Geocentric Celestial Reference System Research Articles

Tidal Effects and Clock Comparison Experiments

Einstein’s general relativity theory provides a successful understanding of the flow of time in the gravitational field. From Einstein’s equivalence principle, the influence of the Sun and Moon masses on clocks is given in the form of tidal potentials. Two clocks fixed on the surface of the Earth, compared to each other, can measure the tidal effects of the Sun and Moon. The measurement of tidal effects can provide a test for general relativity. Based on the standard general relativity method, we rigorously derive the formulas for clock comparison in the Barycentric Celestial Reference System and Geocentric Celestial Reference System, and demonstrate the tidal effects on clock comparison experiments. The unprecedented performance of atomic clocks makes it possible to measure the tidal effects on clock comparisons. We propose to test tidal effects with the laboratory clock comparisons and some international missions, and give the corresponding estimations. By comparing the state-of-the-art clocks over distances of 1000 km, the laboratory may test tidal effects with a level of 1%. Future space missions, such as the China space station and FOCOS mission, can also be used to test tidal effects, and the best accuracy may reach 0.3%.

Relativistic contributions to the rotation of Mars

Context. The orientation and rotation of Mars can be described by a set of Euler angles (longitude, obliquity, and rotation angles) and estimated from radioscience data (tracking of orbiters and landers), which can then be used to infer the planet's internal properties. The data are analyzed using a modeling expressed within the barycentric celestial reference system (BCRS). This modeling includes several relativistic contributions that need to be properly taken into account to avoid any misinterpretation of the data. Aims. We provide new and more accurate (to the 0.1 mas level) estimations of the relativistic corrections to be included in the BCRS model of the orientation and rotation of Mars. Methods. There are two types of relativistic contributions with regard to Mars's rotation and orientation: (i) those that directly impact the Euler angles and (ii) those resulting from the time transformation between a local Mars reference frame and BCRS. The former contribution essentially corresponds to the geodetic effect, as well as to the smaller Lense-Thirring and Thomas precession effects, and we computed their values assuming that Mars evolves on a Keplerian orbit. As for the latter contribution, we computed the effect of the time transformation and compared the rotation angle corrections obtained, based on the assumption that the planets evolve on Keplerian orbits, with the corrections obtained, based on realistic orbits as described by the ephemerides. Results. The relativistic correction in longitude mainly comes from the geodetic effect and results in a geodetic precession (6.754 mas yr−1) and geodetic annual nutation (0.565 mas amplitude). For the rotation angle, the correction is dominated by the effect of the time transformation. The main annual, semiannual, and terannual terms display amplitudes of 166.954 mas, 7.783 mas, and 0.544 mas, respectively. The amplitude of the annual term differs by about 9 mas from the estimate usually considered by the community. We identified new terms at the Mars-Jupiter and Mars-Saturn synodic periods (0.567 mas and 0.102 mas amplitude) that are relevant considering the current level of uncertainty of the measurements, as well as a contribution to the rotation rate (7.3088 mas day−1). There is no significant correction that applies to the obliquity.

A new post-Newtonian long-term precession model for the Earth

ABSTRACT Long-term precession represents the secular motion of the Earth’s axis for a long time interval. In 2015, we calculated the Earth’s long-term precession in a relativistic framework. However, our previous works involving the ecliptic in the Geocentric Celestial Reference System are deficient, because the natural definition of this ecliptic is still ambiguous. To obtain a long-term precession model in accordance with general relativity, improvements are made including the following: all calculations are no longer carried out in the reference related to any ecliptic; a new hybrid integrator is designed and used for this precession model; ecliptic-independent precession parameters are calculated and provided. A detailed comparison analysis is performed to estimate the importance of various relativistic influences on the precession parameters. Valid within the interval of $\pm 1\,$Myr around J2000.0, a consistent post-Newtonian long-term precession model for the Earth has been achieved and is presented here.

