The asteroid ephemerides program at the U.S. Naval Observatory

The U.S. Naval Observatory has begun a program of ephemeris improvement and reference frame determination from the main belt asteroids. The program is, currently, starting out with a limited set of observations of the larger asteroids to determine the equator and equinox corrections for the USNO W1J00 transit circle observations catalog, and, if possible, improve the orbits of these asteroids based on this limited set of observations. For this project, transit circle observations of the Sun and the planets Mercury through Jupiter, are also being used to determine the equator, equinox, and ephemeris corrections, the next goal is to improve the orbits of the larger asteroids in the optical reference frame using observation series that cover a much longer period of time. This will allow the exploration of the differences between the dynamical reference frame based on radar observations of main belt asteroids and its relation with the optical reference frame. Other goals include the exploration of the mass distribution in the main asteroid belt from high precision observations, and the effect of this mass on the ephemerides of the major planets.     

Determinations of precession

Recent determinations of lunisolar precession and of the motion of the equinox are reviewed. Methods of determination are discussed which are based on proper motions referred to fundamental systems, on planetary motions, and on proper motions referred to galaxies. It is concluded that a new fundamental catalogue, which will replace the FK4 at some future date, should be based on revised values of precession and freed from errors in the motion of the equinox.Presented at IAU Colloquium No. 9, The IAU System of Astronomical Constants, Heidelberg, Germany, August 12–14, 1970.     

Precision of the ephemerides of outer planetary satellites

Ephemerides of planetary satellites are needed to address many problems. These ephemerides are used for subsequent observations. A comparison of the available ephemerides with new observations allows the accuracy of the former to be assessed. However, the precision of the ephemerides must be known a priori when solving the tasks. In this paper we formulate and solve the problem of estimating the precision of the ephemerides of outer planetary satellites derived from observations when applied up to the future moments.The methods of assessing the precision of ephemerides involve producing a set of samples of the same ephemeris inferred from observations with different samples of Monte Carlo generated random errors (RO) superimposed onto it. The statistical parameters of simulated observational errors are based on the results of the reduction of real satellite observations. We compute the deviations of the samples of the ephemeris from the standard ephemeris inferred from real observations and adopt the root-mean-square deviation of the apparent coordinates as the precision of the ephemeris. We also use alternative methods: one based on the matrix of covariances of parameter errors (RP), and another one based on bootstrap samples of observations (BS).We use three methods (RO, RP, and BS) to estimate the precision of the ephemerides of all the 107 outer planetary satellites over the 2010-2020 time interval. The precision of the ephemerides of different satellites varies from 0.05 to 4.0 arcsec. For a number of satellites new observations are of vital importance for maintaining the precision of the ephemerides at a level that would allow identification of satellites during the reduction of observations. For some satellites the precision of their ephemerides is of the order of the sizes of their orbits and such satellites can be considered to have been lost. We show that the method of bootstrap samples (BS) can give doubtful results in the cases where there are few observations, which covered a time interval that is shorter than the orbital period of the satellite.Our results suggest obtaining more precise ephemeris making new observations at the times of maximum estimated errors of the ephemeris.All the inferred estimates of the precision of ephemerides are available from the MULTI-SAT ephemeris server: www.imcce.fr/sat (IMCCE), www.sai.msu.ru/neb/nss/index.htm (SAI).     

Variation of the solar diameter from solar eclipse observations, 1715–1991

The diameter of the Sun may be measured at the time of a solar eclipse. We have performed an exhaustive search of the astronomical literature to find all existing observations of solar eclipses suitable for this purpose. We have also taken new observations by new techniques. We have undertaken a project to reduce them systematically, and in an automated, self-consistent way. This will produce determinations of the solar radius at the times of solar eclipses from 1715 to the present. Re-reduction, using newer ephemerides, of observations made in 1984 shows that the component of the residuals caused by the ephemeris is substantially reduced. This paper summarizes the research plan, outlines the detailed astronomical features included in the calculations, and presents the results available.     

