest that the obliquity was close to its present value11. Williams himself suggested that core-mantle dissipation could have caused the obliquity to decrease. However, this is unlikely if the viscosity of the outer core is low, as many have suggested (compare refs 11, 18). Furthermore, even if it could be shown to work, this mechanism should have operated throughout the Earth's history, making it difficult to explain how the obliquity could have remained high as late as 600 Myr ago. An obliquity-reducing mechanism that might have operated preferentially during the late Proterozoic is obliquity-oblateness feedback13, sometimes termed 'climate friction'. A secular obliquity drift can occur as a result of the time delay between a planet's obliquity oscillation, which results from precession12, and obliquity- (insolation-) driven variations in planetary oblateness caused by changes to continental ice volume and sea level (see Fig. 1). The oblateness itself affects the rate at which the obliquity varies with time, thereby completing the obliquity-oblateness feedback loop. Figure 1 Relative rate of obliquity drift as a function of a ice-sheet-formation phase lag. Full legend High resolution image and legend (19k) Rubincam13 demonstrated that such climate friction could account for a +10° drift in the obliquity of Mars over 4.5 Gyr. Bills19 later calculated that a much larger drift (+60° in 100 Myr) was possible for the Earth, assuming a glacial-interglacial variation in oblateness of 1% based on oxygen-isotope data for the Pleistocene glaciations. This estimate was later revised downward (ref. 20) after it was realized that the original calculation had neglected compression of the solid Earth by ice sheets. Subsequent calculations21 that included this effect lowered the estimate of the net change in oblateness to 0.4%. Constrained by this result, subsequent authors20,22 have concluded that the change to the Earth's obliquity cannot have been more than 10-20° over the Earth's entire (450 Myr) glacial history. These calculations, however, assume that all ice ages were of comparable severity to those in the Pleistocene epoch, which is not necessarily true. Different continental configurations, and possibly lower global-average temperatures, could have resulted in larger J2/J2 values for earlier glaciations (see Fig. 1 legend for details of these parameters). A straightforward calculation23 reveals that if the continents were at one time clustered around one of the poles, as may have occurred during the late Proterozoic24, the change in oblateness from ice loading could have been as high as 2.6%, provided that the continents were completely covered by ice with a thickness of several kilometres. Under these assumptions, we calculate that the net oblateness variation (with solid-Earth response included) is only 0.66% on average, owing to differences in insolation cycle amplitude and, thus, maximum ice volume over time. This is still more than 1.5 times the maximum variation thought possible for the Pleistocene epoch, which could have enabled a correspondingly high rate of secular obliquity drift for the late Proterozoic. The sign and magnitude of the obliquity-oblateness feedback depend on the locations and areas of the continents and on the phase lags i and s (see Fig. 1 legend). High-latitude ice sheets cause J2 to decrease because they cancel out part of the Earth's equatorial bulge. For 25° < i < 206°, the resulting secular change in obliquity is positive (see Fig. 1). Low-latitude ice sheets, which might form at times of high obliquity, produce an obliquity drift in the same direction because both the effect on J2 and the phasing with respect to the obliquity cycle are reversed. Previous studies of climate friction13,19,20,22 have assumed that the feedback would be in this direction, based on phase lag estimates for the Pleistocene glaciations. Imbrie et al.25 favour i 80° (or 9 kyr) for the 41-kyr obliquity cycle based on cross-spectral analysis of Northern Hemisphere, high-latitude, summer (NHHLS) insolation and 18O values in marine carbonates over the past 2 Myr. However, the actual ages of marine sediments are not known with great precision before 30 kyr ago, so such inferences are not very firm. A phase lag of <90° is also suggested by analogy with the seasonal cycle, in which the coldest winter temperatures and highest snow accumulation at mid-latitudes occur 1-2 months after winter solstice. Ice volume need not respond in the same manner, though, to the much slower and weaker changes in insolation caused by orbital variations. In colder climates, ice sheets might expand until, or after, NHHLS insolation reaches its peak, causing ice volume to be at least 180° out of phase with the solar forcing. Accurate ages are available for the last deglaciation, which is thought to have been triggered by a precessionally induced increase in NHHLS insolation. As Fig. 2 illustrates, the value of i for this one event