Preliminary study for the measurement of the Lense-Thirring effect with the Galileo satellites

The precession of the orbital node of a particle orbiting a rotating mass is known as Lense-Thirring effect (LTE) and is a manifestation of the general relativistic phenomenon of dragging of inertial frames or frame-dragging. The LTE has already been measured by using the node drifts of the LAGEOS satellites and GRACE-based Earth gravity field models with an accuracy of about 10% and will be improved down to a few percent with the recent LARES experiment. The Galileo system will provide 27 new node observables for the LTE estimation and their combination with the LAGEOS and LARES satellites can potentially reduce even more the error due to the mismodeling in Earth's gravity field. However, the accurate determination of the Galileo orbits requires the estimation of many different parameters, which can absorb the LTE on the orbital nodes. Moreover, the accuracy of the Galileo orbits and hence, of their node drifts, is mainly limited by the mismodeling in the Solar Radiation Pressure (SRP). Using simulated data we analyze the effects of the mismodeling in the SRP on the Galileo nodes and propose optimal orbit parameterizations for the measurement of the LTE from the future Galileo observations

A new laser-ranged satellite for General Relativity and space geodesy: I. An introduction to the LARES2 space experiment

We introduce the LARES 2 space experiment recently approved by the Italian Space Agency (ASI). The LARES 2 satellite is planned for launch in 2019 with the new VEGA C launch vehicle of ASI, ESA and ELV. The orbital analysis of LARES 2 experiment will be carried out by our international science team of experts in General Relativity, theoretical physics, space geodesy and aerospace engineering. The main objectives of the LARES 2 experiment are gravitational and fundamental physics, including accurate measurements of General Relativity, in particular a test of frame-dragging aimed at achieving an accuracy of a few parts in a thousand, i.e., aimed at improving by about an order of magnitude the present state-of-the-art and forthcoming tests of this general relativistic phenomenon. LARES 2 will also achieve determinations in space geodesy. LARES 2 is an improved version of the LAGEOS 3 experiment, proposed in 1984 to measure frame-dragging and analyzed in 1989 by a joint ASI and NASA study

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. 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

LARES Satellite Thermal Forces and a Test of General Relativity

We summarize a laser-ranged satellite test of frame-dragging, a prediction of General Relativity, and then concentrate on the estimate of thermal thrust, an important perturbation affecting the accuracy of the test. The frame dragging study analysed 3.5 years of data from the LARES satellite and a longer period of time for the two LAGEOS satellites. Using the gravity field GGM05S obtained via the Grace mission, which measures the Earth's gravitational field, the prediction of General Relativity is confirmed with a 1-$\sigma$ formal error of 0.002, and a systematic error of 0.05. The result for the value of the frame dragging around the Earth is $\mu$ = 0.994, compared to $\mu$ = 1 predicted by General Relativity. The thermal force model assumes heat flow from the sun (visual) and from Earth (IR) to the satellite core and to the fused silica reflectors on the satellite, and reradiation into space. For a roughly current epoch (days 1460 - 1580 after launch) we calculate an average along-track drag of -0.50 $pm/s^{2}$.Comment: 6 pages, multiple figures in Proceedings of Metrology for Aerospace (MetroAeroSpace), 2016 IEE

Fundamental Physics and General Relativity with the LARES and LAGEOS satellites

Current observations of the universe have strengthened the interest to further test General Relativity and other theories of fundamental physics. After an introduction to the phenomenon of frame-dragging predicted by Einstein's theory of General Relativity, with fundamental astrophysical applications to rotating black holes, we describe the past measurements of frame-dragging obtained by the LAGEOS satellites and by the dedicated Gravity Probe B space mission. We also discuss a test of String Theories of Chern-Simons type that has been carried out using the results of the LAGEOS satellites. We then describe the LARES space experiment. LARES was successfully launched in February 2012 to improve the accuracy of the tests of frame-dragging, it can also improve the test of String Theories. We present the results of the first few months of observations of LARES, its orbital analyses show that it has the best agreement of any other satellite with the test-particle motion predicted by General Relativity. We finally briefly report the accurate studies and the extensive simulations of the LARES space experiment, confirming an accuracy of a few percent in the forthcoming measurement of frame-dragging.Comment: To be publihed in Nuclear Physics. arXiv admin note: substantial text overlap with arXiv:1306.1826, arXiv:1211.137

A Test of General Relativity Using the LARES and LAGEOS Satellites and a GRACE Earth's Gravity Model

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's gravity field model GGM05S produced by the space geodesy mission GRACE. We measure $\mu = (0.994 \pm 0.002) \pm 0.05$, where $\mu$ is the Earth's dragging of inertial frames normalized to its General Relativity value, 0.002 is the 1-sigma formal error and 0.05 is the estimated systematic error mainly due to the uncertainties in the Earth's gravity model GGM05S. Our result is in agreement with the prediction of General Relativity.Comment: 13 pages, 4 figures, published on EPJ

Beyond the Electronic Commerce Diffusion Rate: Efficiency Prevails

The diffusion race of e-commerce applications and solutions in the German industry seems to be concluded. This applies more or less for large firms, but especially for SMEs in the analyzed industry sectors. Independent of firm size, more than one third of all firms responded that the implementation of e-commerce contributed substantially to improve existing operational processes and to expand markets. E-commerce readiness, and due to its relative efficient usage, is observable not only in large firms. The “digital divide” or “digital gap” between large firms and SMEs has disappeared. Increasingly, SMEs may often benefit more from e-commerce applications than large firms. Although e-commerce technologies may be available theoretically in all industries and firms, efficient usage depends directly on the consistent implementation of more sophisticated solutions, such as on-line procurement or Internet-based supply chain management. Firms with defined strategic IT-related goals are more often efficient than firms without such goal

Globalization and E-Commerce II: Environment and Policy in Germany

Due to its economic power as the largest economy in Europe and third largest in the world, Germany inevitably will play an important role in e-commerce. After the improvement and diffusion of high-speed Internet access, like ISDN or DSL, Germany enjoys more ISDN telephone lines than any country; also the highest DSL per capita ratio, in Europe. Germany includes a large, highly educated and relatively wealthy population, which is an important prerequisite for successful e-commerce activities. Due to foreign language skills in the German population (every pupil is required to learn English; a large number know basic French or Spanish, too), the language barrier to using international Web sites is small. Moreover, the German education system puts increasing emphasis on information and communications technology (ICT) skills. Invention activity in some areas of ICT shows signs of improvement. Starting from a low level, patent activity in mobile communications and the Internet grew faster in Germany than anywhere else in Europe. This growth could be viewed as an early indicator of strengthening the mobile e-commerce sector in Germany and may be interpreted as an important effort in catching-up with overall e-commerce development. More than 80% of the GNP is created in mid-sized companies (Mittelstand), which traditionally are considered as more flexible and innovative than large enterprises. The majority of these small and medium-sized enterprises (SMEs) can access the Internet. Looking at Internet penetration, German SMEs are at the top together with SMEs in Scandinavian countries. The central position of Germany as a hub to Europe together with the excellent public and private transport infrastructure is a competitive advantage to attract foreign investments. Germany follows the innovation model be the best imitator of successful developments and within this course exploits the competitive advantage achievable through integration. After e-commerce technologies proved successful, Germany caught up in developing its relevant infrastructure and is now gaining momentum