Geocenter Motion Research Articles

Effects of atmospheric pressure loading and seven‐parameter transformations on estimates of geocenter motion and station heights from space geodetic observations

Variations in fluid loads such as the oceans and the atmosphere deform the surface of the Earth. The accuracy of station coordinates, in particular, heights, that can be estimated depends on how well one can separate these surface deformations from the associated translational motion between the center of mass of the solid Earth and the total Earth (CM). We applied simulated atmospheric pressure loading effects to the coordinates of sites in the CM frame to explore to what level of accuracy both geocenter motion and accurate station coordinates can actually be recovered from geodetic analyses. We found that standard seven‐parameter transformations (three rotations, three translations, scale) generally recover about 80% of the geocenter motion; however, the inclusion of a scale factor permits the aliasing of surface loading deformation, introducing scale errors of up to 0.3 ppb and daily height errors as large as 4 mm. This limits the geophysical studies that can be performed accurately using the results of geodetic analyses where the magnitudes of the signals are small (e.g., tectonic movement of tide gauges, uplift rates for interpreting glacial isostatic adjustment). The quality of the geodetic results is extremely sensitive to the number and distribution of sites used to estimate the transformations and becomes worse when regional (rather than global) sets of sites are used. If the scale factor parameter is omitted, then the amount of aliasing of surface loading effects is reduced considerably and more accurate site velocities and geocenter motion estimates are achieved.

IGS reference frames: status and future improvements

The hierarchy of reference frames used in the International GPS Service (IGS) and the procedures and rationale for realizing them are reviewed. The Conventions of the International Earth Rotation and Reference Systems Service (IERS) lag developments in the IGS in a number of important respects. Recommendations are offered for changes in the IERS Conventions to recognize geocenter motion (as already implemented by the IGS) and to enforce greater model consistency in order to achieve higher precision for combined reference frame products. Despite large improvements in the internal consistency of IGS product sets, defects remain which should be addressed in future developments. If the IGS is to remain a leader in this area, then a comprehensive, long-range strategy should be formulated and pursued to maintain and enhance the IGS reference frame, as well as to improve its delivery to users. Actions should include the official designation of a high-performance reference tracking network whose stations are expected to meet the highest standards possible.

Spin axis behavior of the LAGEOS satellites

The satellites LAGEOS‐I and LAGEOS‐II are essential for the scientific study of various (geo)physical phenomena, such as geocenter motion and absolute scale. The high quality of such science products strongly depends on the absolute quality of the SLR observations and that of the orbit description. Therefore all accelerations experienced by the spacecraft need to be modeled as accurately as possible, the thermal radiation forces being one of them. Traditionally, this is done by estimating so‐called empirical accelerations. However, the rotational dynamics of LAGEOS‐I in particular no longer allows such a simple approach: a full modeling of the spin behavior, the temperature distribution over the spacecraft surface and the resulting net force prove necessary to achieve the best results. As a first step, a new model, Lageos Spin Axis Model (LOSSAM) has been developed. It is unique in its combination of analytical theory and empirical observations. Its mathematics is taken after previous investigators, although flaws have been corrected. LOSSAM describes the full spin behavior of LOSSAM based on the following phenomena: (1) the geomagnetic field, (2) the Earth's gravity field, (3) the satellite center of pressure offset, and (4) the effective difference in reflectivity between the satellite hemispheres. Its accuracy has been demonstrated by an improvement of about a 50% in the RMS residual of the Yarkovsky‐Schach effect signal (as shown by Lucchesi et al. [2004]). Such a high‐quality model for rotational behavior is indispensable for a proper force modeling, and hence also for the quality of typical LAGEOS science products.

Small perturbations on artificial satellites as an inverse problem

The geocentric motion of a satellite is mathematically simulated by a system of second order ordinary differential equations involving two perturbing functions. The first one represents the second term of the gravitational potential of the Earth and the second is due to the atmospheric drag. Assuming that the solutions of the differential equations and their first derivatives are known from measurements, a stepwise computation of the perturbations is made through a deterministic method. Two examples illustrate our method. In a real case our method should help to design an appropriate maneuver to correct the motion of a satellite.

