Equivalence Principle In Space Research Articles

MICROSCOPE’s constraint on a short-range fifth force

The MICROSCOPE experiment was designed to test the weak equivalence principle in space, by comparing the low-frequency dynamics of cylindrical ‘free-falling’ test masses controlled by electrostatic forces. We use data taken during technical sessions aimed at estimating the electrostatic stiffness of MICROSCOPE’s sensors to constrain a short-range Yukawa deviation from Newtonian gravity. We take advantage of the fact that in the limit of small displacements, the gravitational interaction (both Newtonian and Yukawa-like) between nested cylinders is linear, and thus simply characterised by a stiffness. By measuring the total stiffness of the forces acting on a test mass as it moves, and comparing it with the theoretical electrostatic stiffness (expected to dominate), it is a priori possible to infer constraints on the Yukawa potential parameters. However, we find that measurement uncertainties are dominated by the gold wires used to control the electric charge of the test masses, though their related stiffness is indeed smaller than the expected electrostatic stiffness. Moreover, we find a non-zero unaccounted for stiffness that depends on the instrument’s electric configuration, hinting at the presence of patch-field effects. Added to significant uncertainties on the electrostatic model, they only allow for poor constraints on the Yukawa potential. This is not surprising, as MICROSCOPE was not designed for this measurement, but this analysis is the first step to new experimental searches for non-Newtonian gravity in space.

Modeling and compensation of cross-axis coupling in an electrostatic accelerometer for testing the equivalence principle.

Electrostatic accelerometers have extremely high sensitivity and are ideal scientific instruments for measuring very weak acceleration. In particular, a single-sensitive-axis electrostatic accelerometer can be used for testing the equivalence principle in space. Sensitive-axis capacitances formed by axial electrodes and a cylindrical proof mass vary with the axial motion of the mass and are also affected by radial motion, which results in cross-axis coupling disturbances. A quantitative model is built to analyze the cross-axis coupling effect on the sensitive axis from the radial suspension loop, including a nonlinear model for large radial motion and a linear model for small radial motion. Frequency response simulation shows that the cross-axis coupling effect for a small signal case arises mostly in the high-frequency range. Experiments are carried out with a ground-based electrostatic accelerometer made of a single, non-rotating test cylinder, and in this case, the experimental results are utilized to verify the mathematical model. Cross-axis coupling for small signal perturbations is virtually removed if the equilibrium position of the proof mass is calibrated to the null position of the sensor cage. In addition, data post-processing can further attenuate the cross-axis coupling disturbances when dealing with large radial motion. The cross-axis coupling disturbances on both the position and the acceleration measurement signals in the sensitive axis are mostly removed in ground-based experiments. The proposed model and compensation can be extended to space equivalence principle instruments and other electrostatic accelerometers with a cylindrical proof mass.

Testing the equivalence principle in space after the MICROSCOPE mission

Tests of the Weak Equivalence Principle can reveal a new, composition dependent, force of nature or disprove many models of new physics. For the first time such a test is successfully carried out in space by the MICROSCOPE satellite. Early results show no violation sourced by the Earth for Pt and Ti test masses with random errors (after 8.26d of integration time) of about 1 part in 1e14, and similar systematic errors.It improves by 10 times over the best ground tests with rotating torsion balances despite 70 times less sensitivity to differential accelerations, thanks to the much stronger driving signal in orbit. The test is limited by thermal noise from internal damping in the gold wires used for electrical grounding. This noise was shown to decrease when the s/c was set to rotate faster than planned. The result will improve by the end of the mission, as thermal noise decreases with more data. Not so systematic errors. We investigate major non-gravitational effects and find that the Pt-Pt sensor does not allow their separation from the signal. The early test reports an upper limit of systematic errors in the Pt-Ti sensor which are not detected in the Pt-Pt one, hence would not be distinguished from a violation. Once all the integration time is used to reduce random noise there will be no time left to check systematics. MICROSCOPE demonstrates the huge potential of space for WEP tests of very high precision and indicates how to reach it. To realize the potential, a new experiment needs the spacecraft to be in rapid, stable rotation around the symmetry axis, needs high quality state-of-the-art mechanical suspensions, and must allow systematic checks. The design of the "Galileo Galilei" (GG) experiment, aiming to test the WEP to 1 part in 1e17 unites all the needed features, indicating that a quantum leap in space is possible provided the new experiment heeds the lessons of MICROSCOPE.

