The goal of the recently approved space-based LARES mission is to measure the general relativistic Lense-Thirring effect in the gravitational field of the spinning Earth at a repeatedly claimed 1% accuracy by combining its node Omega with those of the existing LAGEOS and LAGEOS II laser-ranged satellites. In this paper we show that, in view of the lower altitude of LARES (h=1450 km) with respect to LAGEOS and LAGEOS II (h\approx 6000 km), the cross-coupling between the effect of the atmospheric drag, both neutral and charged, on the inclination of LARES and its classical node precession due to the Earth's oblateness may induce a 3-9% year^-1 systematic bias on the total relativistic precession. Since its extraction from the data will take about 5-10 years, such a perturbing effect may degrade the total accuracy of the test, especially in view of the large uncertainties in modeling the drag force.
The laser-ranged satellite LARES is expected to provide new refined measurements of relativistic physics, as well as significant contributions to space geodesy and geophysics. The very low area-to-mass ratio of this passive and dense satellite was chosen to reduce as much as possible the disturbing effects of non-gravitational perturbations. However, because of its height, about 1450 km compared with about 5800-5900 km for the two LAGEOS satellites, LARES is exposed to a much stronger drag due to neutral atmosphere. From a precise orbit determination, analyzing the laser ranging normal points …
In three previous papers we presented the LARES 2 space experiment aimed at a very accurate test of frame-dragging and at other tests of fundamental physics and measurements of space geodesy and geodynamics. We presented the error sources in the LARES 2 experiment, its error budget, Monte Carlo simulations and covariance analyses confirming an accuracy of a few parts per thousand in the test of frame-dragging, and we treated the error due to the uncertainty in the de Sitter effect, a relativistic orbital perturbation. Here we discuss the impact in the error budget of the LARES 2 frame-dragging…
We comment on some statements in a recent paper by Paolozzi and Ciufolini concerning certain remarks raised by us on the realistic accuracy obtainable in testing the general relativistic Lense-Thirring effect in the gravitational field of the Earth with the newly launched LARES satellite together with the LAGEOS and LAGEOS II spacecraft in orbit for a long time. The orbital configuration of LARES is different from that of the originally proposed LAGEOS-3. Indeed, while the latter one should have been launched to the same altitude of LAGEOS (i.e. about $h_{\rm L}=5890$ km) in an orbital plane d…
In two previous papers we presented the LARES 2 space experiment aimed at a very accurate test of frame-dragging and at other tests of fundamental physics and measurements of space geodesy and geodynamics. We presented the error sources of the LARES 2 experiment, its error budget and Monte Carlo simulations and covariance analyses confirming an accuracy of a few parts in one thousand in the test of frame-dragging. Here we discuss the impact of the orbital perturbation known as the de Sitter effect, or geodetic precession, in the error budget of the LARES 2 frame-dragging experiment. We show th…
The LARES satellite, a laser-ranged space experiment to contribute to geophysics observation, and to measure the general relativistic Lense-Thirring effect, has been observed to undergo an anomalous along-track orbital acceleration of -0.4 pm/s$^2$ (pm := picometer). This "drag" is not surprising; along track drag has previously been observed with the related LAGEOS satellites (-3.4 pm/s$^2$). It is hypothesized that the drag is principally due to anisotropic thermal radiation from the satellite's exterior. We report the results of numerical computations of the along-track orbital decay of the…
Current observations of the universe have strengthened the interest to further test General Relativity and other theories of fundamental physics. After an introduction to the phenomenon of frame-dragging predicted by Einstein's theory of General Relativity, with fundamental astrophysical applications to rotating black holes, we describe the past measurements of frame-dragging obtained by the LAGEOS satellites and by the dedicated Gravity Probe B space mission. We also discuss a test of String Theories of Chern-Simons type that has been carried out using the results of the LAGEOS satellites. We…
We report the improved test of frame-dragging, an intriguing phenomenon predicted by Einstein's General Relativity, obtained using 7 years of Satellite Laser Ranging (SLR) data of the satellite LARES (ASI, 2012) and 26 years of SLR data of LAGEOS (NASA, 1976) and LAGEOS 2 (ASI and NASA, 1992). We used the static part and temporal variations of the Earth gravity field obtained by the space geodesy mission GRACE (NASA and DLR) and in particular the static Earth's gravity field model GGM05S augmented by a model for the 7-day temporal variations of the lowest degree Earth spherical harmonics. We u…
On February 13th 2012, the LARES satellite of the Italian Space Agency (ASI) was launched into orbit with the qualification flight of the new VEGA launcher of the European Space Agency (ESA). The payload was released very accurately in the nominal orbit. The name LARES means LAser RElativity Satellite and summarises the objective of the mission and some characteristics of the satellite. It is, in fact, a mission designed to test Einstein's General Relativity Theory (specifically 'frame dragging' and Lense-Thirring effect). The satellite is passive and covered with optical retroreflectors that …
