Solar System Ephemeris Research Articles

Velocity-dependent inverse cubic force and solar system gravity tests

Higher mass dimension terms in an effective field theory framework for tests of spacetime symmetries are studied. Using a post-Newtonian expansion method, we derive the spacetime metric and the equations of motion for a binary system. This reveals an inverse cubic force correction to General Relativity that depends on the velocity of the bodies in the system. The results are studied in the context of laboratory and space-based tests including the effects on solar-system ephemeris, laser ranging observations, and gravimeter tests. This work reveals the coefficient combinations for mass dimension 5 operators controlling CPT violation for gravity that can be measured using analysis from these tests. Other tests including light propagation can be used to probe these coefficients. Sensitivity estimates are provided and the results are contrasted with the minimal mass dimension 4 terms in the gravity sector.

Solar-System Studies with Pulsar Timing Arrays

AbstractHigh-precision pulsar timing is central to a wide range of astrophysics and fundamental physics applications. When timing an ensemble of millisecond pulsars in different sky positions, known as a pulsar timing array (PTA), one can search for ultra-low-frequency gravitational waves (GWs) through the spatial correlations that spacetime deformations by passing GWs are predicted to induce on the pulses’ times-of-arrival (TOAs). A pulsar-timing model, requires the use of a solar-system ephemeris (SSE) to properly predict the position of the solar-system barycentre, the (quasi-)inertial frame where all TOAs are referred. Here, I discuss how while errors in SSEs can introduce correlations in the TOAs that may interfere with GW searches, one can make use of PTAs to study the solar system. I discuss work done within the context of the European Pulsar Timing Array and the International Pulsar Timing Array collaborations. These include new updates on the masses of planets from PTA data, first limits on masses of the most massive asteroids, and comparisons between SSEs from independent groups. Finally, I discuss a new approach in setting limits on the masses of unknown bodies in the solar system and calculate mass sensitivity curves for PTA data.

Comparison of pulsar positions from timing and very long baseline astrometry

Pulsar positions can be measured with high precision using both pulsar timing methods and very-long-baseline interferometry (VLBI). Pulsar timing positions are referenced to a solar-system ephemeris, whereas VLBI positions are referenced to distant quasars. Here we compare pulsar positions from published VLBI measurements with those obtained from pulsar timing data from the Nanshan and Parkes radio telescopes in order to relate the two reference frames. We find that the timing positions differ significantly from the VLBI positions (and also differ between different ephemerides). A statistically significant change in the obliquity of the ecliptic of $2.16\pm0.33$\,mas is found for the JPL ephemeris DE405, but no significant rotation is found in subsequent JPL ephemerides. The accuracy with which we can relate the two frames is limited by the current uncertainties in the VLBI reference source positions and in matching the pulsars to their reference source. Not only do the timing positions depend on the ephemeris used in computing them, but also different segments of the timing data lead to varying position estimates. These variations are mostly common to all ephemerides, but slight changes are seen at the 10$\mu$as level between ephemerides.

All correlations must die: Assessing the significance of a stochastic gravitational-wave background in pulsar timing arrays

We present two methods for determining the significance of a stochastic gravitational-wave (GW) background affecting a pulsar-timing array, where detection is based on evidence for quadrupolar spatial correlations between pulsars. Rather than constructing noise simulations, we eliminate the GWB spatial correlations in the true datasets to assess detection significance with all real data features intact. In our first method, we perform random phase shifts in the signal-model basis functions. This phase shifting eliminates signal phase coherence between pulsars, while keeping the statistical properties of the pulsar timing residuals intact. We then explore a method to null correlations between pulsars by using a "scrambled" overlap-reduction function in the signal model for the array. This scrambled function is orthogonal to what we expect of a real GW background signal. We demonstrate the efficacy of these methods using Bayesian model selection on a set of simulated datasets that contain a stochastic GW signal, timing noise, undiagnosed glitches, and uncertainties in the Solar system ephemeris. Finally, we introduce an overarching formalism under which these two techniques are naturally linked. These methods are immediately applicable to all current pulsar-timing array datasets, and should become standard tools for future analyses.

