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.     

Late Holocene estuarine–inner shelf interactions; is there evidence of an estuarine retreat path for Tampa Bay, Florida?

The purpose of this study was to determine if and how a large, modern estuarine system, situated in the middle of an ancient carbonate platform, has affected its adjacent inner shelf both in the past during the last, post-glacial sea-level rise and during the present. An additional purpose was to determine if and how this inner shelf seaward of a major estuary differed from the inner shelves located just to the north and south but seaward of barrier-island shorelines. Through side-scan sonar mosaicking, bathymetric studies, and ground-truthing using surface grab samples as well as diver observations, two large submarine sand plains were mapped – one being the modern ebb-tidal delta and the other interpreted to be a relict ebb-tidal delta formed earlier in the Holocene. The most seaward portion of the inner shelf studied consists of a field of lobate, bathymetrically elevated, fine-sand accumulations, which were interpreted to be sediment-starved 3D dunes surrounded by small 2D dunes composed of coarse molluscan shell gravel. Additionally, exposed limestone hardbottoms supporting living benthic communities were found as well. This modern shelf sedimentary environment is situated on a large, buried shelf valley, which extends eastward beneath the modern Tampa Bay estuary. These observations plus the absence of an incised shelf valley having surficial bathymetric expression, and the absence of sand bodies normally associated with back-tracking estuarine systems indicate that there was no cross-shelf estuarine retreat path formed during the last rise in sea level. Instead, the modern Tampa Bay formed within a mid-platform, low-relief depression, which was flooded by rising marine waters late in the Holocene. With continued sea-level rise in the late Holocene, this early embayment was translated eastward or landward to its present position, whereby a larger ebb-tidal delta prograded out onto the inner shelf. Extensive linear sand ridges, common to the inner shelves to the north and south, did not form in this shelf province because it was a low-energy, open embayment lacking the wave climate and nearshore zone necessary to create such sand bodies. The distribution of bedforms on the inner shelf and the absence of seaward-oriented 2D dunes on the modern ebb-tidal delta indicate that the modern estuarine system has had little effect on its adjacent inner shelf.     

Solar and stellar chromospheric contrast

Positions of active regions estimated from observations of the whole solar disk in Caii K _iv during the period 1977–1989 at the Coimbra Astronomical Observatory are compared with the time-dependent latitudinal distribution of background solar magnetic fields and with the latitudinal shifts of boundaries of their polarities. We confirm that the sunspot groups are located near the zonal boundaries between the opposite polarities of the solar background magnetic field during different phases of the two recent consecutive cycles of activity. We demonstrate a probable connection between the increased number of groups and the commencement of poleward migration of zonal boundaries in both hemispheres. But the influence of the dominant convective rolls seems to he still unclear. A new problem of interrelation between the zonal and sector boundaries has also appeared.     

The solar surface differential rotation from disk-integrated chromospheric fluxes

Disk-integrated solar chromospheric Caii K-line (3933.68 ) fluxes have been measured almost daily at Sacramento Peak Observatory since 1977. Using observing windows selected to mimic seasonal windows for chromospheric measurements of lower Main-Sequence stars such as those observed by Mount Wilson Observatory's HK Project, we have measured the solar rotation from the modulation of the Caii K-line flux. We track the change of rotation period from the decline of cycle 21 through the maximum of cycle 22. This variation in rotation period is shown to behave as expected from the migration of active regions in latitude according to Maunder's butterfly diagram, including an abrupt change in rotation period at the transition from cycle 21 to cycle 22. These results indicate the successful detection of solar surface differential rotation from disk-integrated observations. We argue that the success of our study compared to previous investigations of the solar surface differential rotation from disk-integrated fluxes lies primarily with the choice of the length of the time-series window. Our selection of 200 days is shorter than in previous studies whose windows are typically on the order of one year. The 200-day window is long enough to permit an accurate determination of the rotation period, yet short enough to avoid complications arising from active region evolution. Thus, measurements of the variation of rotation period in lower Main-Sequence stars, especially those that appear to be correlated with long-term changes in chromospheric activity (i.e., cycles), are probably evidence for stellar surface differential rotation.