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( Ti, Pt) = [-1.5 ± 2.3 (stat)± 1.5 (syst)] × 10^-15 at 1σ in statistical errors.

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 (A) and a (B)) of two test masses in terms of the Eotvos parameter eta(A,B)=2aA-aBaA+aB <i . 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 h down to the limit of the statistical error which is smaller than 10(-14) for eta(Ti, Pt). Accumulating data from all segments leads to eta(Ti, Pt) = [-1.5 +/- 2.3 (stat) +/- 1.5 (syst)] x 10(-15) showing no EP violation at the level of 2.7 x 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 Eot-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 Eotvos parameter with a statistical uncertainty of 1.1 x 10(-15).

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±9 (stat)±9 (syst)] ×10^-15 (both 1σ 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 1σ uncertainties leads to a current limit on δ of about 1.3×10^-14.

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.

fundamental physics test, Kennedy-Thorndike, clocks, ultra-stable cavities, iodine spectroscopy, space instrumentation

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(Ti,Pt)= [-1 ± 9 (stat) ± 9 (syst)] × 10^-15 (1σ statistical uncertainty) for the titanium-platinum Eötvös parameter characterizing the relative difference in their free-fall accelerations.

The Weak Equivalence Principle (WEP) is at the basis of General Relativity – the best theory for gravitation today. It has been and still is tested with different methods and accuracies. In this paper an overview of tests of the Weak Equivalence Principle done in the past, developed in the present and planned for the future is given. The best result up to now is derived from the data of torsion balance experiments by Schlamminger et al. (2008). An intuitive test of the WEP consists of the comparison of the accelerations of two free falling test masses of different composition. This has been carried through by Kuroda & Mio (1989, 1990) with the up to date most precise result for this setup. There is still more potential in this method, especially with a longer free fall time and sensors with a higher resolution. Providing a free fall time of 4.74s (9.3s using the catapult) the drop tower of the Center of Applied Space Technology and Microgravity (ZARM) at the University of Bremen is a perfect facility for further improvements. In 2001 a free fall experiment with high sensitive SQUID (Superconductive QUantum Interference Device) sensors tested the WEP with an accuracy of 10-7 (Nietzsche, 2001). For optimal conditions one could reach an accuracy of 10-13 with this setup (Vodel et al., 2001). A description of this experiment and its results is given in the next part of this paper. For the free fall of macroscopic test masses it is important to start with precisely defined starting conditions concerning the positions and velocities of the test masses. An Electrostatic Positioning System (EPS) has been developed to this purpose. It is described in the last part of this paper.

The proposed space mission mini Space-Time Asymmetry Research (mSTAR) aims at a test of special relativity by performing a clock-clock comparison experiment in a low-Earth orbit. Using clocks with instabilies at or below the 1·10-15 level at orbit time, the Kennedy-Thorndike coefficient will be measured with an up to two orders of magnitude higher accuracy than the current limit set by ground-based experiments. In the current baseline design, mSTAR utilizes an optical absolute frequency reference based on molecular iodine and a length-reference based on a high-finesse optical cavity. Current efforts aim at a space compatible design of the two clocks and improving the long-term stability of the cavity reference. In an ongoing Phase A study, the feasibility of accommodating the experiment on a SaudiSat 4 bus is investigated.

We propose a small satellite mission that aims for testing the foundations of special relativity by performing a Kennedy-Thorndike (KT) experiment. A potential boost dependence of the velocity of light is measured by comparing a length reference (i.e. a highly stable optical resonator) with a molecular frequency reference. By employing clocks with 10-16 frequency stability at half orbit time (45 min) and by integration over 5000 orbits (2 years mission lifetime with 50% duty cycle) a 1600-fold improvement in measuring the Kennedy-Thorndike coefficient is targeted, compared to the current best terrestrial test.

Atom interferometers covering macroscopic domains of space-time are a spectacular manifestation of the wave nature of matter. Due to their unique coherence properties, Bose-Einstein condensates are ideal sources for an atom interferometer in extended free fall. In this paper we report on the realization of an asymmetric Mach-Zehnder interferometer operated with a Bose-Einstein condensate in microgravity. The resulting interference pattern is similar to the one in the far-field of a double-slit and shows a linear scaling with the time the wave packets expand. We employ delta-kick cooling in order to enhance the signal and extend our atom interferometer. Our experiments demonstrate the high potential of interferometers operated with quantum gases for probing the fundamental concepts of quantum mechanics and general relativity.

We propose a small satellite mission that aims for testing the postulates of special relativity by performing a Kennedy-Thorndike (KT) experiment. A potential boost dependence of the velocity of light is measured by comparing a length reference (i.e. an optical resonator) with a molecular frequency reference. Both employed clocks reached 10-16 frequency stability at orbit time (90 min) and by integration over 5000 orbits (2 years mission lifetime with 50 % duty cycle) a 1600-fold improvement in measuring the Kennedy-Thorndike coefficient is targeted, compared to the current best terrestrial test

The project "Future Gravity Field Satellite Missions" (FGM) was a logical consequence of two previous phases in Theme 2 "Observation of the System Earth from Space" in the BMBF/DFG (Federal Ministry of Education and Research/German Research Foundation) Research and Development Programme GEOTECHNOLOGIEN.

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.

