arXiv subjects

Benny Rievers

Publications and source records attributed to Benny Rievers.

14 recordsLinked to original sources

arXiv2025

General Relativity and Geodesy

Mass redistribution on Earth due to dynamic processes such as ice melting and sea level rise leads to a changing gravitational field, observable by geodetic techniques. Monitoring this change over time allows us to learn more about our planet and its dynamic evolution. In this paper, we highlight the impact of General Relativity (GR) on geodesy: it provides corrections essential for the interpretation of high-precision measurements and enables a completely novel measurement approach using chronometry, i.e., clock-based observations. Focusing on the latter, we review the construction of the relativistic gravity potential and the corresponding geoid definition as an isochronometric surface to elucidate the comparison to the conventional Newtonian geoid. Furthermore, we comment on additional potentials due to the non-Newtonian degrees of freedom of the relativistic gravitational field, and assess the feasibility of clock-based measurements for Gravity Field Recovery (GFR) from space. Although clock observations in space demonstrate technical promise for GFR, achieving the necessary precision for practical applications remains challenging.

gr-qc↗

arXiv2023

Gravitomagnetic Clock Effect: Using GALILEO to explore General Relativity

All experiments to date are in remarkable agreement with the predictions of Einstein's theory of gravity, General Relativity. Besides the classical tests, involving light deflection, orbit precession, signal delay, and the gravitational redshift, modern technology has pushed the limits even further. Gravitational waves have been observed multiple times as have been black holes, arguably amongst the most fascinating objects populating our universe. Moreover, geodetic satellite missions have enabled the verification of yet another prediction: gravitomagnetism. This phenomenon arises due to the rotation of a central body, e.g., the Earth, which is dragging spacetime along. One resulting effect on satellite orbits is the observed Lense-Thirring effect. Another predicted, yet unverified, effect is the so-called gravitomagnetic clock effect, which was first described by Cohen and Mashhoon as the proper time difference of two counter-revolving clocks in an orbit around a rotating mass. A theoretical framework is introduced that describes a gravitomagnetic clock effect based on a stationary spacetime model. An incremental definition of a suitable observable follows, which can be accessed via orbit data obtained from the European satellite navigation system Galileo, and an implementation of the framework for use with real satellite and clock data is presented. The technical requirements on a satellite mission are studied to measure the gravitomagnetic clock effect at the state-of-the-art in satellite laser ranging and modelling of gravitational and non-gravitational perturbations. Based on the analysis within this work, a measurement of the gravitomagnetic clock effect is highly demanding, but might just be within reach in the very near future based on current and upcoming technology.

gr-qc↗

arXiv2022

Result of the MICROSCOPE Weak Equivalence Principle test

The space mission MICROSCOPE dedicated to the test of the Equivalence Principle (EP) operated from April 25, 2016 until the deactivation of the satellite on October 16, 2018. In this analysis we compare the free-fall accelerations ($a_{\rm A}$ and $a_{\rm B}$) of two test masses in terms of the Eötvös parameter $η({\rm{A, B}}) = 2 \frac{a_{\rm A}- a_{\rm B}}{a_{\rm A}+ a_{\rm B}}$. No EP violation has been detected for two test masses, made from platinum and titanium alloys, in a sequence of 19 segments lasting from 13 to 198 hours down to the limit of the statistical error which is smaller than $10^{-14}$ for $ η({\rm{Ti, Pt}})$. Accumulating data from all segments leads to $η({\rm{Ti, Pt}}) =[-1.5\pm{}2.3{\rm (stat)}\pm{}1.5{\rm (syst)}] \times{}10^{-15}$ showing no EP violation at the level of $2.7\times{}10^{-15}$ if we combine stochastic and systematic errors quadratically. This represents an improvement of almost two orders of magnitude with respect to the previous best such test performed by the Eöt-Wash group. The reliability of this limit has been verified by comparing the free falls of two test masses of the same composition (platinum) leading to a null Eötvös parameter with a statistical uncertainty of $1.1\times{}10^{-15}$.