The space\u2013time references of BeiDou Navigation Satellite System

The BeiDou Navigation Satellite System (BDS) is essentially a precise time measurement and time synchronization system for a large-scale space near the Earth. General relativity is the basic theoretical framework for the information processing in the master control station of BDS. Having introduced the basic conceptions of relativistic space–time reference systems, the space–time references of BDS are analyzed and the function and acquisition method of the Earth Orientation Parameters (EOP) are briefly discussed. The basic space reference of BDS is BeiDou Coordinate System (BDCS), and the time standard is the BDS Time (BDT). BDCS and BDT are the realizations of the Geocentric Terrestrial Reference System (GTRS) and the Terrestrial Time (TT) for BDS, respectively. The station coordinates in the BDCS are consistent with those in International Terrestrial Reference Frame (ITRF)2014 at the cm–level and the difference in scale is about 1.1 times 10^{ - 8}. The time deviation of BDT relative to International Atomic Time (TAI) is less than 50 ns and the frequency deviation is less than 2 times 10^{ - 14}. The Geocentric Celestial Reference System (GCRS) and the solar Barycentric Celestial Reference System (BCRS) are also involved in the operation of BDS. The observation models for time synchronization and precise orbit determination are established within the GCRS framework. The coordinate transformation between BDCS and GCRS is consistent with the International Earth Rotation and Reference Systems Service (IERS). In the autonomous operation mode without the support of the ground master control station, Earth Orientation Parameters (EOP) is obtained by means of long-term prediction and on-board observation. The observation models for the on-board astrometry should be established within the BCRS framework.

General expansion of time transfer functions in optical spacetime

When dealing with highly accurate modeling of time and frequency transfers into arbitrarily moving dielectrics medium, it may be convenient to work with Gordon's optical spacetime metric rather than the usual physical spacetime metric. Additionally, an accurate modeling of the geodesic evolution of observable quantities (e.g., the range and the Doppler) requires us to know the reception or the emission time transfer functions. In the physical spacetime, these functions can be derived to any post-Minkowskian orders through a recursive procedure. In this work, we show that the time transfer functions can be determined to any order in Gordon's optical spacetime as well. The exact integral forms of the gravitational, the refractive, and the coupling contributions are recursively derived. The expression of the time transfer function is given within the post-linear approximation assuming a stationary optical spacetime covered with geocentric celestial reference system coordinates. The light-dragging effect due to the steady rotation of the neutral atmosphere of the Earth is found to be at the threshold of visibility in many experiments involving accurate modeling of the time and frequency transfers.

Modeling the VLBI delay for Earth satellites

Very-long-baseline interferometry (VLBI) observations of satellites orbiting the Earth and emitting an artificial radio signal have the potential of becoming an important technique for improving the frame ties between celestial and terrestrial reference frames. Modeling the delay of the signal reception at one station with respect to the other station of a baseline is a fundamental step for correlation and parameter estimation. The near-field VLBI delay models developed so far include numerical computation, which may become expensive in terms of computation time. This applies especially when partial derivatives are to be computed, which is the normal case for least squares adjustments. Furthermore, all the models are formulated in the barycentric celestial reference system requiring large numbers. Here we present an analytical expression for the VLBI delay for the special case of satellites orbiting the Earth, observed by ground-based radio telescopes. We analytically solve the light time equation for each signal propagation path from the source to receiver one and to receiver two under the simplification of linearizing the trajectory of the satellite. By approximating the motion of the Earth as uniform during the short signal travel times we are able to work in the geocentric celestial reference system. We investigate differences between numerical and analytical solutions by simulating VLBI observations of Earth satellites. These tests reveal that delays computed with the analytical formula are consistent with those computed with the numerical solution below the detection level of VLBI but at less computational cost.

An improved augmented X-ray pulsar navigation algorithm based on the norm of pulsar direction error

Pulsar position error in the Celestial Coordinate System can cause pulsar direction error in the Barycentric Celestial Reference System, which may seriously affect the accuracy of X-ray pulsar navigation. In order to improve the robustness of X-ray pulsar navigation algorithm against the pulsar direction error, an improved augmented X-ray pulsar navigation algorithm is proposed. Different from the previously proposed augmented algorithm, the algorithm introduces the norm of pulsar direction error as the augmented state rather than the systematic bias. At the same time, after the linearization of observation equation, the algorithm uses extended Kalman filter (EKF) as the basic filter, which has faster computation speed and better engineering applicability. The observability of the algorithm is proved by theoretical analysis. Finally, numerical simulations demonstrate that under different error conditions, the improved algorithm not only can effectively reduce the dependence on the state initial value, but also has better real-time performance compared with the previous algorithm.

