A perturbative treatment of motion near the 3/1 commensurability

A semianalytic perturbation theory for motion near the 3/1 commensurability in the planar elliptic restricted three-body problem is presented. The predictions of the theory are in good agreement with the features found on numerically generated surfaces of section; a global understanding of the phase space is achieved. The unusual features of the motion discovered by J. Wisdom (1982, Astron. J.87, 577–593; 1983a, Icarus56, 51–74) are explained. The principal cause of the large chaotic zone near the 3/1 commensurability is identified, and a new criterion for the existence of large-scale chaotic behavior is presented.     

Progress in coronal physics

This paper reviews research highlights of the past five years. Considerable progress has been made in observing and interpreting coronal mass ejections. The stability of coronal loops is much better understood and new observations of the onset of wind streams in coronal holes have been made. Observations from the Solar Maximum Mission should helpt to clarify the physics of the active corona.The mechanisms that heat the corona and accelerate the high-speed wind streams remain to be identified, however.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Bending waves and the structure of Saturn's rings

The surface mass density profiles at four locations within Saturn's rings are calculated using Voyager spacecraft images of spiral bending waves. Bending waves are vertical corrugations in Saturn's rings which are excited at vertical resonances of a moon, e.g., Mimas, whose orbit is inclined with respect to the mean plane of the rings. Bending waves propagate toward Saturn by virtue of the rings' self-gravity; their wavelength depends on the local surface mass density of the rings. Observations of bending waves can thus be used to determine the surface density in regions of Saturn's rings near vertical resonances. The average surface density of the outer B ring near Mimas' 4:2 inner vertical resonance is 54 ± 10 g cm^?2. Surface density in this region probably varies by ～ 30% over radial length scales of tens of kilometers; and irregular radial structure is present on similar length scales in this region. Surface densities ranging from 24 g cm^?2 to 45 g cm^?2 are found in the A ring. Small scale variations in surface density are not seen in the A ring, consistent with its more uniform optical appearance.     

Canonical solution of the two critical argument problem

The solution by Sessin and Ferraz-Mello (Celes. Mech. 32, 307–332) of the Hori auxiliary system for the motion of two planets with periods nearly commensurate in the ratio 21 is considerably simplified by the introduction of canonical variables. An analogous canonical transformation simplifies the elliptic restricted problem.     

Chaotic behavior and the origin of the 31 Kirkwood gap

The sudden eccentricity increases discovered by J. Wisdom (Astron J.87, 577–593, 1982) are reproduced in numerical integrations of the planar-elliptic restricted three-body problem, verifying that this phenomenon is real. Maximum Lyapunov characteristic exponents for trajectories near the $\text{3}\text{1}$ commensurability are computed both with the mappings presented in Wisdom (1982) and by numerical integration of the planar-elliptic problem. In all cases the agreement is excellent, indicating that the mappings accurately reflect whether trajectories are chaotic or quasiperiodic. The mappings are used to trace out the chaotic zone near the $\text{3}\text{1}$ commensurability, both in the planar-elliptic problem and to a more limited extent in the three-dimensional elliptic problem. The outer boundary of the chaotic zone coincides with the boundary of the $\text{3}\text{1}$ Kirkwood gap in the actual distribution of asteroids within the errors of the asteroid orbital elements.     

The volcano-magnetic effect

Summary A geometrically simple volcano is considered, havig a spherical magma chamber of 2.5 km radius centred at 10 km depth. The Curie point isotherm is assumed to be a plane at 20 km depth, except for the spherical volume which is also non-magnetic. The stress pattern in the vicinity of the spherical chamber, due to regional stress of sufficient intensity to cause an eruptions, is used to calculate the change in magnetization which results from the piezomagnetic effect through the volume of solid rock. The consequent magnetic field anomaly at the surface is then obtaied by numerical integration of the dipole law of force over the stressed volume. For rocks of the type found on the volcanic island of St. Vincent (West Indies), this model gives a maximum local volcano-magnet c effect of about 7 gammas.     