MICROSCOPE limits for new long-range forces and implications for unified theories

Many theories beyond the Standard Model involve an extra U(1) gauge group. The resulting gauge boson U, in general mixed with the Z and the photon, may be massless or very light, and very weakly coupled. It may be viewed as a generalized dark photon interacting with matter through a linear combination (\epsilon_Q Q + \epsilon_B B+\epsilon_L L) e, involving B-L in a grand-unified theory, presumably through B-L-.61 Q, inducing effectively a very small repulsive force between neutrons. This new force, if long-ranged, may manifest through apparent violations of the Equivalence Principle. They are approximately proportional to \epsilon_B+\epsilon_L/2, times a combination involving mostly \epsilon_L. New forces coupled to B-L or L should lead to nearly opposite values of the E\"otv\"os parameter \delta, and to almost the same limits for \epsilon_{B-L} or \epsilon_L, as long as no indication for \delta \neq 0 is found. We derive new limits from the first results of the MICROSCOPE experiment testing the Equivalence Principle in space. A long-range force coupled to (\epsilon_Q Q + \epsilon_{B-L} (B-L)) e or (\epsilon_Q Q + \epsilon_L L) e should verify |\epsilon_{B-L}| or |\epsilon_L| < .8 10^{-24}, and a force coupled to (\epsilon_Q Q + \epsilon_B B) e, |\epsilon_B| < 5 10^{-24}. We also discuss, within supersymmetric theories, how such extremely small gauge couplings g", typically \simle 10^{-24}, may be related to a correspondingly large \xi"D" term associated with a huge initial vacuum energy density, \propto 1/g"^2. The corresponding hierarchy between energy scales, by a factor \propto 1/\sqrt g" \simge 10^{12}, involves a very large scale ~ 10^{16} GeV, that may be associated with inflation, or supersymmetry breaking with a very heavy gravitino, leading to possible values of {\delta} within the experimentally accessible range.

MICROSCOPE: five months after launch

MICROSCOPE is a French Space Agency mission that aims to test the Weak Equivalence Principle in space down to an accuracy of 10−15, two orders of magnitude better than the current constraints. The MICROSCOPE satellite was launched on April 25, 2016. We describe the MICROSCOPE mission, its measurement principle and instrument, and report on the status of its in-orbit commissioning as of September 2016.

Testing the strong equivalence principle with spacecraft ranging towards the nearby Lagrangian points

General relativity is supported by great experimental evidence. Yet there is a lot of interest in precisely setting its limits with on going and future experiments. A question to answer is about the validity of the Strong Equivalence Principle. Ground experiments and Lunar Laser Ranging have provided the best upper limit on the Nordtvedt parameter $\sigma[\eta]=4.4\times 10^{-4}$. With the future planetary mission BepiColombo, this parameter will be further improved by at least an order of magnitude. In this paper we envisage yet another possible testing environment with spacecraft ranging towards the nearby Sun-Earth collinear Lagrangian points. Neglecting errors in planetary masses and ephemerides, we forecast $\sigma[\eta]=6.4\,(2.0)\times10^{-4}$ (5 yr integration time) via ranging towards $L_1$ in a realistic (optimistic) scenario depending on current (future) range capabilities and knowledge of the Earth's ephemerides. A combined measurement, $L_1$+$L_2$, gives instead $4.8\,(1.7)\times10^{-4}$. In the optimistic scenario a single measurement of one year would be enough to reach $\approx3\times10^{-4}$. All figures are comparable with Lunar Laser Ranging, but worse than BepiColombo. Performances could be much improved if data were integrated over time and over the number of satellites flying around either of the two Lagrangian points. We point out that some systematics (gravitational perturbations of other planets or figure effects) are much more in control compared to other experiments. We do not advocate a specific mission to constrain the Strong Equivalence Principle, but we do suggest analysing ranging data of present and future spacecrafts flying around $L_1$/$L_2$ (one key mission is, for instance, LISA Pathfinder). This spacecraft ranging would be a new and complementary probe to constrain the Strong Equivalence Principle in space.

