On ‘bimodality of the solar cycle’ and the duration of cycle 21

The period-growth dichotomy of the solar cycle predicts that cycle 21, the present solar cycle, will be of long duration (>133 mo), ending after July 1987. Bimodality of the solar cycle (i.e., cycles being distributed into two groups according to cycle length, based on a comparison to the mean cycle period) is clearly seen in a scatter diagram of descent versus ascent durations. Based on the well-observed cycles 8–20, a linear fit for long-period cycles (being a relatively strong inverse relationship that is significant at the 5% level and having a coefficient of determination r ² 0.66) suggests that cycle 21, having an ascent of 42 mo, will have a descent near 99 mo; thus, cycle duration of about 141 mo is expected. Like cycle 11, cycle 21 occurs on the downward envelope of the sunspot number curve, yet is associated with an upward first difference in amplitude. A comparison of individual cycle, smoothed sunspot number curves for cycles 21 and 11 reveals striking similarity, which suggests that if, indeed, cycle 21 is a long-period cycle, then it too may have an extended tail of sustained, low, smoothed sunspot number, with cycle 22 minimum occurring either in late 1987 or early 1988.     

On the regime of the Earth’s polar motion based on data for the period 1962–2007

The view of the Earth’s polar motion as a completely deterministic process has been called into question in the past decades, because no long-term prediction can be made. At the same time, no fundamental restrictions currently exist in the problem of a long-term prediction of the Earth’s rotation. Determining the boundaries of predictability is related to identifying the regime of the Earth’s polar motion. IERS data for the period 1962–2007 have been used to study the regime of the Earth’s polar motion. Analysis of the plots of polhodes reveals peculiarities in the variations of the pole’s coordinates X and Y in certain intervals along the time axis. The data in the interval from 2003 to 2006 have been analyzed in greatest detail: a model for the Chandler and annual oscillations has been constructed and relations between the parameters of these oscillations have been determined; the shift of the instantaneous pole on the phase plane and the Poincare plane has been investigated. As a result, we have found features inherent in chaotic motion (intermittency) and calculated the period (32 years) of the possible repetitions of such anomalies, as confirmed by our analysis of the plots of polhodes. The intervals where the peculiarities in the motion of the Earth’s instantaneous pole manifest themselves are compared with the intervals of the inflections on the plots of variations in the length of the day (LOD).     

Secular change in the ‘164-day’ period of SS 433

In this paper we present evidence that the 164-day period in the wavelengths of the moving lines in SS 433 has been decreasing at the surprisingly rapid rate of P = –0.010±0.002. An ephemeris of the moving lines for the 1981 observing season is provided for the case P = –0.010.     

