Coordinate gauge conditions in theN-body equations of motion in the first-order post-Newtonian approximation of general relativity

The explicit forms of the metric as well as the equations of motion in the first-order post-Newtonian approximation are worked out under several gauge conditions. It is noted that the so-called EIH (Einstein, Infeld, and Hoffman) equation of motion for an assembly ofN finite mass points mutually interacting via gravitation is identically obtained under three different gauge conditions, namely the harmonic gauge, Chandrasekhar gauge and a composite Chandrasekhar gauge used by Misneret al. (1970), even though the solutions for the metric are found to be all different. In one case the metric has a component apparently diverging, but finally generates regular affine connections so that the equations of motions become free from any singularity. By use of the Chandrasekhar gauge and his formulation, the second-order contribution to the acceleration of planets in the limit of test particle motion around the Sun has been calculated, the inclusion of which in the EIH set of the equations of motion would extend the relative accuracy of computing the total acceleration of any planet to better than one part in 10¹⁷.     

measurement of noise power spectrum in photon counting PMT's and the effect of the observed (1/f) noise on astronomical photometry

In astronomical photometry, the sensitivity of observations is limited by the dark counts of the photomultiplier tube. In the present work, the effect of dark count noise in photon counting systems is investigated by theory and experimental measurements. Dark counts are considered to be originating from two sources, namely: dc fluctuations and random pulses.Experimental measurements were carried out to determine noise effects in different operating regions of noise dominance. The results provide strong evidence that: in normal operating mode, where the effect of random pulses is dominant, dark counts do not follow Poisson statistics. The observed noise shows strong (1/f) power spectrum, where the observed noise power is found to increase with time of observation.The results are important in photon counting systems operating under dark count limited mode. The conclusions drawn can be useful in obtaining more accurate error estimates and in assessing astronomical photometric observations and data reduction techniques.     

Possible meteoroid streams associated with (69230) Hermes and 2002 SY50

The orbits of (69230) Hermes and 2002 SY₅₀ are similar and the Earth approaches both of them twice: at the end of October the local orbital minimum distances are smaller than 0.007 AU, and at the end of April the distances are smaller than 0.04 AU. This gives us opportunities to observe the meteors associated with these asteroids. Using the geocentric parameters of the orbital close encounters (the theoretical radiants) and our D _N distance function (Valsecchi et al. Mon. Not. R. Astron. Soc. 304 (1999) 743), we searched for meteoroids originated by Hermes and 2002 SY₅₀. A search among 1830 good quality photographic meteors gave negative results: we found no meteor dynamically similar to Hermes or 2002 SY₅₀. In a second search, done in a set of 62150 radio meteors, we applied two methods (M1, M2) and in both cases we found two streams; the streams found with the M1 method had 43 and 30 members, those found with the M2 method had 39 and 14 members. However, these results do not look convincing, due to the small number of common members in the corresponding streams. We therefore conclude that amongst the IAU meteors used in our search there are no compact streams associated with Hermes and 2002 SY₅₀.     

A measurement of the 362 GHz absorption line of Mars atmospheric H2O2

The 362.156 GHz absorption spectrum of H₂O₂ in the Mars atmosphere was observed on September 4 of 2003, employing the James Clerk Maxwell Telescope (JCMT) sub-millimeter facility on Mauna Kea, Hawaii. Radiative transfer analysis of this line absorption yields an average volume mixing ratio of 18±0.4 ppbv within the lower (0-30 km) Mars atmosphere, in general accordance with standard photochemical models (e.g., Nair et al., 1994, Icarus 111, 124-150). Our derived H₂O₂ abundance is roughly three times greater than the upper limit retrieved by Encrenaz et al. (2002, Astron. Astrophys. 396, 1037-1044) from infrared spectroscopy, although part of this discrepancy may result from the different solar longitudes (L_s) of observation. Aphelion-to-perihelion thermal forcing of the global Mars hygropause generates substantial (>200%) increases in HO_x abundances above ∼10 km altitudes between the L_s=112° period of the Encrenaz et al. upper limit measurement and the current L_s=250° period of detection (Clancy and Nair, 1996, J. Geophys. Res. 101, 12785-12590). The observed H₂O₂ line absorption weakens arguments for non-standard homogeneous (Encrenaz et al., 2002, Astron. Astrophys. 396, 1037-1044) or heterogeneous (Krasnopolsky, 2003a, J. Geophys. Res. 108; 2003b, Icarus 165, 315-325) chemistry, which have been advocated partly on the basis of infrared (8 μm) non-detections for Mars H₂O₂. Observation of Mars H₂O₂ also represents the first measurement of a key catalytic specie in a planetary atmosphere other than our own.     

On the stability of particular solutions of the singly averaged Hill problem

We consider the particular solutions of the evolutionary system of equations in elements that correspond to planar and spatial circular orbits of the singly averaged Hill problem. We analyze the stability of planar and spatial circular orbits to inclination and eccentricity, respectively. We construct the instability regions of both particular solutions in the plane of parameters of the problem.     

Modes to replace transitional asymptotic ray fields in a vertically inhomogeneous earth model

Summary. Asymptotic ray theory (ART) fails in transition regions near critically reflected, bottom glancing or caustic-forming rays in a vertically inhomogeneous layered earth. These deficiencies are repaired here by replacing the transitional ray fields with guided modes plus truncation remainders. Exact ray-mode equivalences and their high-frequency asymptotic approximations are formulated, and their validity and efficiency are verified by numerical comparisons for SH motion in a two-layer earth model comprised of an inhomogeneous sediment above an homogeneous semi-infinite bedrock.     

Self-similar solutions for the blast wave problem in radiative gasdynamics,I

Similarity solutions, describing the flow of a perfect gas behind spherical shock waves, are investigated including the radiation heat flux. The shock is assumed to be propagating in a medium at rest. Shock radius varies exponentially with time and density is inversely proportional to fifth power of the shock radius immediately ahead of the shock front.