Earth-Moon Lagrangian points as a testbed for general relativity and effective field theories of gravity

We first analyse the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid. This scheme allows us to take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L4 and L5 both in the classical regime and in the context of effective field theories of gravity. A vehicle initially placed at L4 or L5 will not remain near the respective points. In particular, in the classical case the vehicle moves on a trajectory about the libration points for at least 700 days before escaping away. We show that this is true also if the modified long-distance Newtonian potential of effective gravity is employed. We also evaluate the impulse required to cancel out the perturbing force due to the Sun in order to force the spacecraft to stay precisely at L4 or L5. It turns out that this value is slightly modified with respect to the corresponding Newtonian one. In the second part of the paper, we first evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L4 and L5, the corrections of coordinates are of order a few millimeters and describe a tiny departure from the equilateral triangle. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. In other words, we deal with a theory involving quantum corrections to Einstein gravity, rather than to Newtonian gravity. By virtue of the effective-gravity correction to the long-distance form of the potential among two point masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order two millimeters, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. In the latter case, for the point L1, general relativity corrects Newtonian theory by 7.61 meters, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 meters per orbit. The latter is a cumulative effect accurately measured at the centimeter level through the lunar laser ranging positioning technique. Thus, it is possible to study a new laser ranging test of general relativity to measure the 7.61-meter correction to the L1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system. Performing such an experiment requires controlling the propulsion to precisely reach L1, an instrumental accuracy comparable to the measurement of the lunar geodesic precession, understanding systematic effects resulting from thermal radiation and multi-body gravitational perturbations. This will then be the basis to consider a second-generation experiment to study deviations of effective field theories of gravity from general relativity in the Sun-Earth-Moon system

Quantum time delay in the gravitational field of a rotating mass

We examine quantum corrections of time delay arising in the gravitational field of a spinning oblate source. Low-energy quantum effects occurring in Kerr geometry are derived within a framework where general relativity is fully seen as an effective field theory. By employing such a pattern, gravitational radiative modifications of Kerr metric are derived from the energy-momentum tensor of the source, which at lowest order in the fields is modelled as a point mass. Therefore, in order to describe a quantum corrected version of time delay in the case in which the source body has a finite extension, we introduce a hybrid scheme where quantum fluctuations affect only the monopole term occurring in the multipole expansion of the Newtonian potential. The predicted quantum deviation from the corresponding classical value turns out to be too small to be detected in the next future, showing that new models should be examined in order to test low-energy quantum gravity within the solar system

Quantum time delay in the gravitational field of a rotating mass

We examine quantum corrections of time delay arising in the gravitational field of a spinning oblate source. Low-energy quantum effects occurring in Kerr geometry are derived within a framework where general relativity is fully seen as an effective field theory. By employing such a pattern, gravitational radiative modifications of Kerr metric are derived from the energy-momentum tensor of the source, which at lowest order in the fields is modelled as a point mass. Therefore, in order to describe a quantum corrected version of time delay in the case in which the source body has a finite extension, we introduce a hybrid scheme where quantum fluctuations affect only the monopole term occurring in the multipole expansion of the Newtonian potential. The predicted quantum deviation from the corresponding classical value turns out to be too small to be detected in the next future, showing that new models should be examined in order to test low-energy quantum gravity within the solar system

Constraining spacetime torsion with LAGEOS

We compute the corrections to the orbital Lense-Thirring effect (or frame-dragging) in the presence of spacetime torsion. We derive the equations of motion of a test body in the gravitational field of a rotating axisymmetric massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi. We calculate the secular variations of the longitudes of the node and of the pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be used to constrain torsion parameters. We report the experimental constraints obtained using both the nodes and perigee measurements of the orbital Lense-Thirring effect. This makes LAGEOS and Gravity Probe B (GPB) complementary frame-dragging and torsion experiments, since they constrain three different combinations of torsion parameters

Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

Recent work in the literature has shown that the one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., at the Lagrangian libration points of stable equilibrium the planetoid is not exactly at equal distance from the two bodies of large mass, but the Newtonian values of its coordinates are changed by a few millimeters in the Earth-Moon system. First, we assess such a theoretical calculation by exploiting the full theory of the quintic equation, i.e., its reduction to Bring-Jerrard form and the resulting expression of roots in terms of generalized hypergeometric functions. By performing the numerical analysis of the exact formulas for the roots, we confirm and slightly improve the theoretical evaluation of quantum corrected coordinates of Lagrangian libration points of stable equilibrium. Second, we prove in detail that also for collinear Lagrangian points the quantum corrections are of the same order of magnitude in the Earth-Moon system. Third, we discuss the prospects to measure, with the help of laser ranging, the above departure from the equilateral triangle picture, which is a challenging task. On the other hand, a modern version of the planetoid is the solar sail, and much progress has been made, in recent years, on the displaced periodic orbits of solar sails at all libration points, both stable and unstable. The present paper investigates therefore, eventually, a restricted three-body problem involving Earth, Moon and a solar sail. By taking into account the one-loop quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist

White Paper #1: Fundamental Physics

The Standard Model (SM) of particle physics and General Relativity (GR) are the two pillars of our current understanding of Nature. Both theories have been probed individually with ever increasing precision and are consistent with nearly all experimental observations. However, they fail to explain dark matter, dark energy, or the imbalance between matter and anti-matter in the universe. Yet, dark matter and dark energy represent 95% of the energy content of our universe while known matter (atoms, molecules) amounts to only 5%. Today, dark matter and dark energy have an unknown origin and there is a great deal of experimental and theoretical activity to solve this puzzle. In summary, the clustering of large-scale structure and the accelerated behaviour of cosmic fluid could be addressed whether finding out new (unknown) forms of matter or assuming that gravity behaves in different ways at infrared scales. Furthermore, the lack of a self-consistent theory of Quantum Gravity prevents the unification of SM and GR at ultraviolet scales. This is one of the biggest challenges that theoretical physics is facing today. String theory or loop quantum gravity are good candidates to solve this puzzle and interestingly both of them foresee violations of the Einstein's Equivalence Principle. With that respect the Einstein's Equivalence Principle assumes a central role in the search for a quantum theory of gravity. The open problems in fundamental physics investigated in this white paper are: (i) Validity of the Einstein's Equivalence Principle; (ii) Origin and nature of dark matter and dark energy; (iii) Decoherence and collapse models in quantum mechanics; (iv) Quantum many-body physics. They will be addressed from different research corners and with different experimental methods: (i) Ultracold atoms; (ii) High stability and accuracy atomic clocks; (iii) Matter-wave interferometry; (iv) Classical and quantum links. The cosmos is a particularly attractive laboratory as it provides particles (cosmic rays) or objects (black holes, neutron stars) which are not produced in manmade laboratories. Space is also an excellent environment for high precision physics as the absence of atmosphere or drag-free satellites provide unique observation opportunities. For instance the MICROSCOPE mission has taken advantage of extremely long free-fall conditions in Earth orbit to set the record in testing the Equivalence Principle beyond what has been possible on Earth. Large velocity, velocity variations and large variation of the gravitational potential are accessible on board a spacecraft, thus providing wide signals for testing GR. Finally, the huge free propagation distances available in space provide very long baselines to test the spacetime metric with high performance links both classical and quantum

Dalitz plot analysis of e+ e- --> pi0 pi0 gamma events at SQRT(s) ~ M(phi) with the KLOE detector