Earth-orbit-approaching comets and their theoretical meteor radiants

Sixteen comets produce recognizable meteor showers that are found in A. F. Cook's (1973, In Evolutionary and Physical Properties of Meteoroids (C. L. Hemenway, P. M. Millman, and A. F. Cook, Eds.), pp. 183–191, U.S. Govt. Printing Office, Washington, D.C.), working list of meteor streams. Of these, five are long period, including one in a parabolic and one in a hyperbolic orbit. The largest Earth-comet orbit miss distance is 0.20 AU for P/Encke and the Northern and Southern Taurids. Using this is an upper limit for meteor showers from comets, all comets which approach the Earth's orbit to within 0.20 AU were extracted from the Catalogue of Cometary Orbits (B. G. Marsden, 1979. 3rd ed., Central Bureau of Astronomical Telegrams, IAU SAO, Cambridge, Mass.). A compilation of such comets is presented by date minimum approach, along with the distance of closest approach and the theoretical geocentric radiants and velocities of possible associated meteor showers. Both pre- and postpperihelion encounters with the Earth's orbit are considered. There are 240 entries for 178 long-period comets, and 36 for 28 short-period comets. It is noted that all short-period comets that have approached the Earth's orbit to within 0.08 AU have produced meteors, except P/Lexell, P/Finlay, P/Denning-Fujikawa, and P/Grigg-Skjellerup. Attention is called to the favorable observing conditions for detecting meteors from P/Grigg-Skjellerup in April 1982, and for the possibility of another great Draconid storm from P/Giacobini-Zinner in October 1985. A comparison is made between observed sporadic meteor rates and the distribution of theoretical radiants throughout the year, from which it is concluded that the currently known comets can account for sporadic meteors. A criterion is developed to test whether or not an observed meteor shower can be associated with a given theoretical radiant. Based on known examples, a qualitative model for comet/meteor relationships is also presented.     

A comparison of mud- and sand-dominated meanders in a downstream coarsening reach of the mixed bedrock-alluvial Klip River, eastern Free State, South Africa

Along a 28 km reach of the Klip River, eastern Free State, South Africa, mud- and sand-dominated meanders have developed in close proximity within a floodplain wetland up to 1.5 km wide, providing an unusual opportunity to compare their characteristics under similar hydrological conditions. Throughout the reach, the channel bed is grounded on sandstone/shale bedrock although the banks are alluvial, and most river activity occurs during summer high flows. The reach can be divided into three geomorphological zones: Zone 1 (0–11 km), a muddy proximal part with a single meandering channel (w/d < 10) and near-permanent standing water in oxbows and backswamps; Zone 2 (11–17.5 km), a transitional mud-to-sand part with one main channel (w/d  20–30), a number of sinuous palaeochannels and oxbows, and only limited standing water; and Zone 3 (17.5–28 km), a sandy distal part with a single meandering channel (w/d  15–30), scroll bars and oxbows, and little standing water. Each zone also has a distinctive sedimentology: Zone 1 is characterised by an  3–4 m thick succession of basal sand and minor granules overlain by dominantly muddy sediment deposited primarily by oblique accretion in meander bends; Zone 2 is characterised by < 4 m of interbedded sand and mud deposited primarily by lateral point-bar accretion, although a history of avulsions also attests to the importance of abandoned-channel accretion; and Zone 3 is characterised by < 3 m of dominantly sand deposited primarily by lateral point-bar accretion. This unusual downstream sediment coarsening trend, and the associated changes in channel and floodplain character, are independent of sediment inputs from tributaries, and result from a downstream increase in bankfull unit stream power from < 3.5 W m^− 2 (Zone 1) to  4–10 W m^− 2 (Zone 3). Mud is deposited primarily in low-energy Zone 1 but is conveyed in suspension more effectively through higher energy Zones 2 and 3, only forming drapes over sandy lateral accretion deposits during waning flood stages. The downstream increase in unit stream power is controlled in part by a slight downstream increase in floodplain gradient that may be related to a subtle variation in the erosional resistance of the bedrock underlying the channel bed. These findings add to previous work on meandering rivers by demonstrating that mud-dominated meanders can occur in long-term erosional settings where the channel bed is grounded on bedrock, and that downstream fining trends may be reversed locally.