Improvement of the orbit of the Spektr-R spacecraft in the RadioAstron mission and required conditions for improvement using a Kalman filter

This paper is concerned with improvement of the state vector of the Spektr-R spacecraft of the RadioAstron mission. The state vector includes three coordinates of the position of the spacecraft and three components of its velocity in the Geocentric Celestial Reference System. Improvement of the orbit of the spacecraft is understood as improvement of the state vector. The results are compared with the original orbits determined at the Keldysh Institute of Applied Mathematics (IAM). The paper considers both using the Kalman filter based on a single set of radio-range and Doppler data from ground-based stations and the analysis of conditions that will lead to improvement of the orbit. It has been shown that using three ground-based stations that perform simultaneous measurements the problem is solved completely, even when a poor initial approximation is used. Based on the results, a list of requirements is obtained that will provide more accurate information on the orbit of the Spektr-R spacecraft.

Improvement of the orbit of the Spektr-R spacecraft in the RadioAstron mission on the basis of radio range and Doppler measurements

The first results of the improvement of the state vector of the Spektr-R spacecraft of the RadioAstron mission, which is a part of an earth–space radio interferometer, are presented. The state vector includes three components for the spacecraft position and three components for its velocity in the Geocentric Celestial Reference System. Kalman filtering on the basis of radio range and Doppler data allows refinement of the components at each iteration. It is shown that orbit improvement increases the accuracy of the orbit determined at the Keldysh Institute of Applied Mathematics.

Influence of ITRS/GCRS implementation for astrodynamics: Coordinate transformations

Converting between the Geocentric Celestial Reference System (GCRS) and International Terrestrial Reference System (ITRS) is necessary for many applications in astrodynamics, such as orbit determination and analyzing geoscience data from satellite missions. The implementation of this frame transformation and the manner in which the Earth orientation parameters (EOPs) are used have a notable impact on station coordinates and satellite positions. After briefly reviewing the various theories and their mathematical description, we investigate the impact of EOP interpolation methods, ocean tide corrections, precession–nutation simplifications, and Julian date handling on the ITRS/GCRS coordinate transformation. Estimates of the impact on position concern a range of altitudes, from the Earth’s surface to geosynchronous orbit (GEO), and apply to a wide array of astrodynamics applications. We demonstrate that EOP interpolation methods and ocean tide corrections impact the ITRS/GCRS transformation between 5cm and 20cm on the surface of the Earth and at the Global Positioning System (GPS) altitude, respectively. We conclude with a summary of recommendations on EOP usage and bias–precession–nutation model implementations for achieving a wide range of transformation accuracies at several altitudes. This comprehensive set of recommendations allows astrodynamicists, flight software engineers, and Earth scientists to make informed decisions when choosing the best implementation for their application, balancing accuracy and computational complexity.

A long time span relativistic precession model of the Earth**Supported by the National Natural Science Foundation of China.

A numerical solution to the Earth's precession in a relativistic framework for a long time span is presented here. We obtain the motion of the solar system in the Barycentric Celestial Reference System by numerical integration with a symplectic integrator. Special Newtonian corrections accounting for tidal dissipation are included in the force model. The part representing Earth's rotation is calculated in the Geocentric Celestial Reference System by integrating the post-Newtonian equations of motion published by Klioner et al. All the main relativistic effects are included following Klioner et al. In particular, we consider several relativistic reference systems with corresponding time scales, scaled constants and parameters. Approximate expressions for Earth's precession in the interval ±1 Myr around J2000.0 are provided. In the interval ±2000 years around J2000.0, the difference compared to the P03 precession theory is only several arcseconds and the results are consistent with other long-term precession theories.

