Accurate analytical representation of Pluto modern ephemeris

An accurate development of the latest JPL’s numerical ephemeris of Pluto, DE421, to compact analytical series is done. Rectangular barycentric ICRF coordinates of Pluto from DE421 are approximated by compact Fourier series with a maximum error of 1.3 km over 1900–2050 (the entire time interval covered by the ephemeris). To calculate Pluto positions relative to the Sun, a development of rectangular heliocentric ICRF coordinates of the Solar System barycenter to Poisson series is additionally made. As a result, DE421 Pluto heliocentric positions by the new analytical series are represented to an accuracy of better than 5 km over 1900–2050.     

An analytical representation of non-gyrotropic distributions and related space applications

Clear signature of non-gyrotropic energetic electron distributions was found by ISEE 1 and ISEE 2 spacecrafts just upstream of the Earth's bow shock and recently detected by in situ observations of the WIND plasma experiment. On the other hand, the appearance of non-gyrotropic ion velocity distributions is well established in the magnetotail providing evidence of magnetic reconnection processes. Motivated by these findings we introduce an analytical representation of non-Maxwellian/non-gyrotropic distribution functions, accurately fitting the characteristics of observations, where Maxwellians are recovered as special case of these highly general velocity space distributions. In particular, the analytical distribution function model can serve as basis of detailed wave-particle interaction analysis and of studies of the physical background of the evolution of both, non-gyrotropic electron and ion distributions, which is discussed for various space plasma environments.     

An approximate analytical representation of the atmospheric gamma-ray flux at balloon altitudes

The general behaviour of the atmospheric -ray flux as a function of the residual atmosphere, zenith angle, and photon energy is approximated with simple analytical expressions. The free parameters are determined by comparison with the most recent models and the existing experimental measurements. The resulting formulae have an accuracy comparable to the mutual consistency of the available pieces of information, and at the same time are very convenient to use in numerical simulations.     

Improvement of the numerical lunar ephemeris with laser ranging data

Analysis of lunar laser ranging data is underway at several institutions. We describe here our efforts at improving the numerical ephemeris of Moon, based on over three years' span of data. Orbit generation and correction procedures are discussed briefly. Comparisons of the new ephemeris with observations and with a widely available ephemeris are illustrated. The standard deviation of the observation residuals is 7 m.Communication presented at the conference on Lunar Dynamics and Observational Coordinate Systems held January 15–17, 1973 at the Lunar Science Institute, Houston, Tex., U.S.A.     

Russian lunar ephemeris EPM-ERA 2012

The paper describes the lunar ephemeris EPM-ERA 2012. It is a part of the Ephemerides of Planets and the Moon (EPM) developed at the Institute of Applied Astronomy (IAA) of the Russian Academy of Sciences (RAS). In order to construct EPM-ERA 2012, 17580 lunar laser ranging (LLR) observations for 1970–2012 have been processed including 21 observations from the Lunokhod 1 reflector found by the Lunar Reconnaissance Orbiter (LRO) at the end of 2010. EPM-ERA 2012 is compared with American ephemerides DE403, DE405, DE421 ephemeris, and the French ephemeris INPOP10. The possibility of the use of the ephemeris EPM-ERA 2012 to address contemporary problems of ephemeris astronomy is considered.     

The improvement of the lunar ephemeris

At present the fundamental lunar ephemeris is based on Brown's theory of the motion of the Moon with improvements based on the bypassing of Brown's Tables, the removal of the great empirical term, the substitution of the relevant constants of the IAU system of astronomical constants and the retransformation of Brown's series in rectangular coordinates to spherical coordinates. Even so this ephemeris does not represent adequately the recent range and range-rate radio observations, and it will be inadequate for use in the analysis of laser observations of corner reflectors on the Moon. Numerical integrations for these purposes have already been made at the Jet Propulsion Laboratory, but improved theoretical developments are also required; new solutions of the main problem are in hand elsewhere. Work at H.M. Nautical Almanac Office is aimed at obtaining improved values of the constants of the lunar orbit by a rediscussion of occultation observations made since 1943 and at the redevelopment of the series for the planetary perturbations using more precise theories of the motion of the Sun and planets. The techniques and preliminary results of exploratory numerical integrations were briefly described.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, 17–23 August, 1969.     

