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Recently, an accelerometer-based device (Vienna Surface Tester (VST)) has been developed for testing the surface characteristics of floors, beddings and turf grounds. The accelerometers are placed in a sphere, which will be dropped in free fall on a test surface. By observing changes in acceleration during impact, researchers can deduce various material characteristics. A down-sized version of this device (Surface Tester of Food Resilience (STFR)) has been proposed for texture testing of foods. Whereas the movement of the VST can be described by the laws of free fall, the STFR follows a constrained circular path due to its attachment to a rod and swivel. We refined the mathematical representation of the different phases of the STFR spherical probe’s trajectory (fall, impact and rebound), and we modified the mathematical models for the STFR probe to extend the measurement range.

During the final stages of the Cassini mission, the spacecraft flew between the planet and its rings, providing a new view on this spectacular system (see the Perspective by Ida). Setting the scene, Spilker reviews the numerous discoveries made using Cassini during the 13 years it spent orbiting Saturn. Iess et al. measured the gravitational pull on Cassini, separating the contributions from the planet and the rings. This allowed them to determine the interior structure of Saturn and the mass of its rings. Buratti et al. present observations of five small moons located in and around the rings. The moons each have distinctive shapes and compositions, owing to accretion of ring material. Tiscareno et al. observed the rings directly at close range, finding complex features sculpted by the gravitational interactions between moons and ring particles. Together, these results show that Saturn's rings are substantially younger than the planet itself and constrain models of their origin. Science , this issue p. 1046 , p. eaat2965 , p. eaat2349 , p. eaau1017 ; see also p. 1028 Measurement of Saturn’s gravitational field determines the mass of its rings and constrains models of the planet’s interior. The interior structure of Saturn, the depth of its winds, and the mass and age of its rings constrain its formation and evolution. In the final phase of the Cassini mission, the spacecraft dived between the planet and its innermost ring, at altitudes of 2600 to 3900 kilometers above the cloud tops. During six of these crossings, a radio link with Earth was monitored to determine the gravitational field of the planet and the mass of its rings. We find that Saturn’s gravity deviates from theoretical expectations and requires differential rotation of the atmosphere extending to a depth of at least 9000 kilometers. The total mass of the rings is (1.54 ± 0.49) × 10 19 kilograms (0.41 ± 0.13 times that of the moon Mimas), indicating that the rings may have formed 10 7 to 10 8 years ago.

Einstein’s theory of gravity—the general theory of relativity 1 —is based on the universality of free fall, which specifies that all objects accelerate identically in an external gravitational field. In contrast to almost all alternative theories of gravity 2 , the strong equivalence principle of general relativity requires universality of free fall to apply even to bodies with strong self-gravity. Direct tests of this principle using Solar System bodies 3 , 4 are limited by the weak self-gravity of the bodies, and tests using pulsar–white-dwarf binaries 5 , 6 have been limited by the weak gravitational pull of the Milky Way. PSR J0337+1715 is a hierarchical system of three stars (a stellar triple system) in which a binary consisting of a millisecond radio pulsar and a white dwarf in a 1.6-day orbit is itself in a 327-day orbit with another white dwarf. This system permits a test that compares how the gravitational pull of the outer white dwarf affects the pulsar, which has strong self-gravity, and the inner white dwarf. Here we report that the accelerations of the pulsar and its nearby white-dwarf companion differ fractionally by no more than 2.6 × 10 −6 . For a rough comparison, our limit on the strong-field Nordtvedt parameter, which measures violation of the universality of free fall, is a factor of ten smaller than that obtained from (weak-field) Solar System tests 3 , 4 and a factor of almost a thousand smaller than that obtained from other strong-field tests 5 , 6 . The accelerations of a pulsar and a white dwarf in a three-star system differ by at most a few parts per million, providing a much improved constraint on the universality of free fall.

