The use of invariant manifolds for transfers between unstable periodic orbits of different energies

Techniques from dynamical systems theory have been applied to the construction of transfers between unstable periodic orbits that have different energies. Invariant manifolds, trajectories that asymptotically depart or approach unstable periodic orbits, are used to connect the initial and final orbits. The transfer asymptotically departs the initial orbit on a trajectory contained within the initial orbit’s unstable manifold and later asymptotically approaches the final orbit on a trajectory contained within the stable manifold of the final orbit. The manifold trajectories are connected by the execution of impulsive maneuvers. Two-body parameters dictate the selection of the individual manifold trajectories used to construct efficient transfers. A bounding sphere centered on the secondary, with a radius less than the sphere of influence of the secondary, is used to study the manifold trajectories. A two-body parameter, κ, is computed within the bounding sphere, where the gravitational effects of the secondary dominate. The parameter κ is defined as the sum of two quantities: the difference in the normalized angular momentum vectors and eccentricity vectors between a point on the unstable manifold and a point on the stable manifold. It is numerically demonstrated that as the κ parameter decreases, the total cost to complete the transfer decreases. Preliminary results indicate that this method of constructing transfers produces a significant cost savings over methods that do not employ the use of invariant manifolds.     

The 2dF Galaxy Redshift Survey: luminosity dependence of galaxy clustering

We investigate the dependence of the strength of galaxy clustering on intrinsic luminosity using the Anglo-Australian two degree field galaxy redshift survey (2dFGRS). The 2dFGRS is over an order of magnitude larger than previous redshift surveys used to address this issue. We measure the projected two-point correlation function of galaxies in a series of volume-limited samples. The projected correlation function is free from any distortion of the clustering pattern induced by peculiar motions and is well described by a power law in pair separation over the range     . The clustering of     galaxies in real space is well-fitted by a correlation length     and power-law slope     . The clustering amplitude increases slowly with absolute magnitude for galaxies fainter than M *, but rises more strongly at higher luminosities. At low luminosities, our results agree with measurements from the Southern Sky Redshift Survey 2 by Benoist et al. However, we find a weaker dependence of clustering strength on luminosity at the highest luminosities. The correlation function amplitude increases by a factor of 4.0 between     and −22.5, and the most luminous galaxies are 3.0 times more strongly clustered than L * galaxies. The power-law slope of the correlation function shows remarkably little variation for samples spanning a factor of 20 in luminosity. Our measurements are in very good agreement with the predictions of the hierarchical galaxy formation models of Benson et al.     

Metabolic plasticity of nitrogen assimilation by Porphyra umbilicalis (Linnaeus) Kützing

The physical stresses associated with emersion have long been considered major factors determining the vertical zonation of intertidal seaweeds.We examined Porphyra umbilicalis(Linnaeus) Kützing thalli from the vertical extremes in elevation of an intertidal population(i.e.upper and lower intertidal zones) to determine whether Porphyra thalli acclimate to different vertical elevations on the shore with different patterns of nitrate uptake and nitrate reductase(NR) and glutamine synthetase(GS) activities in response to different degrees of emersion stress.We found that the nitrate uptake and NR recovery in the emersed tissues took longer in lower intertidal sub-population than in upper intertidal sub-population;and GS activity was also significantly affected by emersion and,interestingly,such an activity was enhanced by emersion of thalli from both upper and lower intertidal zones.These results suggested that intra-population variability in post-emersion recovery of physiological functions such as nutrient uptake and NR activity enables local adaptation and contributes to the wide vertical distribution of P.umbilicalis.The high GS activity during periodic emersion stress may be a protective mechanism enabling P.umbilicalis to assimilate nitrogen quickly when it again becomes available,and may also be an evidence of photorespiration during emersion.     

Heights of formation of non-magnetic solar lines suitable for velocity studies

Heights of formation of lines that do not exhibit Zeeman splitting are calculated using an LTE, partial non-LTE, and full non-LTE approach. Non-magnetic (g=0) lines are valuable for velocity investigations in quiet-Sun magnetic field regions, and a knowledge of their formation heights is useful for obtaining three dimensional velocity profiles in these regions. Presently at Sacramento Peak Observatory. Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

EUV analysis of an active region

A sequence of extreme ultraviolet (EUV) spectroheliograms of McMath region No. 10283 were obtained by the Harvard College Observatory experiment on OSO-6. The lines Ovi λ1032 Mg × λ625, Si xii λ499 and Fe xvi λ 335 were used to determine coronal temperatures and densities above the active region. A comparison of theoretical and observed line ratios yielded coronal temperatures of 2.2 to 2.3 × 10⁶K above the active region and 2.0 to 2.1 × 10⁶K in the surrounding area. The temperatures derived from ratios involving the O vi intensities are systematically higher than the others. This is attributed to an error in the theoretical O vi intensities. The intensities observed above the limb are compared with intensities predicted with a simple model based on cylindrical geometry. The overall agreement shows that the assumption of an iso-thermal corona in hydrostatic equilibrium above the active region is a reasonable working hypothesis and that the adopted geometrical model for the electron density distribution is adequate.     

