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.     

The effect of various solar ephemerides on equator and equinox solutions from observations of the Sun with the reversible transit circle at Cape observatory from 1907 to 1959

Observations of the Sun were made with the Cape reversible transit circle from 1907 to 1959. We have made least squares solutions for six unknowns viz., equator and equinox corrections and corrections to earth orbital parameters including the ephemeris mean longitude of the Sun, the mean obliquity of the ecliptic, the mean longitude of perihelion, and the mean eccentricity of the earth's orbit based on Newcomb's, DE102, and DE200 Ephemerides for each of six catalogs of observations made during that period. The six unknowns are also determined simultaneously for the six catalogs taken together. The six catalogs are absolute, in that methods of observation and reduction were adopted in such a way as to produce a system of results not closely dependent on the adopted system of assumed clock and azimuth star positions.The observed equator and equinox corrections from a comparison of DE200 with the Cape Sun observations referred to an improved FK4 system are –0.07±0.01 arcsec and –0.20±0.04 arcsec, respectively, at the mean epoch of observation, 1933.02. The time rate of change of the equator correction was not significant. The time rate of change of the observed equinox is –1.02±0.30 arcsec per century.The observed equinox correction of the DE102 at 1933.02 is –0.41±0.04 arcsec, which is 0.5 arcsec less than the NEWCOMB (Herget) equinox correction. This confirms the result based on Washington Sun observations.     

Approximation methods in celestial mechanics. Application to Pluto's motion

Various methods of approximation for the computation of planetary perturbations are investigated: Fourier, Fourier-Chebyschev and Legendre. Application is made to Pluto's motion. Based upon JPL's ephemeris DE200, Pluto's mean elements are provided and also a compact ephemeris covering 2 centuries.     

On the precession expressions based on the de ephemeris

Since 1984, the new IAU (1976) System of Astronomical Constants has become effective; meanwhile, the new lunar and planetary ephemerides (DE200/LE200) have been introduced into the Astronomical Almanac. In order to obtain the best fit of these ephemerides to the observational data, some modifications to the constants were made (Kaplan 1961). The modified values of these constants have been accepted by many users (particularly in the Merit Project), (Melbourne et al. 1983), although there has not been any new resolution of IAU. To avoid these inconsistencies, it seems to be necessary to rediscuss the adopted value of some astronomical constants in the new system. This paper discusses the problems for selection of the precession quantities and derives the precession expressions based on the motion of ecliptic from the DE ephemeris.     

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.     

An analytical representation of ephemeris data

An algebraic method for the resolution of tabulated function into a class of elementary functions is examined on the high precision ephemeris data from the JPL DE 200.     

Principal algorithms for the control of Kourovka Observatory SBG camera

We report the algorithms used in the software of the upgraded SBG camera. Fast-moving satellites are observed in the “rotated” coordinate system where one of the axes points towards the pole of the object’s orbit. The ephemeris for this coordinate system is computed based on the ephemeris for the equatorial coordinate system using special transition matrices. The parameters of the matrices are the coordinates of the orbital pole, which are found by averaging the vector products of the radius vectors of the consecutive positions of the satellite. The position angle of the image is computed as the difference between the hour angles of the orbital and celestial poles in the coordinate system, the pole of which coincides with the optical center of the frame. The speed of object tracking is computed via quadratic interpolation of the ephemeris in the “rotated” coordinate system.     

Multiscale Analysis of the Instantaneous Eccentricity Oscillations of the Planets of the Solar System from 13 000 BC to 17 000 AD

Astronomy Letters - The high-resolution Jet Propulsion Laboratory DE431 and DE432 planetary ephemeris are used to evaluate the instantaneous eccentricity functions of the orbits of the planets of...     

Photographic observations of Saturn’s moons at the MAO NAS of Ukraine in 1961–1990

A catalog of 1385 astrometric positions of Saturn’s moons S2–S9 has been compiled with Tycho-2 as a reference frame from photographic observations obtained at the Main Astronomical Observatory, National Academy of Sciences of Ukraine, in 1961–1990. Astronegatives have been digitized with an Epson Expression 10000XL commercial scanner in 16-bit grayscale with a resolution of 1200 dpi. Reduction has been performed in the LINUX-MIDAS-ROMAFOT software supplemented with additional modules. The internal positional accuracy of the reduction is 0.09…0.23′′ for both coordinates and 0.27…0.37^m for the photographic magnitudes of the Tycho-2 catalog. The calculated topocentric positions of the moons are compared online with the IMCCE ephemeris data (DE405 + TASS1,7). Moon-minus-moon differential coordinates are found for most of the moons and compared with theoretical data (http://lnfm1.sai.msu.ru/neb/nss/nssephmr.htm).     