gr-qc↗

arXiv2022

MICROSCOPE mission: final results of the test of the Equivalence Principle

The MICROSCOPE mission was designed to test the Weak Equivalence Principle (WEP), stating the equality between the inertial and the gravitational masses, with a precision of $10^{-15}$ in terms of the Eötvös ratio $η$. Its experimental test consisted of comparing the accelerations undergone by two collocated test masses of different compositions as they orbited the Earth, by measuring the electrostatic forces required to keep them in equilibrium. This was done with ultra-sensitive differential electrostatic accelerometers onboard a drag-free satellite. The mission lasted two and a half years, cumulating five-months-worth of science free-fall data, two thirds with a pair of test masses of different compositions -- Titanium and Platinum alloys -- and the last third with a reference pair of test masses of the same composition -- Platinum. We summarize the data analysis, with an emphasis on the characterization of the systematic uncertainties due to thermal instabilities and on the correction of short-lived events which could mimic a WEP violation signal. We found no violation of the WEP, with the Eötvös parameter of the Titanium and Platinum pair constrained to $η({\rm Ti, Pt})~=~ [-1.5 \pm 2.3~{\rm (stat)} \pm 1.5~{\rm (syst)}]~\times 10^{-15}$ at $1σ$ in statistical errors.

gr-qc↗

arXiv2020

MICROSCOPE instrument description and validation

Dedicated accelerometers have been developed for the MICROSCOPE mission taking into account the specific range of acceleration to be measured on board the satellite. Considering one micro-g and even less as the full range of the instrument, leads to a customized concept and a high performance electronics for the sensing and servo-actuations of the accelerometer test-masses. In addition to a very accurate geometrical sensor core, a high performance electronics architecture provides the measurement of the weak electrostatic forces and torques applied to the test-masses. A set of capacitive sensors delivers the position and the attitude of the test-mass with respect to a very steady gold coated cage made in silica. The voltages applied on the electrodes surrounding each test-mass are finely controlled to generate the adequate electrical field and so the electrostatic pressures on the test-mass. This field maintains the test-mass motionless with respect to the instrument structure. Digital control laws are implemented in order to enable instrument operation flexibility and a weak position sensor noise. These electronics provide both the scientific data for MICROSCOPE's test of General Relativity and the data for the satellite drag-free and attitude control system (DFACS).

physics.ins-det↗

arXiv2019

Space test of the Equivalence Principle: first results of the MICROSCOPE mission

The Weak Equivalence Principle (WEP), stating that two bodies of different compositions and/or mass fall at the same rate in a gravitational field (universality of free fall), is at the very foundation of General Relativity. The MICROSCOPE mission aims to test its validity to a precision of $10^{-15}$, two orders of magnitude better than current on-ground tests, by using two masses of different compositions (titanium and platinum alloys) on a quasi-circular trajectory around the Earth. This is realised by measuring the accelerations inferred from the forces required to maintain the two masses exactly in the same orbit. Any significant difference between the measured accelerations, occurring at a defined frequency, would correspond to the detection of a violation of the WEP, or to the discovery of a tiny new type of force added to gravity. MICROSCOPE's first results show no hint for such a difference, expressed in terms of Eötvös parameter $δ(Ti,Pt)=[-1\pm{}9{\rm (stat)}\pm{}9{\rm (syst)}] \times{}10^{-15}$ (both 1$σ$ uncertainties) for a titanium and platinum pair of materials. This result was obtained on a session with 120 orbital revolutions representing 7\% of the current available data acquired during the whole mission. The quadratic combination of 1$σ$ uncertainties leads to a current limit on $δ$ of about $1.3\times{}10^{-14}$.

gr-qc↗

arXiv2019

The local dark sector. Probing gravitation's low-acceleration frontier and dark matter in the Solar System neighborhood

We speculate on the development and availability of new innovative propulsion techniques in the 2040s, that will allow us to fly a spacecraft outside the Solar System (at 150 AU and more) in a reasonable amount of time, in order to directly probe our (gravitational) Solar System neighborhood and answer pressing questions regarding the dark sector (dark energy and dark matter). We identify two closely related main science goals, as well as secondary objectives that could be fulfilled by a mission dedicated to probing the local dark sector: (i) begin the exploration of gravitation's low-acceleration regime with a man-made spacecraft and (ii) improve our knowledge of the local dark matter and baryon densities. Those questions can be answered by directly measuring the gravitational potential with an atomic clock on-board a spacecraft on an outbound Solar System orbit, and by comparing the spacecraft's trajectory with that predicted by General Relativity through the combination of ranging data and the in-situ measurement (and correction) of non-gravitational accelerations with an on-board accelerometer. Despite a wealth of new experiments getting online in the near future, that will bring new knowledge about the dark sector, it is very unlikely that those science questions will be closed in the next two decades. More importantly, it is likely that it will be even more urgent than currently to answer them. Tracking a spacecraft carrying a clock and an accelerometer as it leaves the Solar System may well be the easiest and fastest way to directly probe our dark environment.