Evaluation of a possible upgrade of the IAU 2006 precession

Context. The International Astronomical Union (IAU) adopted a new precession model at its 2006 General Assembly. After more than ten years since the publication of the so-called IAU 2006 precession, we have noticed progress in solar system ephemerides and geophysical observations, which can be used to refine the precession model. Another progress is the increase by 30% since 2003, of the length of the very long baseline interferometry (VLBI) observations to be compared with the theoretical model. Aims. The aim of this paper is to investigate the possibility of upgrading the IAU 2006 precession model based on new solutions of the Earth-Moon barycenter (EMB) motion, new theoretical contributions to the precession rates, and the revised J 2 long-term variation obtained from the satellite laser ranging (SLR). Methods. The new precession expressions for the ecliptic are derived by fitting the new analytical planetary theory VSOP2013 to the numerical ephemerides DE422 or INPOP10a. The solution for the precession of the equator was obtained by integrating the dynamical precession equations with the use of an updated Earth model including the J 2 quadratic long-term variation. The new precession expressions (denoted LC solution in this paper) are compared with the IAU 2006 model by using the most accurate VLBI observations up to 2015. Results. For the precession of the ecliptic, the changes in the new solutions with respect to the IAU 2006 are about several tens of microarcseconds in the linear terms of P A and Q A . The upgraded precession of the equator is such that the quadratic and cubic terms in the quantity ψ A differ significantly from IAU 2006 due to the revised J 2 model. The statistics of the VLBI celestial pole offsets (1979–2015) and least squares fits with different empirical models, show that the LC precession is slightly more consistent with the VLBI observations, but the improvement relative to the IAU 2006 model is not definitely convincing at present. Conclusions. The upgraded LC precession obtained with the latest theoretical and observational improvements has shown some advantages with respect to the IAU 2006 model. However, due to negligible changes in the precession of the ecliptic and large uncertainties in the J 2 variation, we recommend that the standard IAU 2006 model be retained for practical use and continuity reason. The next precession-nutation model should be constructed with a uniform dynamical approach in the framework of ICRF3 and Gaia reference frame and without the use of a conventional ecliptic.

Robust approximation of image illumination direction in a segmentation-based crater detection algorithm for spacecraft navigation

This paper describes an efficient and easily implemented algorithmic approach to extracting an approximation to an image’s dominant projected illumination direction, based on intermediary results from a segmentation-based crater detection algorithm (CDA), at a computational cost that is negligible in comparison to that of the prior stages of the CDA. Most contemporary CDAs built for spacecraft navigation use this illumination direction as a means of improving performance or even require it to function at all. Deducing the illumination vector from the image alone reduces the reliance on external information such as the accurate knowledge of the spacecraft inertial state, accurate time base and solar system ephemerides. Therefore, a method such as the one described in this paper is a prerequisite for true “Lost in Space” operation of a purely segmentation-based crater detecting and matching method for spacecraft navigation. The proposed method is verified using ray-traced lunar elevation model data, asteroid image data, and in a laboratory setting with a camera in the loop.

Light propagation in the gravitational field ofNarbitrarily moving bodies in the 1.5PN approximation for high-precision astrometry

High-precision astrometry on sub-micro-arcsecond level in angular resolution requires accurate determination of the trajectory of a light-signal from the celestial light source through the gravitational field of the Solar system toward the observer. In this investigation the light trajectory in the gravitational field of N moving bodies is determined in the 1.5 post-Newtonian approximation. In the approach presented two specific issues of particular importance are accounted for: (1) According to the recommendations of International Astronomical Union, the metric of the Solar system is expressed in terms of intrinsic mass-multipoles and intrinsic spin-multipoles of the massive bodies, allowing for arbitrary shape, inner structure and rotational motion of the massive bodies of the Solar system. (2) The Solar system bodies move along arbitrary worldlines which can later be specified by Solar system ephemeris. The presented analytical solution for light trajectory is a primary requirement for extremely high-precision astrometry on sub-micro-arcsecond level of accuracy and associated massive computations in astrometric data reduction. An estimation of the numerical magnitude for time delay and light deflection of the leading multipoles is given.

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.

