John C. Ries

The Joint Gravity Model 3

An improved Earth geopotential model, complete to spherical harmonic degree and order 70, has been determined by combining the Joint Gravity Model 1 (JGM 1) geopotential coefficients, and their associated error covariance, with new information from SLR, DORIS, and GPS tracking of TOPEX/Poseidon, laser tracking of LAGEOS 1, LAGEOS 2, and Stella, and additional DORIS tracking of SPOT 2. The resulting field, JGM 3, which has been adopted for the TOPEX/Poseidon altimeter data rerelease, yields improved orbit accuracies as demonstrated by better fits to withheld tracking data and substantially reduced geographically correlated orbit error. Methods for analyzing the performance of the gravity field using high-precision tracking station positioning were applied. Geodetic results, including station coordinates and Earth orientation parameters, are significantly improved with the JGM 3 model. Sea surface topography solutions from TOPEX/Poseidon altimetry indicate that the ocean geoid has been improved. Subset solutions performed by withholding either the GPS data or the SLR/DORIS data were computed to demonstrate the effect of these particular data sets on the gravity model used for TOPEX/Poseidon orbit determination.

Gravity model development for TOPEX/POSEIDON: Joint gravity models 1 and 2

The TOPEX/POSEIDON (T/P) prelaunch Joint Gravity Model-1 (JGM-I) and the postlaunch JGM-2 Earth gravitational models have been developed to support precision orbit determination for T/P. Each of these models is complete to degree 70 in spherical harmonics and was computed from a combination of satellite tracking data, satellite altimetry, and surface gravimetry. While improved orbit determination accuracies for T/P have driven the improvements in the models, the models are general in application and also provide an improved geoid for oceanographic computations. The postlaunch model, JGM-2, which includes T/P satellite laser ranging (SLR) and Doppler orbitography and radiopositioning integrated by satellite (DORIS) tracking data, introduces radial orbit errors for T/P that are only 2 cm RMS with the commission errors of the marine geoid for terms to degree 70 being ±25 cm. Errors in modeling the nonconservative forces acting on T/P increase the total radial errors to only 3–4 cm RMS, a result much better than premission goals. While the orbit accuracy goal for T/P has been far surpassed, geoid errors still prevent the absolute determination of the ocean dynamic topography for wavelengths shorter than about 2500 km. Only a dedicated gravitational field satellite mission will likely provide the necessary improvement in the geoid.

Chapter 1 Satellite Altimetry

Publisher Summary The basic concept of satellite altimetry is to measure the range from the satellite to the sea surface. The altimeter transmits a short pulse of microwave radiation with known power toward the sea surface. The pulse interacts with the rough sea surface and a part of the incident radiation reflects back to the altimeter. The chapter emphasizes on the correction algorithms applied to the dual-frequency altimeter onboard the TOPEX/POSEIDON (T/P) satellite. This state-of-the-art altimeter sets the standard for future altimeter missions as it is significantly more accurate than any of the other altimeters that have been launched to date. To provide assurance that the performance requirements for altimeter measurement accuracy are met or exceeded, extensive calibration and validation (cal/val) are important elements of altimeter missions. Cal/val embraces a wide variety of activities, ranging from the interpretation of information from internal-calibration modes of the sensors to the validation of the fully corrected sea-level estimates using in situ data. The chapter concludes with a summary of the T/P mission design and an assessment of the performance of the T/P dual-frequency altimeter in addition, as well as an overview of future altimeter missions.

Precision Orbit Determination Standards for the Jason Series of Altimeter Missions

The Jason-1 altimeter satellite and its follow-on mission Jason-2/OSTM were launched in December 2001 and June 2008, respectively, to provide the scientific community with a high-accuracy continuous record of observations of the ocean surface topography. Both missions carry on board three state-of-the-art tracking systems (DORIS, GPS, SLR) to meet the requirement of better-than-1.5 cm radial accuracy for the operational orbit included in the geophysical data record (GDR) product. This article outlines the common set of models and processing techniques applied to both Jason reprocessed and operational orbits included in version C of the GDR, referred to as GDR-C standards for precision orbit determination (POD), and describes the systematic components of the radial error budget that are of most interest for the altimeter data analysts. The nonsystematic component of the error budget, quantified by intercomparison of orbits using similar models or with reduced dependency on the dynamic models, is generally at or below 7 mm RMS (root-mean-square). In particular, the average daily RMS of the radial difference between the JPL and CNES reduced-dynamic orbits on Jason-2 is below 6 mm. Concerning the dynamic models employed, the principal contributors to residual systematic differences appear to be the time varying gravity and solar radiation pressure, resulting in geographically correlated periodic signals that have amplitudes at the few-mm level. Concerning the drifts of the orbits along the North/South direction, all solutions agree to better than the 1 mm/year level.