The novel device used in this study is a free fall electrostatic separator equipped with flexible electrodes. This special feature enabled the experimentation of different electric field configurations, avoiding as much as possible the impacts of particles on electrode walls, which is the major drawback of standard free-fall electrostatic separators. The present work was focused on the numerical modelling and simulating the trajectories of charged insulating particles. The study was aimed at contributing to a more in-depth understanding of the various physical phenomena that occur during electrostatic separation. An accurate numerical model of particle movement was developed. The results of the numerical simulations were validated using the experimental data obtained with an appropriate image acquisition tool.

From the producers’ point of view, there is no universal and quick method to predict bruise area when dropping an apple from a certain height onto a certain type of substrate. In this study the authors presented a very simple method to estimate bruise volume based on drop height and substrate material. Three varieties of apples were selected for the study: Idared, Golden Delicious, and Jonagold. Their weight, turgor, moisture, and sugar content were measured to determine morphological differences. In the next step, fruit bruise volumes were determined after a free fall test from a height of 10 to 150 mm in 10 mm increments. Based on the results of the research, linear regression models were performed to predict bruise volume on the basis of the drop height and type of substrate on which the fruit was dropped. Wood and concrete represented the stiffest substrates and it was expected that wood would respond more subtly during the free fall test. Meanwhile, wood appeared to react almost identically to concrete. Corrugated cardboard minimized bruising at the lowest discharge heights, but as the drop height increased, the cardboard degraded and the apple bruising level reached the results as for wood and concrete. Contrary to cardboard, the foam protected apples from bruising up to a drop height of 50 mm and absorbed kinetic energy up to the highest drop heights. Idared proved to be the most resistant to damage, while Golden Delicious was medium and Jonagold was least resistant to damage. Numerical models are a practical tool to quickly estimate bruise volume with an accuracy of about 75% for collective models (including all cultivars dropped on each of the given substrate) and 93% for separate models (including single cultivar dropped on each of the given substrate).

Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would signal a violation of local position invariance and be associated with a violation of the universality of free fall, and hence of the weak equivalence principle at the heart of the geometrisation of gravity. It will also reflect the existence of new degrees of freedom that couple to standard matter fields. Thus, testing for the stability of fundamental constants is of utmost importance for our understanding of gravity and for characterizing the domain of validity of general relativity. Besides, it opens an independent window on the dark matter and dark energy components. As a consequence, thanks to the active developments of experiments, fundamental constants have become a key player in our search for physics beyond the standard model of particle physics and general relativity. This review details the various roles of the fundamental constants in the laws of physics and in the construction of the international system of units, which now depends strongly on them. This requires to distinguish the concepts of fundamental units and fundamental parameters . Then, the relations between constants, the tests of the local position invariance and of the universality of free fall are presented, as well as the construction of field theories that account for “varying constants” and the motivations arising from high-energy physics and string theory. From a theoretical perspective any varying fundamental parameter is related to a dynamical field, the dynamics of which is dictated from the whole theory so that it remains fully consistent: no arbitrary law of variation has to be postulated. Then, the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, solar system observations, meteorite dating, quasar absorption spectra, stellar physics, pulsar timing, the cosmic microwave background and Big Bang nucleosynthesis are described. It details the basics of each system, its dependence with respect to the primary parameters the variation of which can be constrained from observations, the known systematic effects and the most recent constraints. It also describes how these primary parameters can be related to the fundamental constants and the model-dependencies that is involved. Both time and space variations are considered. To finish, it contains a short discussion on the more speculative possibility of understanding the numerical values of the fundamental parameters in view of the apparent fine-tuning that they confront us with, by invoking anthropic arguments. Given the huge increase of data and constraints and the difficulty to standardize them, a general scheme to present experimental and observational results and to construct a collaborative data base that will be more efficient for the community and allow us for better traceability, is proposed.