Origin of the International Terrestrial Reference Frame

With recent improvements in space geodesy, the Earth's center of mass (CM) and center of figure (CF) are no longer indistinguishable. The current origin of the International Terrestrial Reference Frame (ITRF) is defined as the CM, which shows measured seasonal variations of several millimeters to 1 cm with respect to true CM. As scientists study Earth's dynamic deformations on seasonal and shorter timescales and begin to compare observed geocenter motion with predictions from geophysical models, the reference frame origin presents significant error due to missing the geocenter motion. This paper discusses the nature of the origin of the ITRF and explores the sensitivity of GPS measurements to geocenter motion. We find that since the values of nonlinear geocenter motion are not included in the positions of the ITRF sites, the behavior of the current ITRF origin reflects CM on secular timescale but reflects CF on seasonal and short timescales. The nature of the ITRF origin depends on both the adopted kinematic model and unmodeled network motion. The realized ITRF origin should be defined by a new nomenclature to reflect its nature accurately. By the new nomenclature, the origin will maintain its current long‐term stability, while improving its stability on seasonal timescales to the submillimeter level. With the degree‐1 deformation approach, GPS measurements are able to provide potentially valuable information on geocenter variations on seasonal and short timescales.

Self‐consistency in reference frames, geocenter definition, and surface loading of the solid Earth

Crustal motion can be described as a vector displacement field, which depends on both the physical deformation and the reference frame. Self‐consistent descriptions of surface kinematics must account for the dynamic relationship between the Earth's surface and the frame origin at some defined center of the Earth, which is governed by the Earth's response to the degree‐one spherical harmonic component of surface loads. Terrestrial reference frames are defined here as “isomorphic” if the computed surface displacements functionally accord with load Love number theory. Isomorphic frames are shown to move relative to each other along the direction of the load's center of mass. The following frames are isomorphic: center of mass of the solid Earth, center of mass of the entire Earth system, no‐net translation of the surface, no‐net horizontal translation of the surface, and no‐net vertical translation of the surface. The theory predicts different degree‐one load Love numbers and geocenter motion for specific isomorphic frames. Under a change in center of mass of surface load in any isomorphic frame, the total surface displacement field consists not only of a geocenter translation in inertial space, but must also be accompanied by surface deformation. Therefore estimation of geocenter displacement should account for this deformation. Even very long baseline interferometry (VLBI) is sensitive to geocenter displacement, as the accompanying deformation changes baseline lengths. The choice of specific isomorphic frame can facilitate scientific interpretation; the theory presented here clarifies how coordinate displacements and horizontal versus vertical motion are critically tied to this choice.

Site distribution and aliasing effects in the inversion for load coefficients and geocenter motion from GPS data

Precise GPS measurements of elastic relative site displacements due to surface mass loading offer important constraints on global surface mass transport. We investigate effects of site distribution and aliasing by higher‐degree (n ≥ 2) loading terms on inversion of GPS data for n = 1 load coefficients and geocenter motion. Covariance and simulation analyses are conducted to assess the sensitivity of the inversion to aliasing and mismodeling errors and possible uncertainties in the n = 1 load coefficient determination. We found that the use of center‐of‐figure approximation in the inverse formulation could cause 10–15% errors in the inverted load coefficients. n = 1 load estimates may be contaminated significantly by unknown higher‐degree terms, depending on the load scenario and the GPS site distribution. The uncertainty in n = 1 zonal load estimate is at the level of 80–95% for two load scenarios.

Seasonal and interannual geocenter motion from SLR and DORIS measurements: Comparison with surface loading data

We present observed seasonal and interannual geocenter motion over 1993–1999 based on laser data on the LAGEOS‐1, LAGEOS‐2, and Topex/Poseidon (T/P) satellites as well as Doppler orbitography and radiopositioning integrated by satellite (DORIS) data from T/P. The amplitude and the phase of the space geodesy‐derived seasonal cycles for each coordinate are further compared to the estimates based on surface mass redistribution on the Earth surface derived from various climatic data sources: surface pressure, soil moisture, snow depth, and ocean mass variations. Geodesy and climatic data present good agreement in terms of seasonal, still not for interannual, geocenter motion.