We summarize a laser-ranged satellite test of frame-dragging, a prediction of General Relativity, and then concentrate on the estimate of thermal thrust, an important perturbation affecting the accuracy of the test. The frame dragging study analysed 3.5 years of data from the LARES satellite and a longer period of time for the two LAGEOS satellites. Using the gravity field GGM05S obtained via the Grace mission, which measures the Earth's gravitational field, the prediction of General Relativity is confirmed with a 1-$σ$ formal error of 0.002, and a systematic error of 0.05. The result for the …
In 2016, we published "A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model. Measurement of Earth's dragging of inertial frames [1]", a measurement of frame-dragging, a fundamental prediction of Einstein's theory of General Relativity, using the laser-ranged satellites LARES, LAGEOS and LAGEOS 2. The formal error, or precision, of our test was about 0.2% of frame-dragging, whereas the systematic error was estimated to be about 5%. In the 2017 paper "A comment on "A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth g…
We present a test of General Relativity, the measurement of the Earth's dragging of inertial frames. Our result is obtained using about 3.5 years of laser-ranged observations of the LARES, LAGEOS and LAGEOS 2 laser-ranged satellites together with the Earth's gravity field model GGM05S produced by the space geodesy mission GRACE. We measure $μ= (0.994 \pm 0.002) \pm 0.05$, where $μ$ is the Earth's dragging of inertial frames normalized to its General Relativity value, 0.002 is the 1-sigma formal error and 0.05 is the estimated systematic error mainly due to the uncertainties in the Earth's grav…
The LARES (LAser RElativity Satellite) satellite was successfully launched in February 2012. The LARES space experiment is based on the orbital determinations of the laser ranged satellites LARES, LAGEOS (LAser GEOdynamics Satellite) and LAGEOS 2 together with the determination of the Earth's gravity field by the GRACE (Gravity Recovery And Climate Experiment) mission. It will test some fundamental physics predictions and provide accurate measurements of the framedragging effect predicted by Einstein's theory of General Relativity. By one hundred Monte Carlo simulations of the LARES experiment…
Laser ranging satellites have proved their efficiency for high precision testing of the effect of frame-dragging, one of remarkable predictions of the General Relativity. The analysis of the randomness properties of the residuals of LAGEOS and LAGEOS 2 satellites reveals the role of the thermal thrust -- Yarkovsky effect -- on the satellite which was in the orbit for longer period (LAGEOS). We also compute Earth's tidal modes affecting the satellite LARES. The recently obtained 5\% accuracy limit reached for the frame dragging effect based on the 3.5 year data of LARES analysed together with t…
The precession of the orbital node of a particle orbiting a rotating mass is known as Lense-Thirring effect (LTE) and is a manifestation of the general relativistic phenomenon of dragging of inertial frames or frame-dragging. The LTE has already been measured by using the node drifts of the LAGEOS satellites and GRACE-based Earth gravity field models with an accuracy of about 10% and will be improved down to a few percent with the recent LARES experiment. The Galileo system will provide 27 new node observables for the LTE estimation and their combination with the LAGEOS and LARES satellites ca…
The laser-tracked geodetic satellites LAGEOS, LAGEOS II and LARES are currently employed, among other things, to measure the general relativistic Lense-Thirring effect in the gravitomagnetic field of the spinning Earth with the hope of providing a more accurate test of such a prediction of the Einstein's theory of gravitation than the existing ones. The secular decay $\dot a$ of the semimajor axes $a$ of such spacecrafts, recently measured in an independent way to a $σ_{\dot a}\approx 0.1-0.01$ m yr$^{-1}$ accuracy level, may indirectly impact the proposed relativistic experiment through its c…
In the next decade or two, extremely accurate tests of general relativity under extreme conditions are expected from gravitational wave observations of binary black hole mergers with a wide range of mass ratios. In addition, major improvements are planned in both strong and weak equivalence principle tests; clock measurements based on the ACES program on the ISS; more accurate light-bending measurements; and other new types of tests. However, whether these tests are all consistent with general relativity or not, it still appears desirable to proceed with a much improved measurement of the Shap…
The MICROSCOPE space mission aims to test the Equivalence Principle with an accuracy of $10^{-15}$. The drag-free micro-satellite will orbit around the Earth and embark a differential electrostatic accelerometer including two cylindrical test masses submitted to the same gravitational field and made of different materials. The experience consists in testing the equality of the electrostatic acceleration applied to the masses to maintain them relatively motionless. The accuracy of the measurements exploited for the test of the Equivalence Principle is limited by our a priori knowledge of severa…