Methode rapide de calcul d'une trajectoire de petite planete par l'approximation de tchebycheff,et son ajustement aux observations

It is shown that the application of the Chebyshev theory of approximation to the calculation of the orbit of a minor planet allows the production of a compact ephemeris, based on data gathered over only a short time, which is both accurate, and simple and rapid to produce. Adjustment of numerical data to fit observational results is readily performed. Using Clenshaw's algorithm, an ephemeris may even be worked out on a pocket calculator. Further applications of Chebyshev polynomials to the calculation of parameters usually obtainable only by interpolation of classical ephemerides, and to the calculation of minor planetary orbits from observations of short duration by an orbiting telescope are discussed.

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Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978.     

The INPOP10a planetary ephemeris and its applications in fundamental physics

Compared to the previous INPOP versions, the INPOP10a planetary and lunar ephemeris has several improvements. For the planets of our Solar System, no big change was brought in the dynamics but improvements were implemented in the fitting process, the data sets used in the fit and in the selection of fitted parameters. We report here the main characteristics of the planetary part of INPOP10a like the fit of the product of the solar mass with the gravitational constant ( GM_\odot{{\rm GM}_{\odot}}) instead of the astronomical unit. Determinations of PPN parameters as well as adjustments of the Sun J2 and of asteroid masses are also presented. New advances of nodes and perihelia of planets were also estimated and are given here. As for INPOP08, INPOP10a provides to the user, positions and velocities of the planets, the Moon, the rotation angles of the Earth and the Moon as well as TT-TDB Chebyshev polynomials at .     

Astrometric observations of the Uranian satellites with the Faulkes Telescope North in 2007 September

The results of astrometric observations of the main Uranian satellites taken with the Faulkes Telescope North are presented. A median filter algorithm was applied to subtract a scattered-light halo caused by Uranus. The Two-Micron All-Sky Survey (2MASS) and USNO-B1.0 were used as reference catalogues. The mean value of the differences between the equatorial coordinates of the satellites determined with 2MASS and USNO-B1.0 is close to 200 mas. A comparison of the observed equatorial coordinates of the satellites and their relative positions with ephemerides based on different combinations of theories of motion of Uranus and its satellites (DE405+GUST86, DE405+GUST06, INPOP+GUST86, INPOP+GUST06) was performed. The satellites' positions obtained with respect to 2MASS are in better agreement with theories. The values of (O−C) of the equatorial coordinates determined with the 2MASS are mainly less than 100 mas. The majority of (O−C) of relative positions are within ±50 mas. The mean values of the standard errors of (O−C) are within 20 to 60 mas.     

用切比雪夫曲线拟合导航卫星广播星历

提出用一种基于切比雪夫曲线多项式拟合的方法,来拟合导航卫星广播星历。该方法对解决 GEO导航卫星的小倾角、小偏心率问题特别有效,并具有精度高、使用方便等特点。     

PMOE精密行星历表研究进展

本文扼要介绍了PMOE行星历表研究当前的进展和工作 ,给出了PMOE2 0 0 2与DE40 5历表的比较。     

Astrometry of Iapetus, Ariel, Umbriel, and Titania from eclipses and occultations

Highly accurate astrometric positions obtained from eclipses and occultations of planetary satellites are reported. These measurements may be used to test existing ephemerides, to improve upon them, and to fit system constants such as satellite masses and planetary zonal harmonics. Eclipse and occultation photometry of 5 uranian satellite mutual events has resulted in precise astrometry for 3 of these moons. Relative satellite positions were determined with an uncertainty of less than 10 milli-arcseconds for 4 of the events. These observations plus two additional data from C. Miller and N.J. Chanover (private communication) indicate that predictions based on the SPICE [Acton, C.H., 1996. Planet. Space Sci. 44, 65-70] ephemeris URA083 and those from the LA06 ephemeris in a paper by Arlot et al. [Arlot, J.-E., Lainey, V., Thuillot, W., 2006. Astron. Astrophys. 456, 1173-1179] are significantly more accurate than predictions generated by Christou [Christou, A.A., 2005. Icarus 178, 171-178] using the GUST86 ephemeris in the along-track component of motion. The observations indicate that Ariel, Umbriel and Titania are lagging behind their predicted positions for all of the ephemerides, but by varying distances and significance levels. Analysis of data recorded by Hidas et al. [Hidas, M.G., Christou, A.A., Brown, T.M., 2008. Mon. Not. R. Astron. Soc. 384, L38-L40] suggests a similar lag for Oberon. Photometry recorded during the ingress portion of a saturnian eclipse of Iapetus on 2007 May 5 indicates that the middle of the event occurred at geocentric UTC 02:14:58. At that moment the center of the satellite disk facing the Sun was intersected by a solar-centered ray refracted at a minimum altitude of 240 km above the 1-bar pressure level in the planet's atmosphere. The uncertainty in the timings due to observational scatter was only 5 s which equates to 16 km of Iapetus motion, but other factors increased the overall uncertainty to 111 km or 16 milli-arcseconds at the distance of Saturn from the Sun. The astrometric result is fit very well by the SPICE ephemeris SAT288.     