Status of MICROSCOPE, a mission to test the Equivalence Principle in space

MICROSCOPE is a French Space Agency mission that aims to test the Weak Equivalence Principle in space down to an accuracy of 10-15. This is two orders of magnitude better than the current constraints, which will allow us to test General Relativity as well as theories beyond General Relativity which predict a possible Weak Equivalence Principle violation below 10-13. In this communication, we describe the MICROSCOPE mission, its measurement principle and instrument, and we give an update on its status. After a successful instrument's commissioning, MICROSCOPE is on track for on-schedule launch, expected in 2016.

Testing the Equivalence Principle in space with MICROSCOPE: the data analysis challenge

AbstractTheories beyond the Standard Model and General Relativity predict a violation of the Weak Equivalence Principle (WEP) just below the current best experimental upper limits. MICROSCOPE (Micro-Satellite à traînée Compensée pour l'Observation du Principe d'Equivalence) will allow us to lower them by two orders of magnitude, and maybe to detect a WEP violation. However, analyzing the MICROSCOPE data will be challenging, mostly because of missing data and a colored noise burrying the signal of interest. In this communication, we apply an inpainting technique to simulated MICROSCOPE data and show that inpainting will help detect a WEP violation signal.

Electrostatic charging of test masses in Equivalence Principle experiments in low-Earth, near-polar orbits

Experiments to test the Equivalence Principle in space are typically suggested for flight in low-Earth, circular, Sun-synchronous orbits at 400–600 km altitude. In these orbits the spacecraft routinely traverses the South Atlantic Anomaly (SAA), where the fluxes of trapped charged particles are enhanced. These particles, together with energetic solar flare protons and galactic cosmic rays, will penetrate the spacecraft structure and develop into a shower of lower energy particles which deposit electrical charge, energy (heat), and momentum on the test masses. Of these, charge leads to the most serious disturbances. Estimates of the charging rates have been computed using the GEANT radiation transport code, in conjunction with realistic proton flux models.

Historical perspective on testing the Equivalence Principle

Few facts in science are more surprising and none has had a longer history than the apparent equivalence of the two kinds of mass in physics, gravitational and inertial. From Galileo and Newton to Eötvös and Einstein, it has been a compelling issue both theoretically and experimentally. Ground-based tests have now a precision of about 1 part in 10 12. Even with this extraordinary agreement, there are profound theoretical reasons for carrying the measurements further. Our generation has the unique oppurtunity to make an advance of a factor of a million in testing the Equivalence Principle in space.

A rotating differential accelerometer for testing the equivalence principle in space: results from laboratory tests of a ground prototype

We have proposed to test the equivalence principle (EP) in low Earth orbit with a rapidly rotating differential accelerometer (made of weakly coupled concentric test cylinders) whose rotation provides high frequency signal modulation and avoids severe limitations otherwise due to operation at room temperature [PhRvD 63 (2001) 101101]. Although the accelerometer has been conceived for best performance in absence of weight, we have designed, built and tested a variant of it at 1-g. Here we report the results of measurements performed so far. Losses measured with the full system in operation yield a quality factor only four times smaller than the value required for the proposed high accuracy EP test in space. Unstable whirl motions, which are known to arise in the system and might be a matter of concern, are found to grow as slowly as predicted and can be stabilized. The capacitance differential read-out (the mechanical parts, electronics and software for data analysis) is in all similar to what is needed in the space experiment. In the instrument described here the coupling of the test masses is 24 000 times stiffer than in the one proposed for flight, which makes it 24 000 times less sensitive to differential displacements. With this stiffness it should detect test masses separations of 1.5·10 −2 μm, while so far we have achieved only 1.5 μm, because of large perturbations—due to the motor, the ball bearings, the non-perfect verticality of the system—all of which, however, are absent in space. The effects of these perturbations should be reduced by 100 times in order to perform a better demonstration. Further instrument improvements are underway to fill this gap and also to reduce its stiffness, thus increasing its significance as a prototype of the space experiment.