Gravitomagnetic field of rotating rings

In the framework of the so-called gravitoelectromagnetic formalism, according to which the equations of the gravitational field can be written in analogy with classical electromagnetism, we study the gravitomagnetic field of a rotating ring, orbiting around a central body. We calculate the gravitomagnetic component of the field, both in the intermediate zone between the ring and the central body, and far away from the ring and central body. We evaluate the impact of the gravitomagnetic field on the motion of test particles and, as an application, we study the possibility of using these results, together with the Solar System ephemeris, to infer information on the spin of ring-like structures.

New upper limits of a braneworld model with recent Solar System tests

As an extension of previous works on classical tests of a braneworld model which is called as the Dadhich, Maartens, Papadopoulos and Rezania (DMPR) solution, and as an attempt to find more stringent constraints on this model, we investigate its effects on physical experiments and astronomical observations conducted in the Solar System by modeling new observable effects and adopting new datasets. First, we investigate gravitational time delay at inferior conjunction (IC) caused by the braneworld model, which was not considered in previous works, because these measurements are not affected by the solar corona noise. Second, the Cassini superior conjunction (SC) experiment is, for the first time, used to test the DMPR model. Third, compared to previous works, we refine the model, which confronts the perihelion shift induced by the braneworld model with modern Solar System ephemerides INPOP10a (IMCCE, France) and EPM2011 (IAA RAS, Russia). The correction of DMPR solution to Einstein’s general relativity (GR) in the four-dimensional spacetime can be characterized by a constant bulk “tidal charge” parameter [Formula: see text], which is confined in the present work. We find that time delay experiment at IC is independent of [Formula: see text] and not suitable for testing the braneworld model. However, the Cassini SC experiment and modern Solar System ephemerides can give better upper bounds on [Formula: see text]: (1) [Formula: see text] by Cassini, and (2) [Formula: see text] based on the supplementary advances of the perihelia provided by INPOP10a and [Formula: see text] based on the ones of EPM2011. The latter upper bounds are improved to be tighter than the ones of previous works by at least two orders of magnitude. Besides, the stronger constraints on the brane tension are given by the modern ephemerides, which are [Formula: see text] for INPOP10a and [Formula: see text] for EPM2011. These improved upper bounds mean that the Solar System tests can serve as a good testbed for high dimensional theories.

Improved upper bounds on Kaluza–Klein gravity with current Solar System experiments and observations

As an extension of previous works on classical tests of Kaluza-Klein (KK) gravity and as an attempt to find more stringent constraints on this theory, its effects on physical experiments and astronomical observations conducted in the Solar System are studied. We investigate the gravitational time delay at inferior conjunction caused by KK gravity, and use new Solar System ephemerides and the observation of \textit{Cassini} to strengthen constraints on KK gravity by up to two orders of magnitude. These improved upper bounds mean that the fifth-dimensional space in the soliton case is a very flat extra dimension in the Solar System, even in the vicinity of the Sun.

Mercury’s resonant rotation from secular orbital elements

We used recently produced Solar System ephemerides, which incorporate two years of ranging observations to the MESSENGER spacecraft, to extract the secular orbital elements for Mercury and associated uncertainties. As Mercury is in a stable 3:2 spin-orbit resonance these values constitute an important reference for the planet's measured rotational parameters, which in turn strongly bear on physical interpretation of Mercury's interior structure. In particular, we derive a mean orbital period of 87.96934962 $\pm$ 0.00000037 days and (assuming a perfect resonance) a spin rate of 6.138506839 $\pm$ 0.000000028 degree/day. The difference between this rotation rate and the currently adopted rotation rate (Archinal et al, 2011) corresponds to a longitudinal displacement of approx. 67 m per year at the equator. Moreover, we present a basic approach for the calculation of the orientation of the instantaneous Laplace and Cassini planes of Mercury. The analysis allows us to assess the uncertainties in physical parameters of the planet when derived from observations of Mercury's rotation.