Corrections to the improved lunar ephemeris

Based primarily upon the formation of new conditional equations using analytical partial derivatives of the moon's mean elements, meridian circle observations of the moon from 1952–67 have been examined to determine corrections to the constants of lunar theory and to the fundamental coordinate system (FK4). With certain exceptions, the new corrections are in agreement with those published earlier by the author. Systematic corrections to FK4 are surprisingly large, although in agreement with some other recent determinations. New corrections to the lunar ephemeris, resulting from the discussion, are also presented.     

On the orientation of ephemeris reference frames

One may construct complete planetary and lunar ephemerides, referred to the equator and dynamical equinox of some epoch, strictly from ranging data alone. Such an ephemeris would be completely independent from any optical data and therefore independent of any stellar catalogue. By using such an ephemeris to then analyse optical observations, one could theoretically derive many of the pertinent features of the catalogue system to which the optical observations are referred. Such features include the equinox offset, equinox motion and systematic proper motion errors. In practice, the optical observations are used in the fitting process, but essentially the same determinations may be made.This paper presents estimates of the equinox offset and equinox motion of the FK4 as determined by the ephemeris fitting process and compares them with corresponding determinations by Fricke. No significant differences are found. Further, it is indicated how one may also estimate a value for precession and the value of the obliquity from the ephemerides. These' values are also compared with the presently adopted ones.     

The representation of magnetic field lines from magnetograph data

Several methods currently used to extrapolate the structure of the solar magnetic field from surface measurements are examined and compared. In particular, the differences between the methods of Schmidt for potential fields and of Nakagawa and Raadu for force-free fields are explained. Suggestions are made regarding the use of these theoretical procedures in making physical conclusions.     

An analytical solution for Kepler's problem

In this paper, we present a framework which provides an analytical (i.e. infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits all singular variables which otherwise would yield discontinuities. This method is based on two simple real functions for which the derivative rules are only required to be known, all other applications – e.g. calculating the orbital velocities, obtaining the partial derivatives of radial velocity curves with respect to the orbital elements – are thereafter straightforward. As it is shown, the presented formalism can be applied to find optimal instants for radial velocity measurements in transiting explanatory systems to constrain the orbital eccentricity as well as to detect secular variations in the eccentricity or in the longitude of periastron.     

An analytical theory of planetary rotation rates

An approximate analytical theory is derived for the rate of rotation acquired by a planet as it grows from the solar nebula. This theory was motivated by a numerical study by Giuli, and yields fair agreement with his results. The periods of planetary rotation obtained are proportional to planetesimal encounter velocity, and appear to suggest lower values of this velocity than are commonly assumed to have existed during planetary formation.     

An exact analytical solution of Kepler's equation

Complex-variable analysis is used to develop an exact solution to Kepler's equation, for both elliptic and hyperbolic orbits. The method is based on basic properties of canonical solutions to appropriately posed Riemann problems, and the final results are expressed in terms of elementary quadratures.     

An analytical averaged model of orbital resonance

After having examined the characteristics of some models used at present in the study of orbital resonance, we propose an analytical averaged model, which offers certain convenience in the study of both the characteristics and the evolution of resonance.     

A revised orbital ephemeris for HAT-P-9b

We present here three transit observations of HAT-P-9b taken on 14 February 2010 and 05 April 2010 UT from the University of Arizona’s 1.55 m Kuiper telescope on Mt. Bigelow. Our two light curves were obtained in the Arizona-I filter for all our observations, and underwent the same reduction process. Both transits occurred approximately 24 min earlier than expected from the ephemeris of Shporer et al. (2009). However, due to the large time span between our observed transits and those of Shporer et al. (2009), a 6.5 s shift downwards in orbital period from the value of Shporer et al. (2009) is sufficient to explain all available transit data. We find a new period of 3.922814 ± 0.000002 days for HAT-P-9b, an order of magnitude more precise than previous measurements, with no evidence for significant nonlinearities in the transit period.     