MICROSCOPE, testing the equivalence principle in space

The test of the equivalence principle can be performed in space with orders of magnitude better resolution than in the laboratory, because of the outstanding steady and soft environment of the in-orbit experiment. The expected new experimental results will contribute to the unification of the four interactions, demonstrate the existence of extra scalar interaction or participate in the research for a quantum gravity theory. The MICROSCOPE space mission is being developed within the framework of the Cnes scientific program with the objective of testing the universality of free fall with a 10 −15 accuracy. The concept and the design of the experiment are discussed and the major performance drivers of the room temperature instrument are pointed out. The launch of the drag-free satellite is scheduled for late 2004. By its specific technology demonstration, the mission will open the way to even more accurate acceleration measurements for other space missions in fundamental physics.

Radiometer effect in space missions to test the equivalence principle

Experiments to test the equivalence principle in space by testing the universality of free fall in the gravitational field of the Earth have to take into account the radiometer effect, caused by temperature differences in the residual gas inside the spacecraft as it is exposed to the infrared radiation from Earth itself. We report the results of our evaluation of this effect for the three proposed experiments currently under investigation by space agencies: mSCOPE, STEP, and GG. It is found that in mSCOPE, which operates at room temperature, and even in STEP, where the effect is greatly reduced by means of very low temperatures, the radiometer effect is a serious limitation to the achievable sensitivity. Instead, by axially spinning the whole spacecraft and with an appropriate choice of the sensitivity axes—as proposed in GG—the radiometer effect averages out and becomes unimportant even at room temperature.

The “Galileo Galilei” (GG) project: Testing the Equivalence Principle in space and on Earth

“ GALILEO GALILEI” ( GG) is a proposal for a small, low orbit satellite devoted to testing the Equivalence Principle ( EP) of Galileo, Newton and Einstein to 1 part in 10 17. At the end of 1997 GG has been selected and funded by ASI (Agenzia Spaziale Italiana) for a 1-year Phase A study. The main novelty of GG is that the concentric hollow test cylinders whose relative motion (in the plane perpendicular to the spin axis) would be affected by an EP violation, spin together with the read-out capacitance sensors placed in between them. The nominal spin rate is 2 Hz, and this is the frequency at which the putative EP violation signal is modulated by the sensors. As compared to other experiments the modulation frequency is increased by more than a factor 10 4, thus reducing 1 f (low frequency) electronic and mechanical noise. GG will have FEEP ion thrusters for drag compensation. The required amount of propellant is of a few grams only. The experiment works at room temperature. To demonstrate the feasibility of the space experiment a payload prototype for EP testing on the ground ( GGG - GG on the Ground) is under development in the laboratories of Laben. The challenge in this field is to fly an experiment able to improve by many orders of magnitude the current best ground sensitivity (≅10 −12). This requires spurious relative motions of the test bodies to be greatly reduced, leaving them essentially motionless. Doing that with more than one pair of bodies appears to be an unnecessary complication. This is why GG is now proposed with a single pair of test masses. Information, research papers and photographs of the ground apparatus are available on the Web ( http://tycho.dm.unipi.it/nobili).

Application of high performance LTS SQUID systems in gravitational experiments

The design of a Galilean-type free-fall experiment to test Einstein's equivalence principle at an improved level of sensitivity is described. Two test bodies of different material fall down from a height of 109 m inside of an evacuated drop tube (Drop Tower Facility Bremen, Germany). Their possible relative displacement is measured using LTS DC SQUID based position sensors. Experiences and results of this experiment meet directly the current STEP project of NASA/ESA to test the Equivalence Principle in space at a level of one part in 10/sup 18/. Several issues of the developed measuring system are discussed, above all, the performance of two types of SQUID position sensors. Furthermore some recent results of free fall tests of components of the measuring system at the Bremen Drop Tower are presented.