The Effects of the IERS Conventions (2010) on High Precision Orbit Propagation

The Earth is not perfectly spherical and its rotational axis is not fixed in space, and these geophysical and kinematic irregularities work as dominant perturbations in satellite orbit propagation. The International Earth Rotation Service (IERS) provides the Conventions as guidelines for using the Earth's model and the reference time and coordinate systems defined by the International Astronomical Union (IAU). These guidelines are directly applied to model orbital dynamics of Earth satellites. In the present work, the effects of the latest conventions released in 2010 on orbit propagation are investigated by comparison with cases of applying the previous guidelines, IERS Conventions (2003). All seven major updates are tested, i.e., for the models of the precession/nutation, the geopotential, the ocean tides, the ocean pole tides, the free core nutation, the polar motion, and the solar system ephemeris. The resultant position differences for one week of orbit propagation range from tens of meters for the geopotential model change from EGM96 to EGM2008 to a few mm for the precession/nutation model change from IAU2000 to IAU2006. The along-track differences vary secularly while the cross-track components show periodic variation. However, the radial-track position differences are very small compared with the other components in all cases. These phenomena reflect the variation of the ascending node and the argument of latitude. The reason is that the changed models tested in the current study can be regarded as small fluctuations of the geopotential model from the point of view of orbital dynamics. The ascending node and the argument of latitude are more sensitive to the geopotential than the other elements. This study contributes to understanding of the relation between the Earth's geophysical properties and orbital motion of satellites as well as satellite-based observations.

MEASURING THE MASS OF SOLAR SYSTEM PLANETS USING PULSAR TIMING

High-precision pulsar timing relies on a solar-system ephemeris in order to convert times of arrival (TOAs) of pulses measured at an observatory to the solar system barycenter. Any error in the conversion to the barycentric TOAs leads to a systematic variation in the observed timing residuals; specifically, an incorrect planetary mass leads to a predominantly sinusoidal variation having a period and phase associated with the planet's orbital motion about the Sun. By using an array of pulsars (PSRs J0437-4715, J1744-1134, J1857+0943, J1909-3744), the masses of the planetary systems from Mercury to Saturn have been determined. These masses are consistent with the best-known masses determined by spacecraft observations, with the mass of the Jovian system, 9.547921(2)E-4 Msun, being significantly more accurate than the mass determined from the Pioneer and Voyager spacecraft, and consistent with but less accurate than the value from the Galileo spacecraft. While spacecraft are likely to produce the most accurate measurements for individual solar system bodies, the pulsar technique is sensitive to planetary system masses and has the potential to provide the most accurate values of these masses for some planets.

The Parkes Pulsar Timing Array Project

AbstractThe Parkes Pulsar Timing Array project is timing 20 millisecond pulsars with the aims of detecting gravitational waves, establishing a time scale based on pulsar periods and improving solar-system ephemerides.

Asteroid mass determination with the Gaia mission: A simulation of the expected precisions

The ESA astrometric mission Gaia, due for a launch in late 2011, will observe a huge number of asteroids ( ∼ 350,000 brighter than V < 20 ) with an unprecedented positional precision (at the sub-milliarcsecond level). This precision will play an important role for the mass determination of about hundred minor planets with a relative precision better than 50%. Presently, due primarily to their perturbations on Mars, the uncertainty in the masses of the largest asteroids is the limiting factor in the accuracy of the solar system ephemerides. Besides, such high precision astrometry will enable to derive direct measurements of the masses of the largest asteroids which are of utmost significance for the knowledge of their physical properties. The method for computing the masses is based on the analysis of orbital perturbations during close encounters between massive asteroids (perturbers) and several smaller minor planets (targets). From given criteria of close approaches selection, we give the list of asteroids for which the mass can be determined, and the expected precision of these masses at mission completion. We next study the possible contribution of the ground-based observations for the mass determination in some special observation cases of close approaches.

Precision Timing of PSR J0437−4715: An Accurate Pulsar Distance, a High Pulsar Mass, and a Limit on the Variation of Newton’s Gravitational Constant

Analysis of ten years of high-precision timing data on the millisecond pulsar PSR J0437-4715 has resulted in a model-independent kinematic distance based on an apparent orbital period derivative, Pbdot, determined at the 1.5% level of precision (Dk = 157.0 +/- 2.4 pc), making it one of the most accurate stellar distance estimates published to date. The discrepancy between this measurement and a previously published parallax distance estimate is attributed to errors in the DE200 Solar System ephemerides. The precise measurement of Pbdot allows a limit on the variation of Newton's gravitational constant, |Gdot/G| < 23 x 10^{-12} 1/yr. We also constrain any anomalous acceleration along the line of sight to the pulsar to |a(Sun)/c| < 1.5 x 10^{-18} 1/s at 95% confidence, and derive a pulsar mass, m(psr) = 1.76 +/- 0.20 M, one of the highest estimates so far obtained.