The weak equivalence principle (WEP), that is, the universality of free fall, states that all point-like neutral particles in a gravitational field fall in the same way. This is the basis of the geometrization of the gravitational interaction. Together with further requirements on the behavior of point particles, light propagation and clocks one can show that gravity is modeled by a Riemannian geometry. Since in the quantum domain all objects are extended, it is not clear whether the notion of a WEP in the quantum domain makes sense at all. We show that for matter wave interferometry the notion of WEP still can be given a meaning. We give a short overview over schemes which allows a violation of the WEP and emphasize that there are also schemes which show that there might be violations of the WEP in the quantum regime which are not present classically. This makes a test of the WEP with quantum matter necessary. We also give a brief outline of the efforts made for testing the WEP with interferometry with cold atoms in the Bremen drop tower carried out by the QUANTUS and PRIMUS collaboration.

The present OSS (Outer Solar System) mission continues a long and bright tradition by associating the communities of fundamental physics and planetary sciences in a single mission with ambitious goals in both domains. OSS is an M-class mission to explore the Neptune system almost half a century after the flyby of the Voyager 2 spacecraft. Several discoveries were made by Voyager 2, including the Great Dark Spot (which has now disappeared) and Triton’s geysers. Voyager 2 revealed the dynamics of Neptune’s atmosphere and found four rings and evidence of ring arcs above Neptune. Benefiting from a greatly improved instrumentation, a mission as OSS would result in a striking advance in the study of the farthest planet of the solar system. Furthermore, OSS would provide a unique opportunity to visit a selected Kuiper Belt object subsequent to the passage of the Neptunian system. OSS would help consolidate the hypothesis of the origin of Triton as a Kuiper Belt object captured by Neptune, and to improve our knowledge on the formation of the solar system. The OSS probe would carry instruments allowing precise tracking of the spacecraft during the cruise. It would facilitate the best possible tests of the laws of gravity in deep space. These objectives are important for fundamental physics, as they test General Relativity, our current theoretical description of gravitation, but also for cosmology, astrophysics and planetary science, as General Relativity is used as a tool in all these domains. In particular, the models of solar system formation uses General Relativity to describe the crucial role of gravity. OSS is proposed as an international cooperation between ESA and NASA, giving the capability for ESA to launch an M-class mission towards the farthest planet of the solar system, and to a Kuiper Belt object. The proposed mission profile would allow to deliver a 500 kg class spacecraft. The design of the probe is mainly constrained by the deep space gravity test in order to minimize the perturbation of the accelerometer measurement.

The magnetic field plays a pivotal role in many fields of Astrophysics. This is especially true for the physics of the solar atmosphere. Measuring the magnetic field in the upper solar atmosphere is crucial to understand the nature of the underlying physical processes that drive the violent dynamics of the solar corona—that can also affect life on Earth. SolmeX, a fully equipped solar space observatory for remote-sensing observations, will provide the first comprehensive measurements of the strength and direction of the magnetic field in the upper solar atmosphere. The mission consists of two spacecraft, one carrying the instruments, and another one in formation flight at a distance of about 200 m carrying the occulter to provide an artificial total solar eclipse. This will ensure high-quality coronagraphic observations above the solar limb. SolmeX integrates two spectro-polarimetric coronagraphs for off-limb observations, one in the EUV and one in the IR, and three instruments for observations on the disk. The latter comprises one imaging polarimeter in the EUV for coronal studies, a spectro-polarimeter in the EUV to investigate the low corona, and an imaging spectro-polarimeter in the UV for chromospheric studies. SOHO and other existing missions have investigated the emission of the upper atmosphere in detail (not considering polarization), and as this will be the case also for missions planned for the near future. Therefore it is timely that SolmeX provides the final piece of the observational quest by measuring the magnetic field in the upper atmosphere through polarimetric observations.

Low thrust engines (e. g. ion thrusters, arcjet engines, magneto-plasmadynamic systems) with high specific impulses became important tools for recent space missions (SMART 1, Hayabusa 1 ...). Although in particular ion thrusters demonstrated high reliability and long term stability, their performance is not sufficient for satellite systems requiring drag-free, high precision attitude and orbit control. An increasing number of missions for geodetic purposes or astronomic science goals as well as formation flight scenarios with precise distance control between single satellites require much better propulsion systems enabling thrust control down to the sub-mu N level. Micropropulsion systems must be able (i) to compensate disturbing forces preventing the spacecraft from flying on an ideal geodetic orbit and (ii) to balance tidal forces and spacecraft dynamics in formation flight scenarios. Recent developments (e. g. Field Emission Electric Propulsion - FEEP) are promising but so far not sufficient approaches, wherefore laser induced ablative thrusters are completely new concepts still under study.

Clouds of ultra-cold atoms and especially Bose–Einstein condensates (BEC) provide a source for coherent matter-waves in numerous earth bound experiments. Analogous to optical interferometry, matter-wave interferometers can be used for precision measurements allowing for a sensitivity orders of magnitude above their optical counterparts. However, in some respects the presence of gravitational forces in the lab limits experimental possibilities. In this article, we report about a compact and robust experiment generating Bose–Einstein condensates in the drop tower facility in Bremen, Germany. We also present the progress of building the succeeding experiment in which a two species atom interferometer will be implemented to test the weak equivalence principle with quantum matter.