摘要:

Conduction solutions of the problem of the moon's thermal history can be unstable to solid state convection. To examine the role of solid convection, the stability of models in which the initial distribution of radioactive heat sources is homogeneous and the initial temperature profile is due to accretional heating is analyzed in detail. Growth rates of instabilities are compared with the appropriate conduction times in order to determine the effective viscosities for which solid convection is a dominant process. It is found that instability growth may not have been rapid enough to prevent the extensive partial melting predicted by conduction theory, but convection after resolidification is likely to have occurred, and thus the moon would have cooled faster than it would if it were purely conducting. In this case convection would probably have ceased by now.

ISSN:0148-0227    

DOI:10.1029/JB078i017p03203

年代:1973

数据来源: WILEY

摘要:

The distribution of stable and radioactive argon isotopes in a lunar breccia has been measured in situ by laser probe mass spectrometry. This new technique determines the spatial distribution of40Ar/39Ar ages on<10−4gram of material. Calculated40Ar/39Ar ages of clasts within this breccia are 3.7 ± 0.1 and 2.9 ± 0.3 × 109years. Parentless radiogenic40Ar exists within the fine‐grained matrix and appears to have been trapped simultaneously with solar argon (36Ar/38Ar ≈ 5.2). This ‘atmosphere’ of ambient gas (radiogenic40Ar/trapped36Ar ≈ 14) appears to have been incorporated into the rock by an impact event ≤

ISSN:0148-0227    

DOI:10.1029/JB078i017p03216

年代:1973

数据来源: WILEY

摘要:

Ringwood and Essene (1970) proposed that the CaO and Al2O3contents of the deep interior of the moon must be less than 6% each. This constraint has been generally accepted and has led to models of the lunar interior that are dominated by ferromagnesium silicates. This constraint is invalid. High CaO and Al2O3peridotites have broader intermediate‐density (3.3–3.4 g/cm3) fields than the Ringwood‐Essene ‘lunar pyroxenite’, and the high‐density phase occurs at higher pressure. Likewise, the gabbro‐eclogite transformation pressure increases with Al2O3content. The moon can have a thick plagioclase rich outer shell and a high C

ISSN:0148-0227    

DOI:10.1029/JB078i017p03222

年代:1973

数据来源: WILEY

摘要:

The isotopic composition of lead was measured in 16 chondrites and 1 achondrite, and the lead contents were determined by isotope dilution. Lead was isolated by volatilization in vacuo and purified by anion exchange procedures. Total procedural blanks (∼10 ng) are small relative to quantities of lead analyzed (≥ 1 μg). The best least squares isochron for the chondrites is (207Pb/204Pb) = (4.718 ± 0.001) + (0.5991 ± 0.0032) (206Pb/204Pb), corresponding to a mean formation age of 4.505 ± 0.008 Gy (using the most recent half‐life values). Individual chondrites yield distinctly different model ages, with a range of ∼50 My about the mean, but this may be due in part to variations in initial lead. The least squares208Pb/204Pb‐206Pb/204Pb correlation line indicates a mean232Th/238U atomic ratio of 3.54 for the suite of chondrites. The Norton County achondrite point does not lie on the isochron for chondrites and yields an age of 4.550 ± 0.003 Gy, confirming Rb‐Sr indications that achondrites may have been formed ∼50 My earlier than the chondrites. The chondrite isochron does not pass through the presently accepted value for primordial lead, based on Canyon Diablo troilite, indicating the possible necessity for a more complicated evolutionary model, with the chondrites forming ∼50 My later than that iron meteorite. Volatilization of radiogenic lead during chondrule formation might introduce variations in the initial lead of meteorites formed at

ISSN:0148-0227    

DOI:10.1029/JB078i017p03227

年代:1973

数据来源: WILEY

摘要:

Isotopic composition of xenon in several carbonaceous chondrites can be understood in terms of a mixture of solar wind and average carbonaceous chondrite xenon.

ISSN:0148-0227    

DOI:10.1029/JB078i017p03245

年代:1973

数据来源: WILEY

摘要:

Radioactivities and He, Ne, and Ar stable isotopes were measured in eight recently fallen meteorites, and H3‐He3, Na22‐Ne22, Al26‐Ne21, and Ar39‐Ar38cosmic‐ray exposure ages were obtained. Except for Malakal and Nejo, the exposure ages from different pairs of isotopes were concordant. The H3‐He3age for Malakal, 2.4 ± 0.3 m.y., is 50% lower than its Na22‐Ne22age of 3.8 ± 0.4 m.y., and the H3‐He3age for Nejo, 6.4 ± 0.8 m.y., is 50% lower than its Na22‐Ne22age of 9.4 ± 1.3 m.y. Malakal and Nejo also have very low amounts of radiogenic He4relative to radiogenic Ar40; essentially all the radiogenic He4was lost from Malakal. The K‐Ar40gas‐retention ages ranged from (0.60 ± 0.13) × 109and (1.0 ± 0.4) × 109years for Malakal and Wethersfield to greater than 4.0 × 109years for the other meteorites. The exposure ages of all the meteorites ranged from 2.4 ± 0.3 m.y. for Malakal to 36 ± 3 m.y. for Denver. Haverö, a ureilite, had an H3‐He3exposure age of 30 ± 4 m.y. and was rich in primordial Ar36(planetary‐type gas). Three of the meteorites, Dwaleni, Kabo, and Wethersfield, had light‐dark structure; however, only Dwaleni was rich in primordial He4and Ne20(solar‐type gas). The two meteorites with large primordial gas contents had unusual Ar radioactivities in their metal, indicating unusual orbits. The aphelion distance of Haverö's orbit was at least 4.3 AU; on the othe

ISSN:0148-0227    

DOI:10.1029/JB078i017p03249

年代:1973

数据来源: WILEY

摘要:

Functional analysis algorithms as developed by Kantorovich provide a rigorous theory for the convergence of iterative methods, specifically Newton's method, to a wide class of nonlinear functional equations on Banach spaces. The numerical application of the Newton‐Kantorovich theorem, quasilinearization, has been demonstrated by Bellman. Here this theorem has also been applied symbolically in order to explore the feasibility of obtaining accurate analytic solutions by automatic formula manipulation. These solution methods are applied to satellite perturbations in polar coordinates or in orbital elements for the relativistic, oblateness, and atmospheric perturbations. The accuracy of these calculations isa prioriset by error bounds; e.g., the well‐known relativistic pericenter precession and a correction to it are found in one iteration. By virtue of the small deviations of perturbed planetary orbits from a Keplerian orbit, accurate initial approximations can be selected that yield very accurate first iterates, and the inverse Frechet derivatives of the appropriate nonlinear operators are linear and easily constructed. The application to differential equations of satellite geodesy provide a potentially efficient method of obtaining analytical expressions for the dependence of satellite orbits, e.g., on geoid and atmospheric paramet

ISSN:0148-0227    

DOI:10.1029/JB078i017p03260

年代:1973

数据来源: WILEY

摘要:

A zonal geopotential is presented to degree 21 from evaluation of mean elements for 21 satellites, including two of low (<20°) inclination. Each satellite is represented by an arc of at least one apsidal rotation. The lengths range from 50 to 660 days. Differential correction of the initial elements in all of the arcs, together with radiation pressure and atmospheric drag coefficients, is accomplished simultaneously with the correction for the zonal harmonics. The satellite orbits and their variations are generated by numerical integration of the Lagrange equations for mean elements. Disturbances due to precession and nutation, atmospheric drag, radiation pressure, and lunisolar gravity are added at 1‐ to 8‐day intervals in the integrated orbits. The results agree well with 1971 and 1972 solutions from other authors using different methods and different satellite and other data sets. These comparisons show the zonal coefficients are now known to better than 0.03 × 10−6(fully normalized) to at least as high as de

ISSN:0148-0227    

DOI:10.1029/JB078i017p03271

年代:1973

数据来源: WILEY

摘要:

Ambiguity in the gravity response of an earth model with transition layers has been assessed by calculating the channel capacity of the transmitter (transition layer). The channel capacity is used to determine the number of false gravity anomalies in a gravity contour, which acts as an index to the ambiguity range. The lower limit of this ambiguity range is fixed by using Gabor's modified formula, the beats produced between signal and noise being taken into account. The, upper limit is obtained by the Hartley‐Tuller‐Shannon formula after Sax (1966). Wider effective applications of this combined approach to various problems of interpretation have been indicated by the illustration of the controversial gravity interpretations of Mono basin in Califor

ISSN:0148-0227    

DOI:10.1029/JB078i017p03281

年代:1973

数据来源: WILEY

摘要:

Interference patterns for em fields due to a subsurface reflector below a layered lossy dielectric are calculated with the geometrical optics approximation for use in interpreting data to be collected on the moon by Apollo 17 as well as data currently being obtained on terrestrial glaciers. The radiating antenna lies on the surface. All six field components are calculated and studied. For the endfire solutions the peak of the first reflected wave is found to be different from that of the broadside ones. To facilitate a physical discussion, we plotted the radiation patterns due to the antenna on the surface. We find that, although the maximum broadside power goes into the first medium at the critical angle, the maximum endfire power enters the first medium at the angle sin−1[2n2/(1 +n2)]1/2, where 1/nis the index of refraction of the first mediu

ISSN:0148-0227    

DOI:10.1029/JB078i017p03287

年代:1973

数据来源: WILEY