astro-ph.IM↗

arXiv2019

Modeling approaches for precise relativistic orbits: Analytical, Lie-series, and pN approximation

Accurate orbit modeling plays a key role in contemporary and future space missions such as GRACE and its successor GRACE-FO, GNSS, and altimetry missions. To fully exploit the technological capabilities and correctly interpret measurements, relativistic orbital effects need to be taken into account. Within the theory of General Relativity, equations of motion for freely falling test objects, such as satellites orbiting the Earth, are given by the geodesic equation. We analyze and compare different solution methods in a spherically symmetric background, i.e. for the Schwarzschild spacetime, as a test bed. We investigate satellite orbits and use direct numerical orbit integration as well as the semi-analytical Lie-series approach. The results are compared to the exact analytical reference solution in terms of elliptic functions. For a set of exemplary orbits, we determine the respective accuracy of the different methods. Within the post-Newtonian approximation of General Relativity, modified orbital equations are obtained by adding relativistic corrections to the Newtonian equations of motion. We analyze the accuracy of this approximation with respect to the general relativistic setting. Therefore, we solve the post-Newtonian equation of motion using the eXtended High Performance Satellite dynamics Simulator. For corresponding initial conditions, we compare orbits in the Schwarzschild spacetime to those in its post-Newtonian approximation. Moreover, we compare the magnitude of relativistic contributions to several typical perturbations of satellite orbits due to, e.g., solar radiation pressure, Earth's albedo, and atmospheric drag. This comparison is done for our test scenarios and for a real GRACE orbit to highlight the importance of relativistic effects in geodetic space missions.

gr-qc↗

arXiv2018

Test of the Gravitational Redshift with Galileo Satellites in an Eccentric Orbit

On August 22, 2014, the satellites GSAT-0201 and GSAT-0202 of the European GNSS Galileo were unintentionally launched into eccentric orbits. Unexpectedly, this has become a fortunate scientific opportunity since the onboard hydrogen masers allow for a sensitive test of the redshift predicted by the theory of general relativity. In the present Letter we describe an analysis of approximately three years of data from these satellites including three different clocks. For one of these we determine the test parameter quantifying a potential violation of the combined effects of the gravitational redshift and the relativistic Doppler shift. The uncertainty of our result is reduced by more than a factor 4 as compared to the values of Gravity Probe A obtained in 1976.

gr-qc↗

arXiv2017

The MICROSCOPE mission: first results of a space test of the Equivalence Principle

According to the Weak Equivalence Principle, all bodies should fall at the same rate in a gravitational field. The MICROSCOPE satellite, launched in April 2016, aims to test its validity at the $10^{-15}$ precision level, by measuring the force required to maintain two test masses (of titanium and platinum alloys) exactly in the same orbit. A non-vanishing result would correspond to a violation of the Equivalence Principle, or to the discovery of a new long-range force. Analysis of the first data gives $δ\rm{(Ti,Pt)}= [-1 \pm 9 (\mathrm{stat}) \pm 9 (\mathrm{syst})] \times 10^{-15}$ (1$σ$ statistical uncertainty) for the titanium-platinum Eötvös parameter characterizing the relative difference in their free-fall accelerations.

