Our previous analyses of radio Doppler and ranging data from distant spacecraft in the solar system indicated that an apparent anomalous acceleration is acting on Pioneer 10 and 11, with a magnitude ${a}_{P}\ensuremath{\sim}8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8} {\mathrm{c}\mathrm{m}/\mathrm{s}}^{2},$ directed towards the Sun. Much effort has been expended looking for possible systematic origins of the residuals, but none has been found. A detailed investigation of effects both external to and internal to the spacecraft, as well as those due to modeling and computational techniques, is provided. We also discuss the methods, theoretical models, and experimental techniques used to detect and study small forces acting on interplanetary spacecraft. These include the methods of radio Doppler data collection, data editing, and data reduction. There is now further data for the Pioneer 10 orbit determination. The extended Pioneer 10 data set spans 3 January 1987 to 22 July 1998. (For Pioneer 11 the shorter span goes from 5 January 1987 to the time of loss of coherent data on 1 October 1990.) With these data sets and more detailed studies of all the systematics, we now give a result of ${a}_{P}=(8.74\ifmmode\pm\else\textpm\fi{}1.33)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ ${\mathrm{c}\mathrm{m}/\mathrm{s}}^{2}.$ (Annual-diurnal variations on top of ${a}_{P},$ that leave ${a}_{P}$ unchanged, are also reported and discussed.)

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Study of the anomalous acceleration of Pioneer 10 and 11

Context. The Gaia spacecraft of the European Space Agency (ESA) has been securing observations of solar system objects (SSOs) since the beginning of its operations. Data Release 2 (DR2) contains the observations of a selected sample of 14,099 SSOs. These asteroids have been already identified and have been numbered by the Minor Planet Center repository. Positions are provided for each Gaia observation at CCD level. As additional information, complementary to astrometry, the apparent brightness of SSOs in the unfiltered G band is also provided for selected observations.Aims. We explain the processing of SSO data, and describe the criteria we used to select the sample published in Gaia DR2. We then explore the data set to assess its quality.Methods. To exploit the main data product for the solar system in Gaia DR2, which is the epoch astrometry of asteroids, it is necessary to take into account the unusual properties of the uncertainty, as the position information is nearly one-dimensional. When this aspect is handled appropriately, an orbit fit can be obtained with post-fit residuals that are overall consistent with the a-priori error model that was used to define individual values of the astrometric uncertainty. The role of both random and systematic errors is described. The distribution of residuals allowed us to identify possible contaminants in the data set (such as stars). Photometry in the G band was compared to computed values from reference asteroid shapes and to the flux registered at the corresponding epochs by the red and blue photometers (RP and BP).Results. The overall astrometric performance is close to the expectations, with an optimal range of brightness G ~ 12 − 17. In this range, the typical transit-level accuracy is well below 1 mas. For fainter asteroids, the growing photon noise deteriorates the performance. Asteroids brighter than G ~ 12 are affected by a lower performance of the processing of their signals. The dramatic improvement brought by Gaia DR2 astrometry of SSOs is demonstrated by comparisons to the archive data and by preliminary tests on the detection of subtle non-gravitational effects.

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Gaia Data Release 2. Observations of solar system objects

Spacecraft-to-spacecraft tracking observations from the Gravity Recovery and Interior Laboratory (GRAIL) have been used to construct a gravitational field of the Moon to spherical harmonic degree and order 420. The GRAIL field reveals features not previously resolved, including tectonic structures, volcanic landforms, basin rings, crater central peaks, and numerous simple craters. From degrees 80 through 300, over 98% of the gravitational signature is associated with topography, a result that reflects the preservation of crater relief in highly fractured crust. The remaining 2% represents fine details of subsurface structure not previously resolved. GRAIL elucidates the role of impact bombardment in homogenizing the distribution of shallow density anomalies on terrestrial planetary bodies.

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Gravity field of the Moon from the Gravity Recovery and Interior Laboratory (GRAIL) mission.

Mars high resolution gravity fields from MRO, Mars seasonal gravity, and other dynamical parameters

The research described in this publication was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. © 2014 California Institute of Technology. U.S. Government sponsorship acknowledged. abstract. — The planetary and lunar ephemerides DE430 and DE431 are generated by fitting numerically integrated orbits of the Moon and planets to observations. The present-day lunar orbit is known to submeter accuracy through fitting lunar laser ranging data with an updated lunar gravity field from the Gravity Recovery and Interior Laboratory (GRAIL) mission. The orbits of the inner planets are known to subkilometer accuracy through fitting radio tracking measurements of spacecraft in orbit about them. Very long baseline interferometry measurements of spacecraft at Mars allow the orientation of the ephemeris to be tied to the International Celestial Reference Frame with an accuracy of 0′′.0002. This orientation is the limiting error source for the orbits of the terrestrial planets, and corresponds to orbit uncertainties of a few hundred meters. The orbits of Jupiter and Saturn are determined to accuracies of tens of kilometers as a result of fitting spacecraft tracking data. The orbits of Uranus, Neptune, and Pluto are determined primarily from astrometric observations, for which measurement uncertainties due to the Earth’s atmosphere, combined with star catalog uncertainties, limit position accuracies to several thousand kilometers. DE430 and DE431 differ in their integrated time span and lunar dynamical modeling. The dynamical model for DE430 included a damping term between the Moon’s liquid core and solid mantle that gives the best fit to lunar laser ranging data but that is not suitable for backward integration of more than a few centuries. The ephemeris DE431 is similar to DE430 but was fit without the core/mantle damping term, so the lunar orbit is less accurate than in DE430 for times near the current epoch, but is more suitable for times more than a few centuries in the past. DE431 is a longer integration (covering years –13,200 to +17,191) than DE430 (covering years 1550 to 2650).

The Planetary and Lunar Ephemerides DE430 and DE431

Foreword. Preface. Acknowledgments. Introduction. Time Scales and Time Differences. Planetary Ephemeris, Small-Body Ephemeris, and Satellite Ephemerides. Spacecraft Ephemeris and Partials File. Geocentric Space-Fixed Position, Velocity, and Acceleration Vectors of Tracking Station. Space-Fixed Position, Velocity, and Acceleration Vectors of a Landed Spacecraft Relative to Center of Mass of Planet, Planetary System, or the Moon. Algorithms for Computing ET-TAI. Light-Time Solution. Angles. Media and Antenna Corrections. Calculation of Precision Light Times and Quasar Delays. Partial Derivatives of Precision Light Times and Quasar Delays. Observables. References. Acronyms. Index.

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Theodore D. Moyer

Papers

Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation

Light‐Time Solution