Comet and asteroid ephemerides for spacecraft encounters

To a significant degree, the success of spacecraft missions to comets and asteroids depends upon the accuracy of the target body ephemerides. In turn, accurate ephemerides depend upon the quality of the astrometric data set used in determining the object's orbit and the accuracy with which the target body's motion can be modelled. Using error analyses studies of the target bodies for the NEAR, Muses-C, Clementine 2, Stardust, and Rosetta missions, conclusions are drawn as to how to minimize target body position uncertainties at the times of encounter, In general, these uncertainties will be minimized when the object has a good number of optical observations spread over several orbital periods. If a target body lacks a lengthy data interval, its ephemeris uncertainties can be dramatically reduced with the use of radar Doppler and delay data taken when the body is relatively close to the Earth. The combination of radar and optical angle data taken at close Earth distances just before a spacecraft encounter can result in surprisingly small target body ephemeris uncertainties.     

The use of radar observations of Near-Earth Asteroids in the determination of the dynamical equinox

Near-Earth Asteroids (NEAs) are Solar system special class objects attracting the attention of astronomical community especially during several of the last decades. To some extent the NEAs have an advantage over the minor planets of the main belt: due to close and regular approaches to the Earth the radar observations of NEAs can be obtained for the greater number of objects than for those of the main belt of the minor planets. In this paper the use of all available radar observations together with optical ones resulting in the combined data analysis solution is discussed for different problems such as the asteroid orbits and catalog orientation parameters determination. In particular the problem of the motion of the dynamical equinox in the Hipparcos reference system is considered. About 13000 radar and optical observations of 24 NEAs and main belt minor planets have been used to obtain the precise asteroid orbits, FK5 catalogue orientation parameters and the motion of the dynamical equinox from 1750 till 2000 in the Hipparcos system.     

Asteroid mass determination at Nikolaev Observatory

Masses of asteroids are topical for research in ephemerides computations and density evaluations. Details of the dynamical method are given for asteroid mass determinations. Preliminary masses of 13 asteroids, obtained with relative errors less than 50%, are presented from non-weighted least squares. Accuracy improvement of mass values for dynamical computations is evident using contemporary observations of 1999-2006. Statistics of the fitting ephemerides to the observations is also discussed.     

Enhancing the Accuracy of Numerical Integration of the Equations of Asteroid Motion with Perturbations from Major Planets and the Moon from the DE Ephemerides

The discontinuous behavior of coordinates of planets and the Moon and their derivatives, which are determined from their modern ephemerides, at the boundaries of adjacent interpolation intervals is illustrated using the example of the DE436 ephemerides. The numerical integration of the equations of motion of two asteroids demonstrates that the integration accuracy increases by several orders of magnitude if the step of numerical integration is matched to the boundaries of ephemeris interpolation intervals. In addition, an algorithm for ephemeris smoothing at the boundaries of interpolation intervals is developed and applied in order to eliminate the jumps of coordinates and their first-order derivatives emerging in extended- and quadprecision calculations. This algorithm allows one to remove the jumps of coordinates and their derivatives up to any given order. It is demonstrated that the use of ephemerides smoothed to the first-order derivatives in quad-precision calculations increases the accuracy of numerical integration by ~10 orders of magnitude.     

Updated Numerical Ephemerides of the Galilean Satellites of Jupiter

New versions of the ephemerides for the Galilean satellites of Jupiter (Io, Europa, Ganymede, and Callisto) constructed by numerically integrating the equations of motion of the satellites are presented. The satellite motionmodel takes into account the non-sphericity of Jupiter, the mutual perturbations of the satellites, and the perturbations from the Sun and major planets. The initial satellite motion parameters have been improved based on all the available series of ground-based optical observations spanning the interval 1891-2017, spacecraft observations, and radar observations. As a result, the coefficients of the expansion of the satellite coordinates and velocities in terms of Chebyshev polynomials in the interval 1891- 2025 have been obtained. The root-mean-square errors of the observations and the graphs of comparison of the constructed ephemerides both with the observations and with Lainey's numerical ephemerides are presented. The constructed ephemerides are publicly accessible.     

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.     

Jovian satellite positions from Hubble Space Telescope images

An accurate technique has been developed for measuring planetocentric positions of Jupiter's satellites from Wide Field/Planetary Camera images. Our method of finding the centers of the satellites and planet is based upon established limb-fitting techniques, but we have adapted those techniques to astrometry. We compare our limb-fitting results with previously published work and discuss its errors. A model ellipse is generated from the physical ephemeris of the planet including its phase defect. Then the planet center coordinates are computed by fitting the model to the limb observations using the method of least squares. A satellite position is determined similarly, and its offset from the planet is calculated. A total of 76 positions of the galileans satellites, the small moon Amalthea, and the shadows of Io and Ganymede cast on Jupiter have been measured on 61 images. Comparison between the observational results and JPL satellite ephemerides demonstrates the validity of this new method of analysis. The accuracy of the galilean satellite measurements is estimated to be 0.04 arcsec in right ascension and in declination.     