Guide and examples for users of the ‘SPACEKAP’ style file

Guide and examples for users of the SPACEKAP style fileBasic instructions     

Guide and examples for users of the ‘SPACEKAP’ style file

Guide and examples for users of the SPACEKAP style fileBasic instructions     

Guide and examples for users of the ‘SPACEKAP’ style file

Guide and examples for users of the SPACEKAP style fileBasic instructions     

Guide and examples for users of the ‘SPACEKAP’ style file

Guide and examples for users of the SPACEKAP style fileBasic instructions     

Guide and examples for users of the ‘SPACEKAP’ style file

Guide and examples for users of the SPACEKAP style fileBasic instructions     

Guide and examples for users of the ‘Spacekap’ style file

Guide and examples for users of the Spacekap style fileBasic Instructions     

Guide and examples for users of the ‘SPACEKAP’ style file

Guide and examples for users of the SPACEKAP style fileBasic instructions     

Guide and examples for users of the ‘spacekap’ style file

Guide and examples for users of the spacekap style fileBasic instructions     

Guide and examples for users of the ‘SPACEKAP’ style file

Guide and examples for users of the SPACEKAP style fileBasic instructions     

On the use of ‘first spotless day’ as a predictor for sunspot minimum

Defining the first spotless day of a sunspot cycle as the first day without spots relative to sunspot maximum during the decline of the solar cycle, one finds that the timing of that occurrence can be used as a predictor for the occurrence of solar minimum of the following cycle. For cycle 22, the first spotless day occurred in April 1994, based on the International sunspot number index, although other indices (Boulder and American) indicated the first spotless day to have occurred earlier (September 1993). For cycles 9–14, sunspot minimum followed the first spotless day by about 72 months, having a range of 62–82 months; for cycles 15–21, sunspot minimum followed the first spotless day by about 35 months, having a range of 27–40 months. Similarly, the timing of first spotless day relative to sunspot minimum and maximum for the same cycle reveals that it followed minimum (maximum) by about 69 (18) months during cycles 9–14 and by about 90 (44) months during cycles 15–21. Accepting April 1994 as the month of first spotless day occurrence for cycle 22, one finds that it occurred 91 months into the cycle and 57 months following sunspot maximum. Such values indicate that its behavior more closely matches that found for cycles 15–21 rather than for cycles 9–14. Therefore, one infers that sunspot minimum for cycle 23 will occur in about 2–3 years, or about April 1996 to April 1997. Accepting the earlier date of first spotless day occurrence indicates that sunspot minimum for cycle 23 could come several months earlier, perhaps late 1995.The U.S. Government right to retain a non-exclusive, royalty free licence in and to any copyright is acknowledged.     

On the evolution of the ‘f’ family in the restricted three-body problem

Poincaré surface of section technique is used to study the evolution of a family ‘f’ of simply symmetric retrograde periodic orbits around the smaller primary in the framework of restricted three-body problem for a number of systems, actual and hypothetical, with mass ratio varying from 10⁻⁷ to 0.015. It is found that as the mass ratio decreases the region of phase space containing the two separatrices shrinks in size and moves closer to the smaller primary. Also the corresponding value of Jacobi constant tends towards 3.     

Rapid changes in the fine structure of a coronal ‘bright point’ and a small coronal ‘active region’

A coronal bright point is resolved into a pattern of emission which, at any given time, consists of 2 or 3 miniature loops (each 2500 km in diameter and 12 000 km long). During the half-day lifetime of the bright point individual loops evolved on a time scale 6 min. A small ctive region seemed to evolve in this way, but the occasional blurring together of several loops made it difficult to follow individual changes.     

On the stability of circular ‘asteroid’ orbits in anN-planetary system

The restricted problem of the motion of a point of negligible mass (asteroid) in anN-planetary system is considered. It is assumed that all the planets move about the central body (Sun) along circular orbits in the same plane and the mean motions of the asteroid and the planets are incommensurable. The asteroid orbit evolution is described as a first approximation by secular equations with the perturbing function averaged by the mean longitudes of the asteroid and the planets. For small values of the asteroid orbit eccentricity an expression for the secular part of the perturbing function has been obtained. This expression holds for the arbitrary values of the asteroid orbit semiaxis which are different from those of the planet orbit radii. The stability of the asteroid circular orbits in a linear approximation with respect to the eccentricity is studied. The critical inclinations for a Solar system model are calculated.     

Asymmetric periodic solutions of the averaged Hill problem with allowance for a planet’s oblateness

We consider asymmetric periodic solutions of the double-averaged Hill problem by taking into account oblateness of the central planet. They are generated by steady-state solutions, which are stable in the linear approximation and correspond to satellite orbits orthogonal to the line of intersection of the planet’s equatorial plane with the orbital plane of a disturbing point. For two model systems [(Sun+Moon)-Earth-satellite] and [Sun-Uranus-satellite], these periodic solutions are numerically continued from a small vicinity of the equilibrium position. The results are illustrated by projecting the solutions onto the (pericenter argument-eccentricity) and (longitude-inclination) planes.     

Redundant variables for ‘global’ regularization of the three-body problem

It has been shown (Heggie, 1974) that the equations of motion for the three-body problem may be cast into a form which is regular for collisions betweenany pair of bodies. The method proceeds by two stages, namely

The annual period of the Earth’s seismic activity for 1964–2007

The catalog of the United States National Earthquake Information Center (NEIC, 2007) was used for a Fourier analysis of planetary seismic activity from 1964 to 2007 (401219 earthquakes with M ≥ 3 and hypocenter depths H ≥ 1 km) for the Northern Hemisphere (248291 events) and for the Southern Hemisphere (152928 events). The annual periodicity of weak earthquakes (M < 5.0) was verified with a high degree of reliability. All regularities (depending on the geographic latitude, hypocenter depths, and north-south asymmetry) revealed earlier (in 1964–1990) for this period are shown to exist for the period of 1964–2007.