Polynomial regression calculation of the Earth's position based on millisecond pulsar timing

Prior to achieving high precision navigation of a spacecraft using X-ray observations, a pulsar rotation model must be built and analysis of the precise position of the Earth should be performed using ground pulsar timing observations. We can simulate time-of-arrival ground observation data close to actual observed values before using pulsar timing observation data. Considering the correlation between the Earth's position and its short arc section of an orbit, we use polynomial regression to build the correlation. Regression coefficients can be calculated using the least square method, and a coordinate component series can also be obtained; that is, we can calculate Earth's position in the Barycentric Celestial Reference System according to pulse arrival time data and a precise pulsar rotation model. In order to set appropriate parameters before the actual timing observations for Earth positioning, we can calculate the influence of the spatial distribution of pulsars on errors in the positioning result and the influence of error source variation on positioning by simulation. It is significant that the threshold values of the observation and systematic errors can be established before an actual observation occurs; namely, we can determine the observation mode with small errors and reject the observed data with big errors, thus improving the positioning result.

Models and nomenclature in Earth rotation

AbstractThe celestial Earth's orientation is required for many applications in fundamental astronomy and geodesy; it is currently determined with sub-milliarcsecond accuracy by astro-geodetic observations. Models for that orientation rely on solutions for the rotation of a rigid Earth model and on the geophysical representation of non-rigid Earth effects. Important IAU 2000/2006 resolutions on reference systems have been passed (and endorsed by the IUGG) that recommend a new paradigm and high accuracy models to be used in the transformation from terrestrial to celestial systems. This paper reviews the consequences of these resolutions on the adopted Earth orientation parameters, IAU precession-nutation models and associated nomenclature. It summarizes the fundamental aspects of the current IAU precession-nutation models and reports on the consideration of General Relativity (GR) in the solutions. This shows that the current definitions and nomenclature for Earth's rotation are compliant with GR and that the IAU precession-nutation is compliant with the IAU 2000 definition of the geocentric celestial reference system in the GR framework; however, the underlying Earth's rotation models basically are Newtonian.

Gravitomagnetism and lunar laser ranging

The problem of measuring gravitomagnetic effects by means of lunar laser ranging (LLR) is investigated. The relevant terms in the Einstein-Infeld-Hoffmann equations of motion in barycentric coordinates are parametrized by a parameter ${\ensuremath{\eta}}_{G}$, which is fitted along with other parameters to LLR data and not derived from postfit residuals as it was done by other authors. The physical relevance of ${\ensuremath{\eta}}_{G}$ and its relation to the preferred frame parameter ${\ensuremath{\alpha}}_{1}$ are discussed. Finally, ${\ensuremath{\alpha}}_{1}$ is fitted to LLR data by choosing the Barycentric Celestial Reference System as preferred frame instead of the cosmic rest frame determined via the temperature anisotropy of the cosmic microwave background radiation.

The effect of the motion of the Sun on the light-time in interplanetary relativity experiments

In 2002, a measurement of the effect of solar gravity upon the phase of coherent microwave beams passing near the Sun was carried out by the Cassini mission, allowing a very accurate measurement of the PPN parameter γ. The data have been analysed with NASA's Orbit Determination Program (ODP) in the Barycentric Celestial Reference System, in which the Sun moves around the centre of mass of the solar system with a velocity v⊙ of about 15 m s−1; the question arises: what correction does this imply for the predicted phase shift? After a review of the way the ODP works, we set the problem in the framework of Lorentz (and Galilean) transformations and evaluate the correction; it is several orders of the magnitude below our experimental accuracy. We also discuss a recent paper (Kopeikin et al 2007 Phys. Lett. A 367 276), which claims wrong and much larger corrections, and clarify the reasons for the discrepancy.