Relativistic astrometry and astrometric relativity

AbstractThe interplay between modern astrometry and gravitational physics is very important for the progress in both these fields. Below some threshold of accuracy, Newtonian physics fails to describe observational data and the Einstein's relativity theory must be used to model the data adequately. Many high-accuracy astronomical techniques have already passed this threshold. Moreover, modern astronomical observations cannot be adequately modeled if relativistic effects are considered as small corrections to Newtonian models. The whole way of thinking must be made compatible with relativity: this starts with the concepts of time, space and reference systems.An overview of the standard general-relativistic framework for modeling of high-accuracy astronomical observations is given. Using this framework one can construct a standard set of building blocks for relativistic models. A suitable combination of these building blocks can be used to formulate a model for any given type of astronomical observations. As an example the problem of four dimensional solar system ephemerides is exposed in more detail. The limits of the present relativistic formulation are also briefly summarized.On the other hand, high-accuracy astronomical observations play important role for gravitational physics itself, providing the latter with crucial observational tests. Perspectives for these astronomical tests for the next 15 years are summarized.

Asteroid mass determination with the Gaia mission

AbstractThe ESA astrometric mission Gaia, due for launch in late 2011, will observe a very large number of asteroids (~ 350,000 down to the magnitude 20), most from the main belt, with an unprecedented positional precision (at the sub-milliarcsecond level). Such high-precision astrometry will enable to considerably improve the orbits of a large number of objects, and also to determine the masses of the largest asteroids by analyzing their gravitational pull during close encounters with smaller ones. A global solution involving simultaneously all the perturbers and the smaller targets should yield about hundred masses with a precision better than 30 percent. The knowledge of these masses will be a rich source of information on the physics of main-belt asteroids and will increase the accuracy of modern solar system ephemerides. We outline the principle of the mathematical method based on variational equations developed to solve for the orbital parameters and the masses of the largest bodies. Calculations have been performed by taking into account realistic simulation of the Gaia observations such as geometry, time sequence, magnitude and by considering possible close approaches among 350,000 asteroids. We give a list of asteroids whose mass can be estimated along with its formal precision.

Contribution of laser ranging to Earth's sciences

Satellite and Lunar Laser Ranging (SLR and LLR, respectively) are based on a direct measurement of a distance by exactly measuring the time transit of a laser beam between a station and a space target. These techniques have proven to be very efficient methods for contributing to the tracking of both artificial satellites and the Moon, and for determining accurately their orbit and the associated geodynamical parameters, although hampered by the non-worldwide coverage and the meteorological conditions. Since more than 40 years, the French community (today ‘Observatoire de la Côte d'Azur’, CNES, ‘Observatoire de Paris’, and IGN) is largely involved in the technological developments as well as in the scientific achievements. The role of the laser technique has greatly evolved thanks to the success of GPS and DORIS; the laser technique teams have learnt to focus their effort in fields where this technique is totally specific and irreplaceable. The role of SLR data in the determination of terrestrial reference systems and in the modelling of the first terms of the gravity field (including the terrestrial constant GM that defines the scale of orbits) has to be emphasized, which is of primary importance in orbitography, whatever the tracking technique used. In addition, the role of LLR data (with two main stations, at Mac Donald (United States) and Grasse (France), since 30 years) has been of particular importance for improving solar system ephemeris and contributing to some features of fundamental physics (equivalence principle). Today, the role of the SLR technique is ( i) to determine and to maintain the scale factor of the global terrestrial reference frame, ( ii) to strengthen the vertical component (including velocity) of the positioning, which is crucial for altimetry missions and tectonic motions, ( iii) to locate the geocenter with respect to the Earth's crust, ( iv) to avoid any secular and undesirable drift of geodetic systems thanks to a very good accuracy. Now, the future of this technique is to enlarge the technical capability of laser ranging stations for long distances, that is the tracking of space targets orbiting through the Solar System. In addition, the laser technique should participate into time transfer experiments and improve, with mobile systems like the FTLRS and the new SLR2000 concept, the coverage of the international laser network (ILRS). To cite this article: P. Exertier et al., C. R. Geoscience 338 (2006).