We have studied the Dalitz plot of the e+ e- --> pi0 pi0 gamma events collected at SQRT(s) ~ M(phi) with the KLOE detector. In the dipion invariant mass (Mpp) region below 700 MeV, the process under study is dominated by the non-resonant process e+ e- --> omega pi0 with omega --> pi0 gamma whereas, for higher Mpp values, the radiative phi decay to the f0(980) is the dominant mechanism. Different theoretical models are used to fit the Dalitz plot, taking also into account a possible contribution of the sigma(600). For each model, we extract the f0(980) mass and its coupling to pipi, KKbar and to the phi.Comment: 21 pages, 15 figures, 5 tables, submitted to European Physics Journal

GENESIS: Co-location of Geodetic Techniques in Space

Improving and homogenizing time and space reference systems on Earth and, more directly, realizing the Terrestrial Reference Frame (TRF) with an accuracy of 1mm and a long-term stability of 0.1mm/year are relevant for many scientific and societal endeavors. The knowledge of the TRF is fundamental for Earth and navigation sciences. For instance, quantifying sea level change strongly depends on an accurate determination of the geocenter motion but also of the positions of continental and island reference stations, as well as the ground stations of tracking networks. Also, numerous applications in geophysics require absolute millimeter precision from the reference frame, as for example monitoring tectonic motion or crustal deformation for predicting natural hazards. The TRF accuracy to be achieved represents the consensus of various authorities which has enunciated geodesy requirements for Earth sciences. Today we are still far from these ambitious accuracy and stability goals for the realization of the TRF. However, a combination and co-location of all four space geodetic techniques on one satellite platform can significantly contribute to achieving these goals. This is the purpose of the GENESIS mission, proposed as a component of the FutureNAV program of the European Space Agency. The GENESIS platform will be a dynamic space geodetic observatory carrying all the geodetic instruments referenced to one another through carefully calibrated space ties. The co-location of the techniques in space will solve the inconsistencies and biases between the different geodetic techniques in order to reach the TRF accuracy and stability goals endorsed by the various international authorities and the scientific community. The purpose of this white paper is to review the state-of-the-art and explain the benefits of the GENESIS mission in Earth sciences, navigation sciences and metrology.Comment: 31 pages, 9 figures, submitted to Earth, Planets and Space (EPS

Precise measurement of Gamma(Ks->pi+pi-(gamma))/Gamma(Ks->pi0pi0) with the KLOE detector at DAFNE

Using a sample of over 400 million phi->KsKl decays produced during the years 2001 and 2002 at the DAFNE e+e- collider, the ratio R=Gamma(Ks->pi+pi-(g))/Gamma(Ks->pi0pi0) has been measured with the KLOE detector. The result is R=2.2555+-0.0012(stat)+-0.0021(syst-stat)+-0.0050(syst), which is in good agreement with the previously published result based on the KLOE data sample from the year 2000. The average of the KLOE results is R=2.2549+-0.0054, reducing the total error by a factor of three, to 0.25%.Comment: 13 pages, 13 figures, submitted to Eur. Phys. J.

High Frequency MEMS Capacitive Mirror for Space Applications

Free space optics laser communication using modulating retroreflectors (MR) is a challenging application for an active mirror, due to the high frequencies (>100 kHz) required to enable sufficient data transfer. Micro Electromechanical (MEMS) mirrors are a promising option for high-frequency applications, given the very small moving mass typical of such devices. Capacitive MEMS mirrors are presented here for free space communications, based on a novel fabrication sequence that introduces a single-layer thin film aluminum mirror structure with an underlying silicon oxide sacrificial layer. The use of aluminum instead of gold as a mirror layer diminishes the heating generated by the absorption of the sun’s radiation once the mirrors exit the earth’s atmosphere. Thanks to the novel fabrication sequence, the presented mirror devices have a full range actuation voltage of less than 40 V, and a high operational frequency with an eigenfrequency above 2 MHz. The devices were manufactured and characterized, and their main parameters were obtained from experimental data combined with finite element analysis, thus enabling future design optimization of the reported MEMS technology. By optical characterization of the far field diffraction pattern, good mirror performance was demonstrated