Testing General Relativity and gravitational physics using the LARES satellite

The discovery of the accelerating expansion of the Universe, thought to be driven by a mysterious form of “dark energy” constituting most of the Universe, has further revived the interest in testing Einstein’s theory of General Relativity. At the very foundation of Einstein’s theory is the geodesic motion of a small, structureless test-particle. Depending on the physical context, a star, planet or satellite can behave very nearly like a test-particle, so geodesic motion is used to calculate the advance of the perihelion of a planet’s orbit, the dynamics of a binary pulsar system and of an Earth-orbiting satellite. Verifying geodesic motion is then a test of paramount importance to General Relativity and other theories of fundamental physics. On the basis of the first few months of observations of the recently launched satellite LARES, its orbit shows the best agreement of any satellite with the test-particle motion predicted by General Relativity. That is, after modelling its known non-gravitational perturbations, the LARES orbit shows the smallest deviations from geodesic motion of any artificial satellite: its residual mean acceleration away from geodesic motion is less than

Gravitomagnetism and Its Measurement with Laser Ranging to the LAGEOS Satellites and GRACE Earth Gravity Models

\ensuremath 0.5\times10^{-12}

Nongravitational effects and the LAGEOS eccentricity excitations

m/s^2. LARES-type satellites can thus be used for accurate measurements and for tests of gravitational and fundamental physics. Already with only a few months of observation, LARES provides smaller scatter in the determination of several low-degree geopotential coefficients (Earth gravitational deviations from sphericity) than available from observations of any other satellite or combination of satellites.

A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model

Dragging of Inertial Frames and gravitomagnetism are predictions of Einstein’s theory of General Relativity. Here, after a brief introduction to these phenomena of Einstein’s gravitational theory, we describe the method we have used to measure the Earth’s gravitomagnetic field using the satellites LAGEOS (LAser GEOdynamics Satellite), LAGEOS 2 and the Earth’s gravity models obtained by the spacecraft GRACE. We then report the results of our analysis with LAGEOS and LAGEOS 2, and with a number of GRACE (Gravity Recovery and Climate Experiment) models, that have confirmed this prediction of Einstein General Relativity and measured the Earth’s gravitomagnetic field with an accuracy of approximately 10%. We finally discuss the error sources in our measurement of gravitomagnetism and, in particular, the error induced by the uncertainties in the GRACE Earth gravity models. Here we both analyze the errors due to the static and time-varying Earth gravity field, and in particular we discuss the accuracy of the GRACE-only gravity models used in our measurement. We also provide a detailed analysis of the errors due to atmospheric refraction mis-modelling and to the uncertainties in measuring the orbital inclination. In the appendix, we report the complete error analysis and the total error budget in the measurement of gravitomagnetism with the LAGEOS satellites.

Neutral Density Measurements from the Gravity Recovery and Climate Experiment Accelerometers

A model for explaining the anomalous eccentricity excitations of the orbit of the LAGEOS I satellite is considered. It is suggested that two phenomena are responsible for the major part of these residuals: (1) about 1.3% mismodeling of the LAGEOS I surface mean radiation pressure coefficient, and (2) the Yarkovsky-Schach thermal effect with a properly modeled evolution of the satellite spin axis. Minor influences are also attributed to the asymmetric reflectivity of the satellite surface and the asymmetric thermal emissivity of the Earth. For these cases we give a suitable and compact formulation for the long-term orbit analysis. It is argued that contrary to the case of the LAGEOS I along-track residuals adjustment, which does not allow the determination of a particular combination of the Yarkovsky-Schach effect parameters, the combined analysis of the along-track residuals and the eccentricity excitations allows for their decorrelation. The resulting value of the Yarkovsky-Schach amplitude is estimated to be approximately 241 pm/s2, more than twice as large as given in previous works. In view of the unexplained part of the eccentricity residuals, we discuss the possible importance of several other nongravitational effects (Yarkovsky thermal effects due to Earths heating, electromagnetic effects, mismodeling of the transitions through Earths penumbra), concluding that none of them is quantitatively a good candidate.

Jason-1 Precision Orbit Determination by Combining SLR and DORIS with GPS Tracking Data

We present a test of general relativity, the measurement of the Earth’s dragging of inertial frames. Our result is obtained using about 3.5 years of laser-ranged observations of the LARES, LAGEOS, and LAGEOS 2 laser-ranged satellites together with the Earth gravity field model GGM05S produced by the space geodesy mission GRACE. We measure