Anisotropy: High energy cosmic rays and the thermal background radiation

The motion of a large (100 Mpc radius) volume of local matter with respect to the frame in which the thermal cosmic background radiation (CBR) appears isotropic is shown to produce a contribution to anisotropy in the arrival directions of the highest energy (>10¹⁹ eV) cosmic rays. The magnitude of the effect predicted is 1%, below that currently observed and below the sensitivity of present experiments.     

Examples of predominantly two-body orbits in the Sun-Jupiter asteroid system

Accurate numerical continuation of families of plane symmetric direct periodic orbits around the large primary in the Sun-Jupiter case of the restricted problem of three bodies allows the determination of the vertical branching points where families of three-dimensional symmetric periodic orbits bifurcate from the planar ones. Three families of plane periodic orbits, and the initial segments of ten bifurcating families of three-dimensional ones are determined. The stability of these families is examined and examples of their orbits are illustrated.     

Interaction of S- and L-bursts in Jupiter's decametric radio spectra

Dynamic spectra of Jupiter's decametric emission are observed with a high-resolution radio spectrograph. Certain events observed in region Io-B display interaction effects between the S- and L-emissions. The effect appears as a gap in the L-emission after a passage of an S-burst. In a typical case the L-emission has a relatively narrow bandwidth, the S-burst appears as a sloping line crossing it, and the duration of the emission gap is a substantial fraction of a second. The gap has sharp, sloped edges; its leading edge has anf-t slope which is the same as that of the S-burst while the slope of the trailing edge is lower. A kind of tilted V-pattern is thus formed. It is suggested that some more complicated spectral patterns may also be produced this way. It seems that an emission model consisting of S-bursts from bunches of gyrofrequency-emitting electrons ascending a flux tube and interacting with L-emitting bunches of electrons having more stationary guiding centers is inadequate to explain the complex S-L interactions.Contribution of No. 36 of the Department of Astronomy, University of Florida, U.S.A.     

A refined measurement of the sunspot radiative flux deficit

New measurements of the radiative flux deficits of two large sunspots are presented, based on detailed isophotometric maps. Results are given separately for umbrae and penumbrae. The umbral and penumbral deficits are 4–5 × 10¹⁰ and 1–1.5 × 10¹⁰ erg cm^–2 s^–1 respectively, the larger figures ref to the larger spot. Over limited areas centered on the umbral cores the deficits for the two spots amount to 76 and 86% of the photospheric flux.     

On the temporal variation of the solar continuous brightness fluctuations

From a sequence of white-light photographs of solar granulation at the centre of the disk, obtained by Spectro-Stratoscope on May 17, 1975, two-dimensional spatial power spectra of photospheric intensity fluctuations were deduced. These show periodicities of 1000 s, 250–450 s (5-min oscillation), and shorter ones in the range 30–120 s. The reality of the shorter periods, however, seems to be questionable.The weighted mean wavenumber of the spatial power spectra and rms of the intensity fluctuation (I _rms) are also computed, showing the same periodicities as the power.Mitteilungen aus dem Kiepenheuer-Institut Nr. 188.On leave of absence from the Institute of Geophysics, University of Tehran.     

The solar power spectrum — a fractal set?

A preliminary numerical analysis of the power spectrum of solar oscillations of the SCLERA group suggests that this curve can be characterized by a Hausdorff-Besicovich dimension close to 3/2 near the present observational resolution (0.03 mHz). We show that this result is not inconsistent with the presence of a component due to non-linear, turbulent-like motions, which, in addition to linear oscillation modes, is shaping the observed spectral distribution.On leave of absence from Institut d'Astrophysique, Cointe-Ougrée, Belgium.     

Second species solutions with an 0(μ v ), 0<v<1, near-Moon passage

This paper illustrates the application of the theory for second species solutions with an 0( ^v ), 0<v<1, near-Moon passage to first species-second species bifurcations and to second species-second species bifurcations. It also corrects and improves the asymptotic approximations obtained in the author's previous work on this subject and it establishes a local form of Broucke's Principle for the types of bifurcations studied in this paper.This work was supported by the National Science Foundation under Grant MCS 7703591.     

On periodic flybys of the moon

This paper considers the plane circular restricted three-body problem for small . Symmetric periodic solutions of the second species (passing near the body of mass ) and their distance from the center of the body of mass are studied by constructing perturbations of arc-solutions (solutions with consecutive collisions) existing for =0. Orbits which also pass near the body of mass 1- are studied in detail. The results are applied to finding periodic orbits in the Earth-Moon system and in the Sun-Jupiter system.Russian version: Preprint No. 91 (1978) of Inst. Appl. Math.; present English translation was made by L. M. Perko and W. C. Schulz (February 1979).     

Radius of convergence of Lie series for some elliptic elements

For equatorial orbits about an oblate body, we show that the Lie series for the elliptic elementse,f,l and diverge when the oblateness exceeds a critical multiple of the transformed eccentricity constant. The use of similar truncated series expansions for such elliptic elements by Brouwer accounts for the first-order errors at low eccentricity in his derived coordinates for an artificial satellite.     

On the perturbation of the anomalistic period of a highly eccentric orbit satellite due to the zonal harmonics

In this note a simple formula is given for the perturbation of the anomalistic period of a highly eccentric orbit due to the zonal harmonics. This perturbation depends essentially only on the semi-major axisa, the eccentricitye (or pericentre radius r =a(1-e)) and the latitude of the pericentre.