Geocentre motion from the DORIS space system and laser data to the Lageos satellites: comparison with surface loading data

Surface mass redistribution within the Earth system, especially in the atmosphere, oceans, continents and ice sheets, causes the position of the centre of mass to vary in a reference frame attached to the solid Earth. Space techniques are now precise enough to measure the centre of mass motion. Here we present a determination of the centre of mass coordinates at regular monthly intervals using DORIS data on SPOT-2, SPOT-3 and Topex–Poseidon (1993–1997) and laser data on Lageos-1 and Lageos-2 (1993–1996). The amplitude and phase of the space-geodesy-derived annual cycle for each coordinate are further compared to estimates based on surface mass redistribution at the Earth surface derived from various climatic data sources: surface pressure, soil moisture, snow depth and ocean mass variations.

Observations of tidally coherent diurnal and semidiurnal variations in the geocenter

The center of mass of the Earth, about which a satellite orbits, is determined by the mass distribution of the solid Earth (including the Earth's interior), the oceans, and the atmosphere. The tracking sites, however, are all located on the lithosphere only, and so the network origin will not generally coincide with the center of mass. Changes in the vector offset between these two points, referred to as apparent geocenter motion, are due to global scale movement of mass. In this study we have extended the approach used by space geodetic techniques for determination of tidally coherent nearly diurnal and semidiurnal variations in the Earth's orientation to include geocenter variations due to ocean tides. We demonstrate the weaker observability of nearly diurnal retrograde motions in x and y, and hence the utility of their separation from the other equatorial terms. We find statistically significant terms at the 99.5% level due to O1, P1, K1, and M2. The solutions, which indicate geocenter motions at the few millimeter level per tide, compare well with predicted values from theoretical ocean tide models and from TOPEX/Poseidon radar altimetry.

A Note on the Solar Radiation Perturbations of Lunar Motion

Solar-radiation and thermal-force effects acting on the Earth and the Moon are studied in detail. Their essential contribution to the lunar geocentric motion consists of a synodic “in-phase” oscillation with 3.65 ± 0.08 (realistic error) millimeters amplitude. This correction must be taken into account when searching for a hypothesized equivalence principle violation signal in the lunar laser ranging data.

Origin and Scale of Coordinate Systems in Satellite Geodesy

AbstractThe center of mass of the Earth is commonly taken as origin for the coordinate systems used in satellite geodesy. In this paper the notion of the “geocenter” is discussed from the point of view of mechanics and geophysics. It is shown that processes in and above the crust have practically no impact on the position of the geocenter. It is possible however that motions of the inner core may cause variations of the geocenter of the order of 1 m. Nevertheless the geocenter is the best point for the origin of a coordinate system. Mather’s method of monitoring geocenter motion is discussed, and some other possibilities are mentioned. Concerning the scale problem, the role of the constant GM and time measurements in satellite net determinations are briefly discussed.

Changes in the position of the geocentre due to variations in sea-level

The hydrostatic equation is used to show that load departures on the ocean floor due solely to the oceans may be determined from the excess of recorded over steric sea-level and a representative density. The effect of these departures on the position of the geocentre is estimated using formulae derived by Stolz (1976) and data compiled from Pattullo et al. (1955) and Pattullo (1960; 1963). The resulting maximum seasonal position change turns out to be about 2mm. Addition of the results calculated here and those published earlier by Stolz (1976) indicates that the maximum geocentre motion due to seasonal variations in air mass, ground water and sea-level is about 5mm, which is about an order smaller than the point-coordination accuracy modern high-precision geodesy aims to achieve.

Changes in the Position of the Geocentre due to Seasonal Variations in Air Mass and Ground Water

Summary A simple method for estimating geocentre motion is presented and applied to the seasonal variation in air mass and moisture stored on the Earth's land surface. Data given by Rosenhead and by van Hylckama indicates that the motion attains a maximum of 4.3 mm near the equinoxes and a minimum of 1.5 mm near the solstices, that is, about an order smaller than the point-co-ordination accuracy modern high-precision geodesy aims to achieve.