Assessment of the resonant perturbation errors in Galilean satellite ephemerides using precisely measured eclipse times

Astrometric satellite positions are derived from timings of their eclipses in the shadow of Jupiter. The 548 data points span 20 years and are accurate to about 0.006 arcsec for Io and Europa and about 0.015 arcsec or better for Ganymede and Callisto. The precision of the data set and its nearly continuous distribution in time allows measurement of regular oscillations with an accuracy of 0.001 arcsec. This level of sensitivity permits detailed evaluation of modern ephemerides and reveals anomalies at the 1.3 year period of the resonant perturbations between Io, Europa and Ganymede. The E5 ephemeris shows large errors at that period for all three satellites as well as other significant anomalies. The L1 ephemeris fits the observations much more closely than E5 but discrepancies for the resonant satellites are still apparent and the measured positions of Io are drifting away from the predictions. The JUP230 ephemeris fits the observations more accurately than L1 although there is still a measurable discordance between the predictions and observations for Europa at the resonance period.     

Detecting the errors in solar system ephemeris by pulsar timing

Pulsar timing uses planetary ephemerides to convert the measured pulse arrival time at an observatory to the arrival time at the Solar System barycenter(SSB). Since these planetary ephemerides cannot be perfect, a method of detecting the associated errors based on a pulsar timing array is developed. By using observations made by an array of 18 millisecond pulsars from the Parkes Pulsar Timing Array, we estimated the vector uncertainty from the Earth to the SSB of JPL DE421, which reflects the offset of the ephemeris origin with respect to the ideal SSB, in different piecewise intervals of pulsar timing data, and found consistent results. To investigate the stability and reliability of our method, we divided all the pulsars into two groups. Both groups yield largely consistent results, and the uncertainty of the Earth-SSB vector is several hundred meters, which is consistent with the accuracy of JPL DE421. As an improvement in the observational accuracy, pulsar timing will be helpful to improve the solar system ephemeris in the future.     

Estimation of the lunar physical librations

The recent long-term integration of JPL ephemeris DE403/LE403 yielded lunar physical librations covering 6000 years. A Fourier analysis of a 718-year subset of this span produced estimates of the component frequencies of the forced and free librations. A subsequent iterative least-squares estimation procedure provided precise values for phases and for time-varying amplitudes and frequencies. Two free libration modes were found; presence of a third is possible but close to the noise.     

The Moon’s physical librations and determination of their free modes

The Lunar Laser Ranging experiment has been active since 1969 when Apollo astronauts placed the first retroreflector on the Moon. The data accuracy of a few centimeters over recent decades, joined to a new numerically integrated ephemeris, DE421, encourages a new analysis of the lunar physical librations of that ephemeris, and especially the detection of three modes of free physical librations (longitude, latitude, and wobble modes). This analysis was performed by iterating a frequency analysis and linear least-squares fit of the wide spectrum of DE421 lunar physical librations. From this analysis we identified and estimated about 130–140 terms in the angular series of latitude librations and polar coordinates, and 89 terms in the longitude angle. In this determination, we found the non-negligible amplitudes of the three modes of free physical libration. The determined amplitudes reach 1.296′′ in longitude (after correction of two close forcing terms), 0.032′′ in latitude and 8.183′′ × 3.306′′ for the wobble, with the respective periods of 1056.13 days, 8822.88 days (referred to the moving node), and 27257.27 days. The presence of such terms despite damping suggests the existence of some source of stimulation acting in geologically recent times.     

Determining parameters of Moon’s orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models

The aim of this work is to combine the model of orbital and rotational motion of the Moon developed for DE430 with up-to-date astronomical, geodynamical, and geo- and selenophysical models. The parameters of the orbit and physical libration are determined in this work from lunar laser ranging (LLR) observations made at different observatories in 1970–2013. Parameters of other models are taken from solutions that were obtained independently from LLR. A new implementation of the DE430 lunar model, including the liquid core equations, was done within the EPM ephemeris. The postfit residuals of LLR observations make evident that the terrestrial models and solutions recommended by the IERS Conventions are compatible with the lunar theory. That includes: EGM2008 gravitational potential with conventional corrections and variations from solid and ocean tides; displacement of stations due to solid and ocean loading tides; and precession-nutation model. Usage of these models in the solution for LLR observations has allowed us to reduce the number of parameters to be fit. The fixed model of tidal variations of the geopotential has resulted in a lesser value of Moon’s extra eccentricity rate, as compared to the original DE430 model with two fit parameters. A mixed model of lunar gravitational potential was used, with some coefficients determined from LLR observations, and other taken from the GL660b solution obtained from the GRAIL spacecraft mission. Solutions obtain accurate positions for the ranging stations and the five retroreflectors. Station motion is derived for sites with long data spans. Dissipation is detected at the lunar fluid core-solid mantle boundary demonstrating that a fluid core is present. Tidal dissipation is strong at both Earth and Moon. Consequently, the lunar semimajor axis is expanding by 38.20 mm/yr, the tidal acceleration in mean longitude is \(-25.90 {{}^{\prime \prime }}/\mathrm{cy}^2\), and the eccentricity is increasing by \(1.48\times 10^{-11}\) each year.