On the ephemeris of the eclipsing polar HU Aquarii

The magnetic cataclysmic variable HU Aquarii displayed pronounced quasi‐periodic modulations of its eclipse timing. These were interpreted in terms of the light‐travel time (LTT) effect caused by a circumbinary planet or planetary system. We report new photometric observations that revealed another precise eclipse timing for the October 2013 epoch, the first obtained in a high accretion state after many years in low or intermediate states. The eclipse was observed to occur earlier by 95.3 ± 2.0 s or 62.8 ± 2.0 s than expected for an assumed linear or quadratic ephemeris, respectively. The implied apparent strong evolution of the orbital period calls for a revision of the current planetary model or the planetary parameters. The object deserves further monitoring to uncover the true nature of the observed variability and to constrain the properties of the proposed planet or planetary system. The new observations prove that advanced amateur equipment can successfully be used in the growing field of planet search in wide circumbinary orbits via the LTT effect. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An analytical approach to fluctuations in showers

We review the problem of fluctuations in particle shower theory. By using a generalization of Furry equation, we find relations between the n-particle correlation function and the number of particles average or 1-particle correlation function. Such relations show that the average is the only independent dynamical variable. We also develop a numerical code to solve the equation for the correlation functions and compare the results with those from a Monte Carlo simulation which show a perfect agreement between both methods.     

An analytical simulation of the geosynchronous plasma environment

A procedure for analytically simulating the parameters necessary to characterize the geosynchronous plasma is developed in terms of the daily A_p index and local time. Although based on a limited set of ATS-5 data, the simulation adequately models the simultaneous variations in the warm plasma (50 eV–50 keV) electron and ion populations during injection events. Developed primarily to estimate the varying potentials expected on a shadowed, electrically isolated surface, the simulation can also be employed in a variety of cases where knowledge of the general characteristics of the geosynchronous plasma is necessary.     

Spherical harmonic representation of the gravity field from dynamic satellite data

Spherical harmonics are the natural parameters for the Earth's gravity field as sensed by orbiting satellites, but problems of resolution arise because the spectrum of effects is narrow and unique to each orbit. Comprehensive gravity models now contain many hundreds of thousands of observations from more than thirty different near-Earth artificial satellites. With refinements in tracking systems, newer data is capable of sensing the spherical harmonics of the field experienced by these satellites to very high degree and order. For example, altimeter, laser and satellite-tracking-satellite systems contain gravitational information well above present levels of satellite gravity field recovery (l = 20), but significant aliasing results because the orbital parameters are too restricted compared to the large number of spherical harmonics.It is shown however that the unique spectrum of information for each satellite contained within a comprehensive spherical harmonic model can be represented by simple gravitational constraint equations (lumped harmonics). All such constraints are harmonic in the argument of perigee (ω) with constants determinable directly from tracking data or reconstituted from the comprehensive solution:

$\text{(C}{}^1\text{, S}{}^1\text{) = (C}{}_{\mathrm{o}}\text{, S}{}_{\mathrm{o}}\text{) + Σ}{}_{\mathrm{i}}\text{= 1 (C}{}_{\mathrm{Ci}}\text{, S}{}_{\mathrm{Ci}}\text{) cos i ω + (C}{}_{\mathrm{Si}}\text{, S}{}_{\mathrm{Si}}\text{) sin i ω}$

. The constants are simple linear combinations of the geopotential harmonics. Through these lumped harmonics any satellite gravity field can be decomposed and then uniformly extended to any degree or tailored to a given orbit without reintegration of the trajectory and variational equations. They also make possible the inclusion of information into the field from special deep resonance passages, long arc zonal analyses, and satellites unique to other models. Numerous examples of the derivation, combination, extension and tailoring of the harmonics are presented. The importance of using data spanning an apsidal period is emphasized.     

An analytical theory for tesseral gravitational harmonics

An analytical method has been developed for the treatment of tesseral harmonic perturbations. The procedure is an iterative Lie transformation technique which avoids the typical eccentricity expansions as well as the numerical singularities normally associated with resonance conditions. At each iteration, terms of the perturbing potential become multiplied by the ratio of the satellite's orbital period to the earth's rotational period. Following a suitable number of iterations, the potential is deemed to be sufficiently small that it may be ignored, with the tesseral effects captured in the transformation. This revised version was published online in July 2006 with corrections to the Cover Date.