We describe the Quantum Test of the Equivalence principle and Space Time (QTEST), a concept for an atom interferometry mission on the International Space Station (ISS). The primary science objective of the mission is a test of Einstein's equivalence principle with two rubidium isotope gases at a precision of better than 10−15, a 100-fold improvement over the current limit on equivalence principle violations, and over 1,000,000 fold improvement over similar quantum experiments demonstrated in laboratories. Distinct from the classical tests is the use of quantum wave packets and their expected large spatial separation in the QTEST experiment. This dual species atom interferometer experiment will also be sensitive to time-dependent equivalence principle violations that would be signatures for ultralight dark-matter particles. In addition, QTEST will be able to perform photon recoil measurements to better than 10−11 precision. This improves upon terrestrial experiments by a factor of 100, enabling an accurate test of the standard model of particle physics and contributing to mass measurement, in the proposed new international system of units (SI), with significantly improved precision. The predicted high measurement precision of QTEST comes from the microgravity environment on ISS, offering extended free fall times in a well-controlled environment. QTEST plans to use high-flux, dual-species atom sources, and advanced cooling schemes, for N > 106 non-condensed atoms of each species at temperatures below 1 nK. Suppression of systematic errors by use of symmetric interferometer configurations and rejection of common-mode errors drives the QTEST design. It uses Bragg interferometry with a single laser beam at the 'magic' wavelength, where the two isotopes have the same polarizability, for mitigating sensitivities to vibrations and laser noise, imaging detection for correcting cloud initial conditions and maintaining contrast, modulation of the atomic hyperfine states for reduced sensitivity to magnetic field gradients, two source-regions for simultaneous time reversal measurements and redundancy, and modulation of the gravity vector using a rotating platform to reduce otherwise difficult systematics to below 10−16.

The merging of quantum information science with the relativity theory presents novel opportunities for understanding the enigmas surrounding the transmission of information in relation to black holes. For this purpose, we study the quantumness near a Schwarzschild black hole in a practical model under decoherence. The scenario we consider in this paper is that a stationary particle in the flat region interacts with its surroundings while another particle experiences free fall in the vicinity of a Schwarzschild black hole’s event horizon. We explore the impacts of Hawking radiation and decoherence on the system under investigation and find that these effects can limit the survival of quantum characteristics, but cannot destroy them completely. Hence, the results of this study possess the potential to yield valuable insights into the comprehension of the quantum properties of a real system operating within a curved space-time framework.

A bstract De Sitter space-time, essentially our own universe, is plagued by problems at the quantum level. Here we propose that Lorentzian de Sitter space-time is not fundamental but constitutes only an effective description of a more fundamental quantum gravity ground state. This cosmological ground state is a graph, appearing on large scales as a Riemannian manifold of constant negative curvature. We model the behaviour of matter near this equilibrium state as Brownian motion in the effective thermal environment of graph fluctuations, driven by a universal time parameter. We show how negative curvature dynamically induces the asymptotic emergence of relativistic coordinate time and of leading ballistic motion governed by the isometry group of an “effective Lorentzian manifold” of opposite, positive curvature, i.e. de Sitter space-time: free fall in positive curvature is asymptotically equivalent to the leading behaviour of Brownian motion in negative curvature. The local limit theorem for negative curvature implies that the large-scale spectral dimension of this “effective de Sitter space-time” is (3+1) independently of its microscopic topological dimension. In the effective description, the sub-leading component of asymptotic Brownian motion becomes Schrödinger quantum behavior on a 3D Euclidean manifold.

This study incorporates aerodynamic three-force perturbations alongside celestial perturbations to perform six-degree-of-freedom orbital dynamics modeling, thereby establishing a comprehensive six-degree-of-freedom ballistic and attitude simulation model, accompanied by illustrative simulation examples. In the context of the low-Earth orbit satellite space environment, by integrating the effects of sparse gas with an optimal atmospheric environment model, the Boltzmann equation can be employed to compute corrections to aerodynamic coefficients using a unified algorithm based on gas dynamics theory. Simultaneously, by integrating the BP neural network with historical aerodynamic data, we predict the resultant aerodynamic forces and moments, which are subsequently employed for the calibration of a six-degree-of-freedom orbital dynamics model. In conclusion, the flight trajectory and attitude information of an uncontrolled reentry spacecraft are presented and compared with official data. The results indicate that the attitude and orbital parameters extrapolated from the model developed in this study closely align with the officially released observational data, demonstrating high precision. This model offers enhanced accuracy for spacecraft orbit determination and forecasting.