Low-latitude thermal structure of Jupiter in the region 0.1–5 bars

The radiative heat flux from 0.1 to 10 bars is estimated on the basis of a “two-cloud” scattering model that fits available spectral data and Pioneer photometry. Deeper than a few bars, the flux is 4.5 W m^?2, compared with the 18.8 W m^?2 used in an earlier study by Trafton and Stone. A temperature profile is computed, with the H₂ pressure-induced opacity; the temperature at 1 bar is found to be 156°K, rather than the commonly accepted 170°K. An additional optical depth of unity at the 0.67-bar level could restore the conventional value; otherwise a considerably cooler atmosphere is a serious possibility.     

The main problem of lunar theory solved by the method of Brown

Brown's method for solving the main problem of lunar theory has been adapted for the computation by machine with the help of an algebraic processor. Brown's results are first recovered and refined. The solution is then expanded to include most terms of order nine. The terms in the series for the longitude and latitude are listed with an accuracy of 0.000 01 and of 0.000 001 for the parallax.This research was supported in parts by the National Science Foundation grant MCS 78-01425.     

The quasi integrals

The usual Von Zeipel transformations of the Hamiltonian Mechanics are presented, they lead to state functions with extremely slow variations: the quasi-integrals.The Von Zeipel transformations are implicit: an explicit and direct construction of the quasi-integrals is also presented and the quasi-invariance property of these functions is demonstrated.These results are applied to the problem of the motion of artificial satellites perturbed by the zonal harmonics of the Earth potential, the quasi-integral is given, it is then so constant that the problem can be considered as integrable.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

Long term modulation of cosmic rays and inferable electromagnetic state in solar modulating region

It is demonstrated that the long term variation in cosmic ray intensity I(t) can be described by an integral equation,

$\text{I(t)=I}{}_{\mathrm{\infty }}\text{?}\text{∫}\text{0}\text{∞}\text{f(τ)S(t?τ)}\text{d}\text{τ}$

, which is derived from a generalization of Simpson's coasting solar wind model. A source function S(t?τ) is given by some appropriate solar activity index at a time t?τ(τ ? 0) and the characteristic functionf(τ)(?0 forτ ? 0) expresses the time dependence of the efficiency of the intensity depression due to solar disturbances represented by S(t ?τ) when the disturbances generated at the solar surface propagate through the modulating region with the solar wind. It is demonstrated further that the equation can be derived from the general diffusion-convection theory on some assumptions, and as a result, the source and characteristic functions can be related to diffusion coefficient and its transition in space. Assuming the sunspot number R (or two activity indices including R) as the source function, the characteristic function f(τ) [or f(τ)'s] is obtained with data of the cosmic ray intensity extended over several decades. Based on the theory, one can obtain from f(τ) the following physical quantities in space, such as the transition and life time of solar disturbances, the boundary of the modulating region, and the radial and time dependences of the diffusion coefficient, radial density gradient and modulated intensity of cosmic rays. Results deduced from the present analysis are consistent with those obtained directly or indirectly by space observations.     

Polyoxymethylene co-polymers on grains

Conditions prevalent in dense molecular clouds are shown to favour the polymerization of H₂CO molecules and the deposition of formaldehyde co-polymer mantles, with typical radii 10^–5 cm, on smaller refractory grains. If a significant fraction of such co-polymer coated grains are expelled with systematic gas flows into the general interstellar medium, these moderately refractory grains may be responsible for the bulk of interstellar extinction and polarization at optical wavelengths. Mie calculations for a mixture consisting of iron, graphite and POM particles are presented as an example where POM grains of radii 0.15 dominate the extinction at optical wavelengths, providing a satisfactory overall fit to a range of extinction data. A size distribution of POM needles with a mean radius 0.15 also provides good agreement with data on interstellar linear as well as circular polarization. Suitably end-capped and stabilized co-polymer-coated grains, with either silicate or graphite cores, may survive at temperatures 450 K under interstellar ambient conditions and be responsible for the 10 emission feature in many sources. Theoretically computed band profiles of the 10 -feature in POM coated grains, in general, provide better agreement with observations than most types of silicate grains considered so far. We also note that an unexplained dip at 10 in the 8–12 feature of the infrared source OH 231.8+4.2 may be a signature of POM grains; likewise, a persistent 3.3 emission feature in many different types of infrared source could be attributed to the CH stretching mode in formaldehyde co-polymer grains.