Orbits of new outer planetary satellites based on observations

More than 70 new distant satellites of major planets have been discovered over the past five years. Until recently, the Jet Propulsion Laboratory (JPL) in the USA was the only institution that modeled the motion of these satellites based on observational data and computed their ephemerides. New independent computations are needed to ensure the reliability and to assess the accuracy of satellite ephemerides. In this paper, the results of our determination of orbital parameters for 73 new distant satellites of major planets based on all available observations are reported and the adopted model of perturbing forces acting on a satellite is described. The satellite motions are computed via numerical integration. A special program—an ephemeris server—is used to compute the ephemerides of satellites, which are freely available to any user on the Internet at http://lnfm1.sai.msu.ru/neb/nss/index.htm. The server offers ample choice in terms of the form and composition of the ephemerides produced. The paper gives examples of deviations of the theory from observations and comparisons of our results with JPL ephemerides. Standard deviations of observational results from the theory are equal to 0.3–0.5 for most of the satellites. A comparison of our models of the motion of satellites with those developed at JPL shows that deviations in topocentric coordinates do not exceed 0.01 over a six-year interval.__________Translated from Astronomicheskii Vestnik, Vol. 39, No. 2, 2005, pp. 128–140.Original Russian Text Copyright © 2005 by Emelyanov, Kanter.     

Mass determinations for 27 asteroids by the dynamic method

The masses of 27 asteroids are found from optical and radar observations of perturbed asteroids (test particles). The masses of 18 objects have been previously determined by other authors in the construction of ephemerides EPM2011, DE423, and INPOP10a. Their values are based on observations of the delay time of radio signals from spacecraft. Our values have smaller errors for most of the asteroids. Comparing our results with the latest determinations based only on optical observations of asteroids also shows their accuracy.     

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.     

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.     

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.     

天球和地球历书原点

国际天球参考系的使用、观测精度的提高和方法的改善要求采用与地球轨道运动无关的运动赤道上的起算点，Guinot提出的非旋转原点可作为这样一种选择。非旋转原点依赖于天球参考极。IAU决定从2003年起采用天球中间极作为天球参考极。非旋转原点在天球参考系的使用，可给出在天球中间极赤道上的天球历书原点，非旋转原点在地球参考系的使用，可给出在天球中间极赤道上的地球历书原点。回顾了非旋转原点的概念、以历书原点为参考的天球参考系和地球参考系的坐标变换，经出了在微角秒精度下天球参考极的坐标和历书原点的位置，讨论了采用历书原点对测定UT1的影响，指出当岁差章动模型、天极补偿、分点改正得到改善时，基于历书原点的UT1定义不需要更改，从而保证了UT1的连续。     

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.     

On the accuracy of lunar ephemerides using the data provided by the future Russian lunar laser ranging system

The potential effect of the future Russian lunar laser ranging system (LLRS) on the accuracy of lunar ephemerides is discussed. In addition to the LLRS in Altai, several other observatories suitable for the LLRS installation are considered. The variation of accuracy of lunar ephemerides in the process of commissioning of new LLRS stations is estimated by mathematical modeling. It is demonstrated that the error in the determination of certain lunar ephemeris parameters may be reduced by up to 16% after seven years of operation of the Altai LLRS with a nearly optimal observational program.     

Transit timing variations and linear ephemerides of confirmed Kepler transiting exoplanets

We determine new linear ephemerides of transiting exoplanets using long-cadence de-trended data from quarters Q1 to Q17 of the Kepler mission. We analysed transit-timing variation(TTV) diagrams of 2098 extrasolar planets. The TTVs of 121 objects were excluded(because of insufficient datapoints, influence of stellar activity, etc.). Finally, new linear ephemerides of 1977 exoplanets from the Kepler archive are presented. A significant linear trend was observed on TTV diagrams of approximately 35% of the exoplanets studied. Knowing the correct linear ephemeris is key for successful follow-up observations of transits. Residual TTV diagrams of 64 analysed exoplanets show periodic variation, and 43 of these TTV planets were not previously reported.