Green's theorem and Green's functions for the steady-state cosmic-ray equation of transport

Green's Theorem is developed for the spherically-symmetric steady-state cosmic-ray equation of transport in interplanetary space. By means of it the momentum distribution functionF _o(r,p), (r=heliocentric distance,p=momentum) can be determined in a regionr _arr_bwhen a source is specified throughout the region and the momentum spectrum is specified on the boundaries atr _a andr _b . Evaluation requires a knowledge of the Green's function which corresponds to the solution for monoenergetic particles released at heliocentric radiusr _o , Examples of Green's functions are given for the caser _a =0,r _b = and derived for the cases of finiter _a andr _b . The diffusion coefficient is assumed of the form = _o(p)r ^b . The treatment systematizes the development of all analytic solutions for steady-state solar and galactic cosmic-ray propagation and previous solutions form a subset of the present solutions.     

Far-infrared spectral observations of Saturn and its rings

The spectrum of Saturn and its rings between 45 and 115 μm has been measured at an average resolving power of 14 from the NASA Lear Jet. The combined brightness temperature of the rings and planetary disk decreases beyond 65 μm, in disagreement with previous results. A brightness temperature of 65 ± 10°K is obtained for the planetary disk in the 80–110-μm wavelength range if a large-particle, constant-emissivity model is assumed for the rings. The possible effects of small particles in the rings are briefly considered.     

The structure of the planets Jupiter and Saturn

Planetary models for Jupiter and Saturn are computed using a fourth-order theory and a new molecular equation of state. The equation of state for the molecular hydrogen and helium planetary envelopes is taken from the Monte Carlo calculations of Slattery and Hubbard [Icarus 29, 187–192 (1976)]. Models for Jupiter are found that have a small amount of heavy elements either mixed with hydrogen and helium throughout the interior of the planet or concentrated in a small dense core. Saturn is modeled with a solar-composition hydrogen and helium envelope and a small derse core. We conclude that the molecular equation of state linked with suitable interior equations of state can produce Jovian models which satisfy the observational data. The planetary models show that the enrichment of heavy elements (relative to solar composition) is approximately 3 times for Jupiter and 10 times for Saturn.     

Energetic properties of interplanetary plasma at the earth's orbit following the August 4, 1972 flare

Solar wind and interplanetary magnetic field data were obtained by the PROGNOZ 1 and PROGNOZ 2 satellites during the period following the August 4, 1972 (0621 UT) solar flare. A thermalized plasma was recorded one hour after the shock followed two hours later by the plasma piston with a bulk velocity higher than 1700 km s^-1. The comparison between the PROGNOZ and PIONEER 9 solar wind data shows an attenuation of the plasma properties with the deflection from the flare's meridian.     

Auroral recombination of N and O: A possible source for emission in the γ and δ bands of NO

Radiative recombination of N and O provides a significant source for auroral emission in the γ and δ bands of NO with selective population of vibrational levels in the A²Σ⁺ and C²Π states. This mechanism may account for emissions detected near 2150 Å. Models are derived for the auroral ionosphere and include estimates for the concentrations of N and NO. The concentration of NO is estimated to have a value of about 10⁸ cm^?1 near 140 km in an IBC III aurora. The corresponding density for N is about 5 × 10⁷cm^?3 and the concentration ratio $\text{NO}{}^{\mathrm{+}}\text{O}{}_2{}^{\mathrm{+}}$ has a value of about 5.5.     

A relation in families of periodic solutions

We show the existence of a general relation between the parameters of periodic solutions in dynamical systems with ignorable coordinates. In particular, for time-independent systems with an axis of symmetry, the relation takes the form T/A=–/E, whereT is the period,A is the angular momentum, is the angle through which the system has rotated after one period, andE is the energy.     

Magnetic properties of x-ray bright points

Using high resolution KPNO magnetograms and sequences of simultaneous S-054 soft X-ray solar images we have compared the properties of X-ray bright points (XBP) and ephemeral active regions (ER). All XBP appear on the magnetograms as bipolar features, except for very newly emerged or old and decayed XBP. We find that the separation of the magnetic bipoles increases with the age of the XBP, with an average emergence growth rate of 2.2 ± 0.4 km s^–1. The total magnetic flux in a typical XBP living about 8 hr is found to be 2 x 10¹⁹ Mx. A proportionality is found between XBP lifetime and total magnetic flux, equivalent to 10²⁰ Mx per day of lifetime.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.     

The north-south distribution of major solar flare events,sunspot magnetic classes and sunspot areas (1955–1974)

The north-south incidence has been studied of 31 white-light flares observed since 1859 and of 1669 events meeting the criteria for major flares of Dodson and Hedeman (1971) for the period 1955–1974. The asymmetry in favor of the northern hemisphere increases strikingly with the importance of the events. Similarly, magnetically complex sunspot groups (Mt. Wilson classes, and) display a more pronounced asymmetry in favor of the north than non-complex groups for 1962–1970. Contrary to the flare asymmetry, the spottedness asymmetry is independent of the size of sunspots.     

The intermediate anomaly

A Sundman time transformation of the form $$dt = cr^n ds$$ , wheren=3/2 andc is a constant, is integrated analytically for Keplerian motion. The integral involves an elliptic integral of the first kind. The variable s is called theintermediate anomaly.     

Operational requirements and the geometry of a station-keeping maneuver

In this paper station-keeping is regarded as the specialization of relative motion referred to a moving, orbiting origin. For this study a well-known linear solution to this problem serves as a base formulation from which the investigation begins.Even though the overall problem could be separated into three parts—necessitating two distinct studies for coverage—this paper examines only the last phase of the operation. That is, it is the continuation, or retention, of a relative motion sub-orbit which is of interest in this analysis.The situation becomes one of determining what is needed to maintain the sub-orbit, and/or to adjust it. In addition, the consequences of these actions, and the results predicted from theory are established, examined, and commented upon. In the presentation of information gathered from this study, various graphs have been prepared; however, these are expressed in a dimensionless format so that the results apply equally to all reasonable reference orbits.For this analysis the separate and combined influences, due to both the initial relative motion state and to a thrusting condition, are examined. Also, the consequences of referencing the acquired sub-orbits to an inertially aligned frame of reference (rather than the familiar rotating one) are illustrated, discussed, and commented upon.Formerly: Sr. Analyst and Manager, Seabrook Office, AMA, Inc., Seabrook, Md., U.S.A.