A technique to deduce atmospheric temperature and constituent profiles from a planet's limb radiance profile

The concept is described of deducing the temperature and constituent profile of a planetary atmosphere from orbiter measurements of the planet's ir limb radiance profile. Expressions are derived for the weighting functions associated with the limb radiance profile for a Goody random band model. Analysis of the weighting functions for the Martian atmosphere indicates that a limb radiance profile in the 15 μm CO₂ band can be used to determine the Martian atmospheric temperature profile from 20 to 60 km. Simulation of the Martian limb radiance profile in the rotational water vapor band indicates that Martian water vapor mixing ratios can be inferred from limb radiance observations in a water vapor band.     

Long term storage of relativistic particles in the solar corona

A model is presented which shows that large numbers of energetic electrons (0.3-> 10 MeV) and protons (1–30 MeV) can be stored in the solar corona at altitudes around 3 × 10⁵ km for periods in excess of 5 days. Specific reference is made to the time period July 6–16 1968 as an excellent example of energetic solar particle storage. Time histories of interplanetary charged particle intensities observed by the IMP-4 and Pioneer 8 satellites are used to substantiate this contention. Detailed reference is also made to solar X-ray, optical and radio data obtained during the period in question, in addition to interplanetary magnetometer data. This model provides a unique solution to many hitherto unexplained solar particle events, and can also account for the lack of prompt particle emission from certain large solar flares recorded in the past.     

An analysis of the distribution of boulders in the vicinity of small lunar craters

Nine Orbiter 3 high-resolution photographs were examined at three sites for distributions of boulders around craters 110 m in diameter; three kinds of distributions were noted. Some had boulders inside and far outside (designated), others had boulders only inside or on their ramparts (), and some had no detectable boulders (). Additionally, shapes or morphologies of craters were classified according to their resemblance to one of three Jaffe models (1965); a third classification involved the depth of particulate overlay (Jaffe, 1965). Crater morphologies were classified (A) if they were relatively shallow with sharp, raised rims, (B) if they were rimless and shallow, and (C) if they were relatively deep and had low, broad rims. The data suggested that there were strong relationships between crater types and boulder distributions in which, generally, A-type was related to the-distribution, B-type to-distribution, and C-type to-distribution. Plots of numbers of craters of each crater type and each kind of boulder distribution versus steps of overlay for each site and for the totality of craters considered indicated that neither boulder distribution nor crater type represented orderly progression of age or erosional evolution. The apparent overlays for the A's and C's and for the's and's were similar, implying similar ages or stages of erosion. It is suggested that they represent two kinds of primary craters and that the A's are of impact origin while the C's are of volcanic origin. The B's probably represent later stages of erosion of the C's and possibly of some A's.Now at the University of Maryland.Receipt delayed by postal strike in Great Britain.     

Lyman-alpha observations of Comet West (1975n)

Images of Comet West in atomic hydrogen (1216 Å) emission were obtained from a sounding rocket on 1976 March 5.5 (R = 0.38 AU). The hydrogen production rate derived from the fit of a simple radial-outflow model to the observed inner isophotes was 3.2 × 10³⁰ atoms/sec. The outer isophotes did not fit the predictions of the complex dynamic model of Keller and Meier, partly because of optical depth effects, but also because the nucleus was breaking up at about this time and it is quite possible that additional hydrogen was being emitted from smaller chunks of the nucleus distributed along the orbit. The above production rate, taken with data on C and O obtained simultaneously by Feldman and Brune, gives Q_H: Q_o: Q_c = 8:3.5:1. For Comet Kohoutek we obtained the ratio 7:1.7:1. The difference, if real, may be due to minor differences in composition or evolution, but in any case it appears that the two comets are similar.     

Biocalcification in the Eastern Oyster (<Emphasis Type="Italic">Crassostrea virginica)</Emphasis> in Relation to Long-term Trends in Chesapeake Bay pH

Anthropogenic carbon dioxide (CO₂) emissions reduce pH of marine waters due to the absorption of atmospheric CO₂ and formation of carbonic acid. Estuarine waters are more susceptible to acidification because they are subject to multiple acid sources and are less buffered than marine waters. Consequently, estuarine shell forming species may experience acidification sooner than marine species although the tolerance of estuarine calcifiers to pH changes is poorly understood. We analyzed 23 years of Chesapeake Bay water quality monitoring data and found that daytime average pH significantly decreased across polyhaline waters although pH has not significantly changed across mesohaline waters. In some tributaries that once supported large oyster populations, pH is increasing. Current average conditions within some tributaries however correspond to values that we found in laboratory studies to reduce oyster biocalcification rates or resulted in net shell dissolution. Calcification rates of juvenile eastern oysters, Crassostrea virginica, were measured in laboratory studies in a three-way factorial design with 3 pH levels, two salinities, and two temperatures. Biocalcification declined significantly with a reduction of ∼0.5 pH units and higher temperature and salinity mitigated the decrease in biocalcification.