Proposed noncryogenic, nondrag-free test of the equivalence principle in space

Ever since Galileo scientists have known that all bodies fall with the same acceleration regardless of their mass and composition. Known as the Universality of Free Fall, this is the most direct experimental evidence of the Weak Equivalence Principle, a founding pillar of General Relativity according to which the gravitational (passive) mass m g and the inertial mass m i are always in the same positive ratio in all test bodies. A space experiment offers two main advantages: a signal about a factor of a thousand bigger than on Earth and the absence of weight. A new space mission named GALILEO GALILEI (GG) has been proposed (Nobili et al., 1995 [J. Astronautical Sciences, 43, 219]; GALILEO GALILEI (GG), PRE PHASE A REPORT, ASI (Agenzia Spaziale Italiana), September 1996) aimed at testing the weak Equivalence Principle (EP) to 1 part in 10 17 in a rapidly spinning (5 Hz) drag-free spacecraft at room temperature, the most recent ground experiments having reached the level of 10 −12 (Adelberger et al., 1990 [PhRvD, 42, 3267]; Su et al., 1994 [PhRvD, 50, 3614]). Here we present a nondrag-free version of GG which could reach a sensitivity of 1 part in 10 16. The main feature of GG is that, similarly to the most recent ground experiments, the expected (low frequency) signal is modulated at higher frequency by spinning the system, in this case by rotating the test bodies (in the shape of hollow cylinders) around their symmetry axes, the signal being in the perpendicular plane. They are mechanically suspended inside the spacecraft and have very low frequencies of natural oscillation (due to the weakness of the springs that can be used because of weightlessness) so as to allow self-centering of the axes; vibrational noise around the spin/signal frequency is attenuated by means of mechanical suspensions. The signal of an EP violation would appear at the spin frequency as a relative ( differential) displacement of the test masses perpendicularly to the spin axis, and be detected by capacitance sensors; thermal stability across the test masses and for the required integration time is obtained passively thanks to both the fast spin and the cylindrical symmetry. In the nondrag-free version the entire effect of atmospheric drag is retained, but a very accurate balancing of the test bodies must be ensured (through a coupled suspension) so as to reach a high level of Common Mode Rejection and reduce the differential effects of drag below the target sensitivity. In so doing the complexities of a drag-free spacecraft are avoided by putting more stringent requirements on the experiment. The spacecraft must have a high area-to-mass ratio in order to reduce the effects of nongravitational forces; it is therefore a natural choice to have three pairs of test masses (in three experimental chambers) rather than one as by Nobili et al. (1995) [J. Astronautical Sciences, 43, 219] and the mission called GALILEO GALILEI [PRE PHASE A REPORT, ASI (Agenzia Spaziale Italiana), September 1996]. The GG setup is specifically designed for space; however, a significant EP test on the ground is possible — because the signal is in the transverse plane — by exploiting the horizontal component of the gravitational and the centrifugal field of the Earth. This ground test is underway.

Orbital mechanics of free-falling bodies for testing the weak equivalence principle in space

Various proposed space experiments to test the weak equivalence principle (EP) use ultra-precise differential accelerometers in Earth orbit. A common feature of these accelerometers is that their test masses are physically constrained in some manner, thus imposing a limit on the achievable sensitivity. An alternative approach, analogous to the familiar drop-tower experiments, would be to release the masses inside an orbiting protective cavity, and infer the EP violation from observations of their relative trajectory. This paper addresses the errors inherent to such a scheme, focusing on the orbital mechanics aspects. Quantitative results are presented for a candidate sensing system. It is concluded that the technique is limited by initial condition errors, and will not reach the expected sensitivity of the spaceborne accelerometers.

Test of the equivalence principle in space

Any violation of the equivalence principle (EP) between test masses in the near-Earth orbit is about 500 times bigger than on the ground, which makes the case for a space experiment very strong. Indeed, ESA and NASA (the European Space Agency and the American National Aeronautics and Space Administration) are currently studying at Phase A level the space mission STEP, whose main goal is to test the universality of free fall to 1 part in 1017 by means of a combination of very advanced technologies (drag free with proportional thrusters, superfluid-He temperature, SQUID sensors). We discuss the key features of STEP as well as some novel ideas about the possibility of testing the equivalence principle at room temperature in a non-drag-free satellite.