The Expansion of the Distance Between Two Arbitrary Gravitating Points as Applied to Specific Models of Celestial Bodies

For the complete system of biharmonic functions a suitable representation in spheroidal coordinates is found. It is used for expanding the distance between two arbitrary gravitating points and its inverse quantity in appropriate series. Such expansions can be of interest and useful in a number of problems of celestial mechanics and stellar dynamics.     

Estimation of snow water equivalent using microwave radiometry over Arctic first‐year sea ice

The magnitude and spatial distribution of snow on sea ice are both integral components of the ocean–sea‐ice–atmosphere system. Although there exists a number of algorithms to estimate the snow water equivalent (SWE) on terrestrial surfaces, to date there is no precise method to estimate SWE on sea ice. Physical snow properties and in situ microwave radiometry at 19, 37 and 85 GHz, V and H polarization were collected for a 10‐day period over 20 first‐year sea ice sites. We present and compare the in situ physical, electrical and microwave emission properties of snow over smooth Arctic first‐year sea ice for 19 of the 20 sites sampled. Physical processes creating the observed vertical patterns in the physical and electrical properties are discussed. An algorithm is then developed from the relationship between the SWE and the brightness temperature measured at 37 GHz (55°) H polarization and the air temperature. The multiple regression between these variables is able to account for over 90% of the variability in the measured SWE. This algorithm is validated with a small in situ data set collected during the 1999 field experiment. We then compare our data against the NASA snow thickness algorithm, designed as part of the NASA Earth Enterprise Program. The results indicated a lack of agreement between the NASA algorithm and the algorithm developed here. This lack of agreement is attributed to differences in scale between the Special Sensor Microwave/Imager and surface radiometers and to differences in the Antarctic versus Arctic snow physical and electrical properties. Copyright © 2003 John Wiley & Sons, Ltd.     

Resonant Periodic Orbits of Trans-Neptunian Objects

We study two and three-dimensional resonant periodic orbits, usingthe model of the restricted three-body problem with the Sun andNeptune as primaries. The position and the stability character ofthe periodic orbits determine the structure of the phase space andthis will provide useful information on the stability and longterm evolution of trans-Neptunian objects. The circular planarmodel is used as the starting point. Families of periodic orbitsare computed at the exterior resonances 1/2, 2/3 and 3/4 withNeptune and these are used as a guide to select the energy levelsfor the computation of the Poincaré maps, so that all basicresonances are included in the study. Using the circular planarmodel as the basic model, we extend our study to more realisticmodels by considering an elliptic orbit of Neptune and introducingthe inclination of the orbit. Families of symmetric periodicorbits of the planar elliptic restricted three-body problem andthe three-dimensional problem are found. All these orbitsbifurcate from the families of periodic orbits of the planarcircular problem. The stability of all orbits is studied. Althoughthe resonant structure in the circular problem is similar for allresonances, the situation changes if the eccentricity of Neptuneor the inclination of the orbit is taken into account. All theseresults are combined to explain why in some resonances there aremany bodies and other resonances are empty.     

F stars, metallicity and the ages of red galaxies at z > 1

We explore whether the rest-frame near-ultraviolet spectral region, observable in high-redshift galaxies via optical spectroscopy, contains sufficient information to allow the degeneracy between age and metallicity to be lifted. We do this by first testing the ability of evolutionary synthesis models to reclaim the correct metallicity when fitted to the near-ultraviolet spectra of F stars of known (subsolar and supersolar) metallicity. F stars are of particular interest because the rest-frame near-ultraviolet spectra of the oldest known elliptical galaxies at   z > 1  appear to be dominated by F stars near to the main-sequence turn-off.
We find that, in the case of the F stars, where the Hubble Space Telescope ultraviolet spectra have a high signal-to-noise ratio, fitting models in which the metallicity is allowed to vary as a free parameter is rather successful at deriving the correct metallicity. As a result, the estimated turn-off ages of these stars yielded by model-fitting are well constrained. Encouraged by this we have fitted these same variable-metallicity models to the deep, optical spectra of the   z ≃ 1.5 mJy  radio galaxies 53W091 and 53W069 obtained with the Keck telescope. While the age and metallicity are not so easily constrained for these galaxies, we find that even when metallicity is allowed as a free parameter, the best estimates of their ages are still ≥3 Gyr, with ages younger than 2 Gyr now strongly excluded. Furthermore, we find that a search of the entire parameter space of metallicity and star formation history using MOPED leads to the same conclusion. Our results therefore continue to argue strongly against an Einstein–de Sitter universe, and favour a Λ-dominated universe in which star formation in at least these particular elliptical galaxies was completed somewhere in the redshift range   z = 3–5  .     

An Instantaneous-Frequency Filtering Technique for High-Frequency Radar Oceanography

High-frequency (HF) radar systems are remote sensing tools that can be used to measure oceanographic parameters. Problems can occur when using the conventional periodogram (PG) method for computing power spectral estimates from backscattered radar signals. Temporal and spatial inhomogeneities within the radar measurement region can cause distortion in the spectra. This paper describes an instantaneous-frequency (IF) filtering technique that has been developed to measure the first-order modulation contained within the radar signal. Successful removal of this modulation is shown to yield an increased quality and quantity of ocean measurements     

A sensitivity study of the role of continental location and area on Paleozoic climate

The seasonal variation of the surface temperature is calculated for various idealized paleogeographic conditions with a 1.5-dimensional (1.5-D) coupled climate-sea ice model. The sensitivity of the annual and summer polar temperatures to the meridional oceanic heat transport and to the parameterizations adopted for the snow and sea ice albedos is examined in connection with the location and size of a polar global super-continent. It is shown that the high latitude summer temperatures remain below the freezing point in all numerical simulations with a polar super-continent, thus suggesting the potential role played by a large polar continental mass in the initiation of glaciations. These results are in agreement with a previous 1.5-D energy balance model (EBM) study but in conflict with two-dimensional (2-D) EBMs suggesting above-freezing high latitude summer temperatures in the case of a polar-centered super-continent. It is also found that the amount of seasonality is strongly dependent on the details of the surface albedo feedback parameterizations and could explain the various model diverging results.If a simplified temperature dependence of the silicate weathering rate controlling the long-term carbon cycle is included, the atmospheric CO₂ level is significantly increased in the case of a polar-centered continent but summer temperatures still remain below freezing.