Observations of a variable radio source associated with the planet Jupiter

A source of variable 22.2-Mc/sec radiation has been detected with the large “Mills Cross” antenna of the Carnegie Institution of Washington. The source is present on nine records out of a possible 31 obtained during the first quarter of 1955. The appearance of the records of this source resembles that of terrestrial interference, but it lasts no longer than the time necessary for a celestial object to pass through the antenna pattern. The derived position in the sky corresponds to the position of Jupiter and exhibits the geocentric motion of Jupiter. There is no evident correlation between the times of appearance of this phenomenon and the rotational period of the planet Jupiter, or with the occurrence of solar activity. There is evidence that most of the radio energy is concentrated at frequencies lower than 38 Mc/sec.

High resolution radio astronomy at 13.5 meters.

view Abstract Citations (1) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS High resolution radio astronomy at 13.5 meters. Burke, B. F. ; Franklin, R. L. Abstract The large "Mills Cross" antenna system of the Carnegie Institution of Washington consists of two crossed 2047-ft. arrays of 66 dipoles each. When used with a phase-switching receiver, the array gives a pencil beam which in the present system is slightly elliptical in cross-section, measuring 10.6 X 2?4 at half-power points. During the preliminary testing and adjustment of the apparatus, provisional intensities of the radio sources Cyg A, Cas A, M I, IC 443, and NGC 1275 have been obtained. These observations, made at 13.5 meters, indicate that all these sources are several times more intense than at wave lengths of 3-4 m, where most of the previous measurements have been made. A general survey of the sky was begun in the region of = $ 220, using the cross as a transit instrument. Located in this declination band are the Crab Nebula and IC 443 as well as a weak extended source at about a = 7h 30 m. Obscuring this extended source on nine out of thirty transits was a very intense, irregular burst of radio noise. A plot of the right ascensions of the beginning and end of the disturbance, as a function of the date, was compared with a similar plot of the positions of NGC 2392, NGC 2420, Uranus, and Jupiter. There is poor or no correlation with Uranus or the galactic objects; Jupiter, however, exhibits the same right ascension and change of right ascension with time, as the center of the disturbance, this change being due to Jupiter's geocentric motion. It is then concluded that this radio noise is associated with Jupiter. This radiation may originate in events in Jupiter's atmosphere similar to terrestrial thunderstorms. There is some evidence that this phenomenon cannot be observed at a wave length of 7.8 meters. Other information is not yet available. Department of Terrestrial Magnetism, Carnegie Institution of Washington, Washington, D. C. Publication: The Astronomical Journal Pub Date: 1955 DOI: 10.1086/107147 Bibcode: 1955AJ.....60R.155B full text sources ADS |

Our Astronomical Column

THE SATELLITES OF MARS.—In the Introduction to his Tables of the satellites of Uranus, Prof. Newcomb points out the advantage that might be derived, in systematic observations of the satellites by the preparation of a table showing the angles of position and distances corresponding to every 10° in u or the longitude of the satellite in its orbit, counted from the point in which it crosses the plane parallel to the earth's equator. From such a table the approximate positions of the satellites would be obtainable at any one opposition, with no further calculation than is required to determine the value of u for the time of observation. The more rapid geocentric motion of the planet Mars does not of course allow of this principle of computation being applied so as to attain the same degree of approximation as in the case of Uranus, but even with Mars it is likely that such a table, prepared with the values of the various auxiliary quantities for the date of opposition November 12, may facilitate observations, and we accordingly present one below:—

On some properties of the geocentric motion of a heavenly body

On some properties of the geocentric motion of a heavenly body

On the Deducing of the Parallax of Mars, and hence that of the Sun from the Geocentric Motion of the former when in opposition, and especially when near the Node of his Orbit

On the Deducing of the Parallax of Mars, and hence that of the Sun from the Geocentric Motion of the former when in opposition, and especially when near the Node of his Orbit