Explore the vast range of titles available.

We describe here how planetary ephemerides are built in the framework of General Relativity and how they can be used to test alternative theories. We focus on the definition of the reference frame (space and time) in which the planetary ephemeris is described, the equations of motion that govern the orbits of solar system bodies and electromagnetic waves. After a review on the existing planetary and lunar ephemerides, we summarize the results obtained considering full modifications of the ephemeris framework with direct comparisons with the observations of planetary systems, with a specific attention for the PPN formalism. We then discuss other formalisms such as Einstein-dilaton theories, the massless graviton and MOND. The paper finally concludes on some comments and recommendations regarding misinterpreted measurements of the advance of perihelia.

Observers in relative motion or at different gravitational potentials measure disparate clock rates. These predictions of relativity have previously been observed with atomic clocks at high velocities and with large changes in elevation. We observed time dilation from relative speeds of less than 10 meters per second by comparing two optical atomic clocks connected by a 75-meter length of optical fiber. We can now also detect time dilation due to a change in height near Earth's surface of less than 1 meter. This technique may be extended to the field of geodesy, with applications in geophysics and hydrology as well as in space-based tests of fundamental physics.

The double pulsar system PSR J0737-3039A/B is unique in that both neutron stars are detectable as radio pulsars. They are also known to have much higher mean orbital velocities and accelerations than those of other binary pulsars. The system is therefore a good candidate for testing Einstein's theory of general relativity and alternative theories of gravity in the strong-field regime. We report on precision timing observations taken over the 2.5 years since its discovery and present four independent strong-field tests of general relativity. These tests use the theory-independent mass ratio of the two stars. By measuring relativistic corrections to the Keplerian description of the orbital motion, we find that the \"post-Keplerian\" parameter s agrees with the value predicted by general relativity within an uncertainty of 0.05%, the most precise test yet obtained. We also show that the transverse velocity of the system's center of mass is extremely small. Combined with the system's location near the Sun, this result suggests that future tests of gravitational theories with the double pulsar will supersede the best current solar system tests. It also implies that the second-born pulsar may not have formed through the core collapse of a helium star, as is usually assumed.

The present Editorial introduces the Special Issue dedicated by the journal Universe to the General Theory of Relativity, the beautiful theory of gravitation of Einstein, a century after its birth. It reviews some of its key features in a historical perspective, and, in welcoming distinguished researchers from all over the world to contribute it, some of the main topics at the forefront of the current research are outlined.

When a test particle moves about an oblate spheroid, it is acted upon, among other things, by two standard perturbing accelerations. One, of Newtonian origin, is due to the quadrupole mass moment J 2 of the orbited body. The other one, of order O 1 / c 2 , is caused by the static, post-Newtonian field arising solely from the mass of the central object. Both of them concur to induce indirect, mixed orbital effects of order O J 2 / c 2 . They are of the same order of magnitude of the direct ones induced by the post-Newtonian acceleration arising in presence of an oblate source, not treated here. We calculate these less known features of motion in their full generality in terms of the osculating Keplerian orbital elements. Subtleties pertaining the correct calculation of their mixed net precessions per orbit to the full order of O J 2 / c 2 are elucidated. The obtained results hold for arbitrary orbital geometries and for any orientation of the body’s spin axis k ^ in space. The method presented is completely general, and can be extended to any pair of post-Keplerian accelerations entering the equations of motion of the satellite, irrespectively of their physical nature.

For the first time, we have introduced the tetrahedron constellation of gravitational wave observatory (TEGO) composed of four identical spacecrafts (S/Cs). The laser telescopes and their pointing structures are mounted on the S/C platform and are evenly distributed at three locations 120 degrees apart. These structures form automatically a stable mass center for the platform. The time delay interferometry (TDI) is used to suppress the frequency noise of gravitational wave (GW) detector. The unequal-arm Michelson TDI configuration and the Sagnac TDI configuration are equally effective at eliminating the laser frequency noise based on the TEGO configuration. Furthermore, compared with the configurations of LISA, Taiji, and TianQin, the TEGO has more combinations of optical paths in its TDI system sensitive to GW signals. The six arms of TEGO are simultaneously sensitive to the six polarization modes of GWs. The sensitivity implies that GW modes beyond the predictions of general relativity (GR) can be detected directly. For instance, a scalar longitudinal mode of GWs, which is not predicted by GR, has been identified as a dominant polarization component. This mode is found to be evident in the response amplitudes of the TEGO arms, such as between S/C1 and S/C4, and S/C3 and S/C4, at certain orbital positions.