astro-ph.IM↗

arXiv2014

Design of a dual species atom interferometer for space

Atom interferometers have a multitude of proposed applications in space including precise measurements of the Earth's gravitational field, in navigation & ranging, and in fundamental physics such as tests of the weak equivalence principle (WEP) and gravitational wave detection. While atom interferometers are realized routinely in ground-based laboratories, current efforts aim at the development of a space compatible design optimized with respect to dimensions, weight, power consumption, mechanical robustness and radiation hardness. In this paper, we present a design of a high-sensitivity differential dual species $^{85}$Rb/$^{87}$Rb atom interferometer for space, including physics package, laser system, electronics and software. The physics package comprises the atom source consisting of dispensers and a 2D magneto-optical trap (MOT), the science chamber with a 3D-MOT, a magnetic trap based on an atom chip and an optical dipole trap (ODT) used for Bose-Einstein condensate (BEC) creation and interferometry, the detection unit, the vacuum system for $10^{-11}$ mbar ultra-high vacuum generation, and the high-suppression factor magnetic shielding as well as the thermal control system. The laser system is based on a hybrid approach using fiber-based telecom components and high-power laser diode technology and includes all laser sources for 2D-MOT, 3D-MOT, ODT, interferometry and detection. Manipulation and switching of the laser beams is carried out on an optical bench using Zerodur bonding technology. The instrument consists of 9 units with an overall mass of 221 kg, an average power consumption of 608 W (819 W peak), and a volume of 470 liters which would well fit on a satellite to be launched with a Soyuz rocket, as system studies have shown.

physics.ins-det↗

arXiv2014

Atom Interferometry in Space: Thermal Management and Magnetic Shielding

Atom interferometry is an exciting tool to probe fundamental physics. It is considered especially apt to test the universality of free fall by using two different sorts of atoms. The increasing sensitivity required for this kind of experiment sets severe requirements on its environments, instrument control, and systematic effects. This can partially be mitigated by going to space as was proposed, for example, in the Spacetime Explorer and Quantum Equivalence Principle Space Test (STE-QUEST) mission. However, the requirements on the instrument are still very challenging. For example, the specifications of the STE-QUEST mission imply that the Feshbach coils of the atom interferometer are allowed to change their radius only by about 260 nm or 2.6E-4% due to thermal expansion although they consume an average power of 22 W. Also Earth's magnetic field has to be suppressed by a factor of 10E5. We show in this article that with the right design such thermal and magnetic requirements can indeed be met and that these are not an impediment for the exciting physics possible with atom interferometers in space.

physics.ins-det↗

arXiv2011

High precision thermal modeling of complex systems with application to the flyby and Pioneer anomaly

Thermal modeling of complex systems faces the problems of an effective digitalization of the detailed geometry and properties of the system, calculation of the thermal flows and temperature maps, treatment of the thermal radiation including possible multiple reflections, inclusion of additional external influences, extraction of the radiation pressure from calculated surface data, and computational effectiveness. In previous publications the solution to these problems have been outlined and a first application to the Pioneer spacecraft have been shown. Here we like to present the application of our thermal modeling to the Rosetta flyby anomaly as well as to the Pioneer anomaly. The analysis outlines that thermal recoil pressure is not the cause of the Rosetta flyby anomaly but likely resolves the anomalous acceleration observed for Pioneer 10.

gr-qc↗

arXiv2011

Astrodynamical Space Test of Relativity using Optical Devices I (ASTROD I) - A class-M fundamental physics mission proposal for Cosmic Vision 2015-2025: 2010 Update

This paper on ASTROD I is based on our 2010 proposal submitted for the ESA call for class-M mission proposals, and is a sequel and an update to our previous paper [Experimental Astronomy 23 (2009) 491-527; designated as Paper I] which was based on our last proposal submitted for the 2007 ESA call. In this paper, we present our orbit selection with one Venus swing-by together with orbit simulation. In Paper I, our orbit choice is with two Venus swing-bys. The present choice takes shorter time (about 250 days) to reach the opposite side of the Sun. We also present a preliminary design of the optical bench, and elaborate on the solar physics goals with the radiation monitor payload. We discuss telescope size, trade-offs of drag-free sensitivities, thermal issues and present an outlook. ASTROD I is a planned interplanetary space mission with multiple goals. The primary aims are: to test General Relativity with an improvement in sensitivity of over 3 orders of magnitude, improving our understanding of gravity and aiding the development of a new quantum gravity theory; to measure key solar system parameters with increased accuracy, advancing solar physics and our knowledge of the solar system; and to measure the time rate of change of the gravitational constant with an order of magnitude improvement and the anomalous Pioneer acceleration, thereby probing dark matter and dark energy gravitationally. It is envisaged as the first in a series of ASTROD missions. ASTROD I will consist of one spacecraft carrying a telescope, four lasers, two event timers and a clock. Two-way, two-wavelength laser pulse ranging will be used between the spacecraft in a solar orbit and deep space laser stations on Earth, to achieve the ASTROD I goals.

gr-qc↗