Definition and realization of the celestial intermediate reference system

AbstractThe transformation between the International Terrestrial Reference System (ITRS) and the Geocentric Celestial Reference system (GCRS) is an essential part of the models to be used when dealing with Earth's rotation or when computing directions of celestial objects in various systems. The 2000 and 2006 IAU resolutions on reference systems have modified the way the Earth orientation is expressed and adopted high accuracy models for expressing the relevant quantities for the transformation from terrestrial to celestial systems. First, the IAU 2000 Resolutions have refined the definition of the astronomical reference systems and transformations between them and adopted the IAU 2000 precession-nutation. Then, the IAU 2006 Resolutions have adopted a new precession model that is consistent with dynamical theories and have addressed definition, terminology or orientation issues relative to reference systems and time scales that needed to be specified after the adoption of the IAU 2000 resolutions. These in particular provide a refined definition of the pole (the Celestial intermediate pole, CIP) and the origin (the Celestial intermediate origin, CIO) on the CIP equator as well as a rigorous definition of sidereal rotation of the Earth. These also allow an accurate realization of the celestial intermediate system linked to the CIP and the CIO that replaces the classical celestial system based on the true equator and equinox of date. This talk explains the changes resulting from the joint IAU 2000/2006 resolutions and reviews the consequences on the concepts, nomenclature, models and conventions in fundamental astronomy that are suitable for modern and future realizations of reference systems. Realization of the celestial intermediate reference system ensuring a micro-arc-second accuracy is detailed.

Geodesy and relativity

Relativity, or gravitational physics, has widely entered geodetic modelling and parameter determination. This concerns, first of all, the fundamental reference systems used. The Barycentric Celestial Reference System (BCRS) has to be distinguished carefully from the Geocentric Celestial Reference System (GCRS), which is the basic theoretical system for geodetic modelling with a direct link to the International Terrestrial Reference System (ITRS), simply given by a rotation matrix. The relation to the International Celestial Reference System (ICRS) is discussed, as well as various properties and relevance of these systems. Then the representation of the gravitational field is discussed when relativity comes into play. Presently, the so-called post-Newtonian approximation to GRT (general relativity theory) including relativistic effects to lowest order is sufficient for practically all geodetic applications. At the present level of accuracy, space-geodetic techniques like VLBI (Very Long Baseline Interferometry), GPS (Global Positioning System) and SLR/LLR (Satellite/Lunar Laser Ranging) have to be modelled and analysed in the context of a post-Newtonian formalism. In fact, all reference and time frames involved, satellite and planetary orbits, signal propagation and the various observables (frequencies, pulse travel times, phase and travel-time differences) are treated within relativity. This paper reviews to what extent the space-geodetic techniques are affected by such a relativistic treatment and where—vice versa—relativistic parameters can be determined by the analysis of geodetic measurements. At the end, we give a brief outlook on how new or improved measurement techniques (e.g., optical clocks, Galileo) may further push relativistic parameter determination and allow for refined geodetic measurements.

Implementation of the new nomenclature in The Astronomical Almanac

AbstractThis talk charts the implementation of the resolutions of the IAU XXIV General Assembly in 2000 (IAU 2000) in The Astronomical Almanac (AsA).

High precision methods for locating the celestial intermediate pole and origin

Context.The precession-nutation transformation describes the changing directions on the celestial sphere of the Earth's pole and an adopted origin of right ascension. The coordinate system for the celestial sphere is the geocentric celestial reference system, and the two directions are the celestial intermediate pole (CIP) and the celestial intermediate origin (CIO), the latter having supplanted the equinox for this purpose following IAU resolutions in 2000. The celestial coordinate triad based on the CIP and CIO is called the celestial intermediate reference system; the prediction of topocentric directions additionally requires the Earth rotation angle (ERA), the counterpart of Greenwich sidereal time (GST) in the former equinox based system.

Physically adequate proper reference system of a test observer and relativistic description of the GAIA attitude

A relativistic definition of the physically adequate proper reference system of a test observer is suggested within the framework of the parametrized post-Newtonian formalism. According to the nomenclature accepted within the GAIA project this reference system is called the center-of-mass reference system (CoMRS). The interrelation between the suggested definition of the CoMRS and the International Astronomical Union (IAU) Resolutions 2000 on relativity are elucidated. The tetrad representation of the CoMRS at its origin is also explicated. It is demonstrated how to use this tetrad representation to calculate the relation between the observed direction of a light ray and the corresponding coordinate direction in the barycentric celestial reference system of the IAU. It is argued that the kinematically nonrotating CoMRS is the natural choice of the reference system where the attitude of the observer (e.g., of the GAIA satellite) should be modeled. The relativistic equations of rotational motion of a satellite relative to its CoMRS are briefly discussed. A simple algorithm for the attitude description of the satellite is proposed.