Erricos C. Pavlis

The Development of the NASA GSFC and NIMA Joint Geopotential Model

The NASA Goddard Space Flight Center, the National Imagery and Mapping Agency (NIMA; formerly the Defense Mapping Agency or DMA) and The Ohio State University have collaborated to produce EGM96, an improved degree 360 spherical harmonic model representing the Earth’s gravitational potential. This model was developed using: (1) satellite tracking data from more than 20 satellites, including new data from GPS and TDRSS, as well as altimeter data from TOPEX, GEOSAT and ERS-1. (2) 30’ x 30’ terrestrial gravity data from NIMA’s comprehensive archives, including new measurements from areas such as the former Soviet Union, South America, Africa, Greenland, and elsewhere. (3) 30’ x 30’ gravity anomalies derived from the GEOSAT Geodetic Mission altimeter data, as well as altimeter derived anomalies derived from ERS-1 by KMS (Kort and Matrikelstyrelsen, Denmark) in regions outside the GEOSAT coverage. The high degree solutions were developed using two different model estimation techniques: quadrature, and block diagonal. The final model is a composite solution consisting a combination solution to degree 70, a block diagonal solution to degree 359, and the quadrature model at degree 360. This new model will be used to define an undulation model that will be the basis for an update of the WGS-84 geoid. In addition, the model will contribute to oceanographic studies by improving the modeling of the ocean geoid and to geodetic positioning using the Global Positioning System (GPS).

A confirmation of the general relativistic prediction of the Lense–Thirring effect

An important early prediction of Einsteins general relativity was the advance of the perihelion of Mercurys orbit, whose measurement provided one of the classical tests of Einsteins theory. The advance of the orbital point-of-closest-approach also applies to a binary pulsar system and to an Earth-orbiting satellite. General relativity also predicts that the rotation of a body like Earth will drag the local inertial frames of reference around it, which will affect the orbit of a satellite. This Lense–Thirring effect has hitherto not been detected with high accuracy, but its detection with an error of about 1 per cent is the main goal of Gravity Probe B—an ongoing space mission using orbiting gyroscopes. Here we report a measurement of the Lense–Thirring effect on two Earth satellites: it is 99 ± 5 per cent of the value predicted by general relativity; the uncertainty of this measurement includes all known random and systematic errors, but we allow for a total ± 10 per cent uncertainty to include underestimated and unknown sources of error.

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.

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}

New high‐resolution model developed for Earth's gravitational field

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.

The GAVDOS Mean Sea Level and Altimeter Calibration Facility: Results for Jason-1

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.

Expected orbit determination performance for the TOPEX/Poseidon mission

After 3 years of intense work by some two dozen collaborating scientists at three institutions and after scores of evaluation tests, the Earth Gravitational Model 1996 (EGM96) was completed and released to the scientific community in September 1996. This model was developed jointly by the NASA Goddard Space Flight Center (GSFC), the National Imagery and Mapping Agency (NIMA, formerly the Defense Mapping Agency), and The Ohio State University. EGM96 provides a more accurate reference surface for the topography, improves models of the ocean circulation, improves orbit determination for low-orbiting satellites, and contributes to global and regional studies in tectonics and geodynamics. The new spherical harmonic model, is complete to degree 360, corresponding to a global resolution of about 55 km. EGM96 incorporates newly released surface gravity data from around the globe, over three decades of precise satellite tracking data and altimeter measurements of the ocean surface from the TOPEX/POSEIDON, ERS-1 and GEOSAT missions. Figure l a shows a global map of the geoid undulations implied by EGM96, while Figure l b shows the corresponding gravity anomaly field.

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

The location of the GAVDOS facility is under a crossing point of the original ground-tracks of TOPEX/Poseidon and the present ones for Jason-1, and adjacent to an ENVISAT pass, about 50 km south of Crete, Greece. Ground observations and altimetry comparisons over cycles 70 to 90, indicate that a preliminary estimate of the absolute measurement bias for the Jason-1 altimeter is 144.7 ± 15 mm. Comparison of Jason microwave radiometer data from cycles 37 and 62, with locally collected water vapor radiometer and solar spectrometer observations indicate a 1–2 mm agreement.

On the measurement of the Lense–Thirring effect using the nodes of the LAGEOS satellites, in reply to “On the reliability of the so-far performed tests for measuring the Lense–Thirring effect with the LAGEOS satellites” by L. Iorio☆

The research that has been conducted in the Space Geodesy Branch at NASA/Goddard Space Flight Center in preparation for meeting the 13-cm radial orbit accuracy requirement for the TOPEX/Poseidon (T/P) mission is described. New developments in modeling the Earths gravitational field and modeling the complex nonconservative forces acting on T/P are highlighted. The T/P error budget is reviewed, and a prelaunch assessment of the predicted orbit determination accuracies is summarized. >