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The perturbing potential due to the tidal interaction between the earth, sun, and moon is obtained without restrictive assumptions on the internal constitution of the earth. The derived potential is used in Gauss's equations for the time rate of change of the eccentricity, semimajor axis, and inclination of the moon's orbit. The tidal forces perturb the elements describing the earth's motion about the sun by a negligibly small amount. The variation in the earth's angular momentum due to the solar and lunar tides is described by Euler's equations. It is assumed that the moment of inertia of the earth corresponds to that appropriate for a rotating fluid with the density distribution of the present earth. The rate of change of the moon's orbital elements is determined by the phase lag in the elastic component of the tidal bulge raised by the sun and moon. Astronomical data give a current value of the lag of the lunar tidal bulge of 2.16°. The present phase lag corresponds to a rate of increase of the semimajor axis of 3.2 cm yr−1, a rate of decrease of the inclination of the moon's orbital plane of 9.35 × 10−12 rad yr−1, and a rate of increase in the eccentricity of 1.2 × 10−10 yr−1. The obliquity of the earth's equator to the ecliptic and the period of rotation are increasing at present, owing to the combined effects of the lunar and solar tides. The effects of the solar tides are small at present but become important in the future. Numerical integrations of the coupled Gauss‐Euler equations are used to describe both the past history and the future evolution of the earth‐moon system. If the moon traveled a circular orbit, a backward tracing of the history shows the moon approaching the earth, reaching a minimum distance of 2.72 present earth radii. During the time of closest approach, the inclination and obliquity change rapidly, with the moon's orbital plane passing over the pole and the moon's motion becoming retrograde. If the orbit is eccentric, the eccentricity increases rapidly at the time of close approach. The perigee height remains nearly constant, while the apogee increases without bounds over a time of about 1000 years. If the current phase lag remains constant, the time of closest approach is only 1.78 × 109 years ago. Thus, the current phase lag is not consistent with the hypothesis that the earth‐moon system has existed throughout geologic time. The rotational parameters of Mars, Venus, and Mercury are discussed in terms of the dynamical theory. The distribution of rotational angular momentum of the solar system is described, and it is proposed that the major planets and Mars have lost only a very small proportion of their initial rotational angular momentum. The observed dependence of rotational angular momentum on planetary mass yields an estimate of the initial rotational period of the earth of between 9 and 13 hours. The mechanisms by which the earth's rotational energy can be dissipated are reviewed. It is argued that the phase lag in the tides may have remained constant over geologic time or may...

Methane clathrates are stable at depths greater than about 200 m in permafrost regions and in ocean sediments at water depths greater than about 250 m, provided bottom waters are sufficiently cold. The thickness of the clathrate stability zone depends on surface temperature and geothermal gradient. Average stability zone thickness is about 400 m in cold regions where average surface temperatures are below freezing, 500 m in ocean sediments, and up to 1,500 m in regions of very cold surface temperature (<-15 ~ or in the deep ocean. The concentration of methane relative to water within the zone of stability determines whether or not clathrate will actually occur. The geologic setting of clathrate occurrences, the isotopic composition of the methane, and the methane to ethane plus propane ratio in both the clathrates and the associated pore fluids indicate that methane in clathrates is produced chiefly by anaerobic bacteria. Methane occurrences and the organic carbon content of sediments are the bases used to estimate the amount of carbon currently stored as clathrates. The estimate of about 11,000 Gt of carbon for ocean sediments, and about 400 Gt for sediments under permafrost regions is in rough accord with an independent estimate by Kvenvolden of 10,000 Gt.The shallowness of the clathrate zone of stability makes clatbxates vulnerable to surface disturbances. Warming by ocean flooding of exposed continental shelf, and changes in pressure at depth, caused, for example, by sea-level drop, destabilize clathrates under the ocean, while ice-cap growth stabilizes clathrates under the ice cap. The time scale for thermal destabilization is set by the thermal properties of sediments and is on the order of thousands of years. The time required to fix methane in clathrates as a result of surface cooling is much longer, requiring several tens of thousands of years. The sensitivity of clathrates to surface change, the time scales involved, and the large quantities of carbon stored as clathrate indicate that clathrates may have played a significant role in modifying the composition of the atmosphere during the ice ages. The release of methane and its subsequent oxidation to carbon dioxide may be responsible for the observed swings in atmospheric methane and carbon dioxide concentrations during glacial times. Because methane and carbon dioxide are strong infrared absorbers, the release and trapping of methane by clathrates contribute strong feedback mechanisms to the radiative forcing of climate that results from earth's orbital variations.

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Data from a wide variety of igneous rock types show that the ratio of potassium to uranium is approximately 1 X 10(4). This suggests that the value of K/U approximately 1 X 10(4) is characteristic of terrestrial materials and is distinct from the value of 8 X 10(4) found in chondrites. In a model earth with K/U approximately 10(4), uranium and thorium are the dominant sources of radioactive heat at the present time. This will permit the average terrestrial concentrations of uranium and thorium to be 2 to 4.7 times higher than that observed in chondrites. The resulting models of the terrestrial heat production will be considerably different from those for chondritic heat production because of the longer half-life of U(238) and Th(238) compared with K(40).