A Multi-Angle Averaging Theorem Applied to the J2 Problem

A particular multi-angle averaging theorem for systems admitting a finite Fourier expansion of the field is presented, together with its application to the problem of motion around an oblate planet (the J₂ problem), in harmonic oscillator formulation. This method of approximate integration has the advantage of working with (close on) directly measurable elements. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bifurcation of Relative Equilibria in the Main Problem of Artificial Satellite Theory for a Prolate Body

In this paper, we study circular orbits of the J ₂ problem that are confined to constant-z planes. They correspond to fixed points of the dynamics in a meridian plane. It turns out that, in the case of a prolate body, such orbits can exist that are not equatorial and branch from the equatorial one through a saddle-center bifurcation. A closed-form parametrization of these branching solutions is given and the bifurcation is studied in detail. We show both theoretically and numerically that, close to the bifurcation point, quasi-periodic orbits are created, along with two families of reversible orbits that are homoclinic to each one of them.     

Analytical short-term orbit predictions withJ 3 andJ 4 in terms of KS elements

Analytical theory for short-term orbit motion of satellite orbits with Earth's zonal harmonicsJ ₃ andJ ₄ is developed in terms of KS elements. Due to symmetry in KS element equations, only two of the nine equations are integrated analytically. The series expansions include terms of third power in the eccentricity. Numerical studies with two test cases reveal that orbital elements obtained from the analytical expressions match quite well with numerically integrated values during a revolution. Typically for an orbit with perigee height, eccentricity and inclination of 421.9 km, 0.17524 and 30 degrees, respectively, maximum differences of 27 and 25 cm in semimajor axis computation are noted withJ ₃ andJ ₄ term during a revolution. For application purposes, the analytical solutions can be used for accurate onboard computation of state vector in navigation and guidance packages.     

Quasi-critical orbits for artificial lunar satellites

We study the problem of critical inclination orbits for artificial lunar satellites, when in the lunar potential we include, besides the Keplerian term, the J ₂ and C ₂₂ terms and lunar rotation. We show that, at the fixed points of the 1-D averaged Hamiltonian, the inclination and the argument of pericenter do not remain both constant at the same time, as is the case when only the J ₂ term is taken into account. Instead, there exist quasi-critical solutions, for which the argument of pericenter librates around a constant value. These solutions are represented by smooth curves in phase space, which determine the dependence of the quasi-critical inclination on the initial nodal phase. The amplitude of libration of both argument of pericenter and inclination would be quite large for a non-rotating Moon, but is reduced to <0°.1 for both quantities, when a uniform rotation of the Moon is taken into account. The values of J ₂, C ₂₂ and the rotation rate strongly affect the quasi-critical inclination and the libration amplitude of the argument of pericenter. Examples for other celestial bodies are given, showing the dependence of the results on J ₂, C ₂₂ and rotation rate.     

Preliminary Analysis of Photometric Variations of the Central Star of the Planetary Nebula Sh 2-71

We confirm the presence of regular UBV(RI)_C light variations of the object in the center of the planetary nebula Sh 2-71, with an improved period of P = 68.132 ± 0.005 days. The shapes and amplitudes of light curves, in particular colours, are briefly discussed.     

A Search for Variability in the HCCN to H2CO Ratio in Comet Hale-Bopp

We observed submillimeter lines of H₂CO and HCN in comet Hale-Bopp near perihelion. One of our goals was to search for short term variability. Our observations are suggestive, but not conclusive, of temporal and/or spatial changes in the coma's HCN/H₂CO abundance ratio of ∼25%. If due to spatial variability, the ratio on the sunward side of the coma is enhanced over other regions. If due to temporal variability, we find the bulk ratio in the coma changed in less than 16 hours. This revised version was published online in July 2006 with corrections to the Cover Date.     

Simulated responses of Pinus halepensis forest productivity to climatic change and CO2 increase using a statistical model

Tree ring chronologies provide long-term records of growth in natural environmental conditions and may be used to evaluate impacts of climatic change and CO₂ increase on forest productivity. This study focuses on 21 Pinus halepensis forest stands in calcareous Provence (in the south-east of France). A chronology of net primary productivity (NPP) both for the 20th century and for each stand was estimated using tree ring data (width and density). The response of each stand to climate in terms of NPP was statistically modelled using response functions. Anomalies between estimated NPP and NPP reconstructed by response functions were calculated to evaluate the fertilising effect of CO₂ increase on tree growth. The changes in anomalies during the 20th century were attributed to the effect of CO₂ increase. A multiplying factor (β) linking CO₂ concentration and stand productivity was then calculated, on the basis of the trend observed during the 20th century. In this study, the value of the β factor obtained under natural conditions (β=0.50) is consistent with those from controlled CO₂ enrichment experiments. Both response functions and the β factor were used to predict NPP changes for a 2×CO₂ scenario. The 2×CO₂ climate was obtained using predictions from Météo France's ARPEGE atmospheric general circulation model (AGCM) downscaled to Marseilles meteorological station. NPP increased significantly for nine stands solely when the climatic effect was taken into account. The main factors responsible for this enhancement were increased winter and early spring temperatures. When the fertilising effect of the CO₂ increase was added, NPP was significantly enhanced for 14 stands (i.e. NPP enhancement ranged from 8% to 55%). Although the effects of global change were slightly detectable during the 20th century, their acceleration is likely to lead to great changes in the future productivity of P. halepensis forests.     

A Radiative Pumping Scheme for OH and H<Subscript>2</Subscript>O Masers in Massive Star Forming Regions

Interstellar H₂O and OH masers associated with massive star-forming regions can be classified into three morphological types: isolated H₂O masers; isolated OH masers; and spatially overlapping OH/H₂O maser groups. In a large sample of star-forming regions the total number of maser groups of each type is approximately equal. In order to account for these statistics we propose a pumping scheme based on a broadband radiative pump which produces inverted populations of both OH and H₂O masers by a process involving predissociation and dissociation of H₂O. This scheme overcomes some drawbacks of earlier radiative pumping models, and may account for the association of OH and H₂O masers in massive star forming regions.