could lie anywhere above 45°, depending on how one interprets the shape of the sea-level (ice-volume) curve. The response of ice volume to NHHLS insolation is evidently not sinusoidal, and presumably depends in a complicated manner on both climate and continental positions. With this in mind, it is quite conceivable that climate friction could act to decrease a planet's obliquity, as required to make Williams's hypothesis work. Figure 2 Insolation and relative sea level for the period defining the last deglaciation. Full legend High resolution image and legend (16k) To determine what changes to the Earth's obliquity might have been possible, we integrated the equations of motion for the planets in the Solar System26 and the equations of precession for the Earth27 over 100 Myr using several different values of i. We assumed, somewhat arbitrarily, that the Earth's obliquity was 55° at 600 Myr ago--the age of the youngest low-latitude glacial deposits3,4,5. Williams suggested that the obliquity must originally have been >54° because this is the critical latitude above which the poles receive more annually averaged insolation than does the Equator. However, ice sheets are more sensitive to changes in seasonal insolation extremes than to annually averaged insolation, so the Earth's obliquity during Precambrian times need not actually have been this high. Figure 3 shows that under extreme polar ice loading, the Earth's obliquity could have been reduced to within 3° of its present value by 500 Myr ago if i = 230°. (A phase lag near 0° yields a comparable rate of drift in the same direction (Fig. 2)). This result is in good agreement with the geological data referenced earlier11. Figure 3 Obliquity 600-500 Myr ago. Full legend High resolution image and legend (10k) Support for the hypothesis that the Earth's obliquity has decreased comes from analysing the orbit of the Moon. The lunar orbit is presently inclined at 5° to the ecliptic plane. Backwards integrations by Goldreich28 and others29 have predicted that the lunar orbit was inclined by at least 10° to the Earth's equatorial plane when it formed. This result is in apparent conflict with the widely accepted giant-impact theory of lunar origin, in which the Moon accretes from an impact-generated debris disk aligned with the Earth's Equator30. Had the Moon formed in the Earth's equatorial plane, as predicted, its orbit should have aligned itself with the ecliptic plane as the Moon receded from the Earth31. The present 5° lunar inclination with respect to the ecliptic plane implies that either the Moon was never in the equatorial plane (that is, that the giant-impact model is wrong) or that it was perturbed away from the equatorial plane early in its history, perhaps as a result of spin-orbit resonances encountered by the Earth and Moon when they were much closer31,32. (The Moon's orbit might also have been inclined by a giant impact, but the extreme size of the necessary impactor23 (>1,100 km) makes such an event unlikely.) Alternatively, the lunar orbit may have tilted away from the ecliptic plane more recently in gravitational response to the secular downward drift of the Earth's obliquity around 600 Myr ago. At present, the Earth's mean obliquity is slowly increasing as a result of tidal interactions with the Moon28. The lunar inclination is decreasing at the same time, so the angular momentum of the Earth-Moon system is approximately conserved. Momentum conservation between the Earth's spin and the Moon's orbit may be approximately written sin(o/2) = -(Lm/L) sin(i/2), where L = C is the spin angular momentum of the Earth, Lm = Mm(GM)1/2a1/2m is the orbital angular momentum of the Moon, and o and i are the angular change to the Earth's obliquity and lunar inclination, respectively, C is one of Earth's principal inertia moments, defined in legend to Fig. 1, and Mm and M are the masses of the Moon and the Earth, respectively. For the late Proterozoic, the distance to the Moon, am 57 Earth radii, and the rotational velocity of the Earth, 2/(21 hours) (ref. 33). If we assume that the lunar inclination was originally zero, and that the change that occurred as a result of climate friction was i = +6° (allowing for a subsequent 1° reduction, to 5°, as a result of tidal friction), then the required change to the Earth's obliquity is o = - 25.4°. This implies that the Earth's obliquity may have been 23.5° + 25.4° 49° for much of the Precambrian period, which is only slightly less than the 54° obliquity suggested by Williams. Given the uncertainty in the actual obliquity that would be required to cause low-latitude glaciation, we believe that the information obtained from the lunar orbit provides additional support for the idea that the low-latitude glaciations in Precambrian times were a consequence of high planetary obliquity. Received 12 January;accepted 10 September 1998. References Evans, D. A., Beukes, N. 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