To the first post-Newtonian order, the orbital angular momentum of the fast-revolving inner binary of the triple system PSR J0337+1715, made of a millisecond pulsar and a white dwarf, induces an annular gravitomagnetic field which displaces the line of apsides of the slower orbit of the other, distant white dwarf by −1.2 milliarcseconds per year. The current accuracy in determining the periastron of the outer orbit is 63.9 milliarcseconds after 1.38 years of data collection. By hypothesizing a constant rate of measurement of the pulsar’s times of arrivals over the next 10 years, assumed equal to the present one, it can be argued that the periastron will be finally known to a ≃0.15 milliarcseconds level, while its cumulative gravitomagnetic retrograde shift will be as large as −12 milliarcseconds. The competing post-Newtonian gravitolectric periastron advance due to the inner binary’s masses, nominally amounting to 74.3 milliarcseconds per year, can be presently modelled to an accuracy level as good as ≃0.04 milliarcseconds per year. The mismodeling in the much larger Newtonian periastron rate due to the quadrupolar term of the multipolar expansion of the gravitational potential of a massive ring representing the inner binary, whose nominal size for PSR J0337+1715 is 0.17 degrees per year, might be reduced down to the ≃0.5 milliarcseconds per year level over the next 10 years. Thus, a first measurement of such a novel form of gravitomagnetism, although undoubtedly challenging, might be, perhaps, feasible in a not too distant future.

To the first post–Newtonian order, the gravitational action of mass–energy currents is encoded by the off–diagonal gravitomagnetic components of the spacetime metric tensor. If they are time–dependent, a further acceleration enters the equations of motion of a moving test particle. Let the source of the gravitational field be an isolated, massive body rigidly rotating whose spin angular momentum experiences a slow precessional motion. The impact of the aforementioned acceleration on the orbital motion of a test particle is analytically worked out in full generality. The resulting averaged rates of change are valid for any orbital configuration of the satellite; furthermore, they hold for an arbitrary orientation of the precessional velocity vector of the spin of the central object. In general, all the orbital elements, with the exception of the mean anomaly at epoch, undergo nonvanishing long–term variations which, in the case of the Juno spacecraft currently orbiting Jupiter and the double pulsar PSR J0737–3039 A/B turn out to be quite small. Such effects might become much more relevant in a star–supermassive black hole scenario; as an example, the relative change of the semimajor axis of a putative test particle orbiting a Kerr black hole as massive as the one at the Galactic Centre at, say, 100 Schwarzschild radii may amount up to about 7% per year if the hole’s spin precessional frequency is 10% of the particle’s orbital one.

The new geodetic satellite LARES 2, cousin of LAGEOS and sharing with it almost the same orbital parameters apart from the inclination, displaced by 180 deg, was launched last year. Its proponents suggest using the sum of the nodes of LAGEOS and of LARES 2 to measure the sum of the Lense–Thirring node precessions independently of the systematic bias caused by the even zonal harmonics of the geopotential, claiming a final ≃0.2 percent total accuracy. In fact, the actual orbital configurations of the two satellites do not allow one to attain the sought for mutual cancellation of their classical node precessions due to the Earth’s quadrupole mass moment, as their sum is still ≃5000 times larger than the added general relativistic rates. This has important consequences. One is that the current uncertainties in the eccentricities and the inclinations of both satellites do not presently allow the stated accuracy goal to be met, needing improvements of 3–4 orders of magnitude. Furthermore, the imperfect knowledge of the Earth’s angular momentum S impacts the uncancelled sum of the node precessions, from 150 to 4900 percent of the relativistic signal depending on the uncertainty assumed in S. It is finally remarked that the real breakthrough in reliably testing the gravitomagnetic field of the Earth would consist in modeling it and simultaneously estimating one or more dedicated parameter(s) along with other ones characterising the geopotential, as is customarily performed for any other dynamical feature.

We analytically calculate some orbital effects induced by the Lorentz-invariance momentum-conservation parameterized post-Newtonian (PPN) parameter \\(_3\\) in a gravitationally bound binary system made of a primary orbited by a test particle. We neither restrict ourselves to any particular orbital configuration nor to specific orientations of the primary's spin axis \\( \\). We use our results to put preliminary upper bounds on \\(_3\\) in the weak-field regime by using the latest data from Solar System's planetary dynamics. By linearly combining the supplementary perihelion precessions \\(\\) of the Earth, Mars and Saturn, determined by astronomers with the Ephemerides of Planets and the Moon (EPM) 2011 ephemerides for the general relativistic values of the PPN parameters \\(==1\\), we infer \\(|_3| 6 10^-10\\). Our result is about three orders of magnitude better than the previous weak-field constraints existing in the literature and of the same order of magnitude of the constraint expected from the future BepiColombo mission to Mercury. It is, by construction, independent of the other preferred-frame PPN parameters \\(_1,_2\\), both preliminarily constrained down to a \\( 10^-6\\) level. Future analyses should be performed by explicitly including \\(_3\\) and a selection of other PPN parameters in the models fitted by the astronomers to the observations and estimating them in dedicated covariance analyses.