Satellite tracking involves sending electromagnetic signals to Earth. Both the orbit of the spacecraft and the electromagnetic signals themselves are affected by the curvature of spacetime. The arrival time of the pulses is compared to the ticks of local clocks to reconstruct the orbital path of the satellite to high accuracy, and to implicitly measure general relativistic effects. In particular, Schwarzschild space curvature (static) and frame-dragging (stationary) due to the planet's spin affect the satellite's orbit. The dominant relativistic effect on the path of the signal photons is Shap…
Future drag-free missions for space-based experiments in gravitational physics require a Gravitational Reference Sensor with extremely demanding sensing and disturbance reduction requirements. A configuration with two cubical sensors is the current baseline for the Laser Interferometer Space Antenna (LISA) and has reached a high level of maturity. Nevertheless, several promising concepts have been proposed with potential applications beyond LISA and are currently investigated at HEPL, Stanford, and EADS Astrium, Germany. The general motivation is to exploit the possibility of achieving improve…
The UV LED mission demonstrates the precise control of the potential of electrically isolated test masses that is essential for the operation of space accelerometers and drag free sensors. Accelerometers and drag free sensors were and remain at the core of geodesy, aeronomy, and precision navigation missions as well as gravitational science experiments and gravitational wave observatories. Charge management using photoelectrons generated by the 254 nm UV line of Hg was first demonstrated on Gravity Probe B and is presently part of the LISA Pathfinder technology demonstration. The UV LED missio…
The analysis of non-radiative sources of static or time-dependent gravitational fields in the Solar System is crucial to accurately estimate the free-fall orbits of the LISA space mission. In particular, we take into account the gravitational effects of Interplanetary Dust (ID) on the spacecraft trajectories. The perturbing gravitational field has been calculated for some ID density distributions that fit the observed zodiacal light. Then we integrated the Gauss planetary equations to get the deviations from the LISA keplerian orbits around the Sun. This analysis can be eventually extended to …
The successful miniaturization of extremely accurate atomic clocks invites prospects for satellite missions to perform precise timing experiments. This will allow effects predicted by general relativity to be detected in Earth's gravitational field. In this paper we introduce a convenient formalism for studying these effects, and compute the fractional timing differences generated by them for the orbit of a satellite capable of accurate time transfer to a terrestrial receiving station on Earth, as proposed by planned missions. We find that (1) Schwarzschild perturbations would be measurable th…
We present a new measurement of the Lense-Thirring effect on the orbits of the geodetic satellites LAGEOS, LAGEOS II and LARES. This secular precession is a general relativity effect produced by the gravitomagnetic field of the Earth generated by its rotation. The effect is a manifestation of spacetime curvature generated by mass-currents, a peculiarity of Einstein's theory of gravitation. This measurement stands out, compared to previous measurements in the same context, for its precision ($\simeq7.4\times10^{-3}$) and accuracy ($\simeq16\times10^{-3}$), i.e. for a reliable and robust evaluat…
HERO (Highly Eccentric Relativity Orbiter) is a space-based mission concept aimed to perform several tests of post-Newtonian gravity around the Earth with a preferably drag-free spacecraft moving along a highly elliptical path fixed in its plane undergoing a relatively fast secular precession. We considered two possible scenarios: a fast, 4-hr orbit with high perigee height of $1,047\,\mathrm{km}$, and a slow, 21-hr path with a low perigee height of $642\,\mathrm{km}$. HERO may detect, for the first time, the post-Newtonian orbital effects induced by the mass quadrupole moment $J_2$ of the Ear…
With continuous advances in technology, future satellite gradiometry missions will be capable of performing precision relativistic experiments and imposing constraints on modern gravity theories. To this end, the full first-order post-Newtonian tidal tensor under inertially guided and Earth-pointing local frames along post-Newtonian orbits is worked out. The physical picture behind the "Mashhoon-Theiss anomaly" is explained at the post-Newtonian level. The relativistic precession of the local frame with respect to the sidereal frame will produce modulations of Newtonian tidal forces along cert…
Accurate orbit modeling plays a key role in contemporary and future space missions such as GRACE and its successor GRACE-FO, GNSS, and altimetry missions. To fully exploit the technological capabilities and correctly interpret measurements, relativistic orbital effects need to be taken into account. Within the theory of General Relativity, equations of motion for freely falling test objects, such as satellites orbiting the Earth, are given by the geodesic equation. We analyze and compare different solution methods in a spherically symmetric background, i.e. for the Schwarzschild spacetime, as …
Fundamental Physics with the Laser Astrometric Test Of Relativity
激光天体测量相对论（Laser Astrometric Test Of Relativity，LATOR）是一个由欧洲和美国联合进行的迈克尔逊-莫雷型实验，旨在测试引力的纯张量度量性质--这是爱因斯坦广义相对论的一个基本假设。通过使用独立的时间序列的高度精确的引力偏转光在太阳附近的组合，以及行星际尺度上的夏皮罗时间延迟的测量（精度分别优于0.1皮弧度和1厘米），LATOR将显着提高我们的知识相对论引力。任务的主要目标是：i）测量关键的后牛顿爱丁顿参数γ，精度为10^9分之一。(1-γ）是引力理论中新相互作用存在的直接度量，在其搜索中，LATOR比卡西尼2003年的测试结果超出了30，000倍。特派团还将提供：ii）首次测量重力对光的非线性影响，精度约为0.01%;包括爱丁顿β参数和空间度量的二阶势贡献（以前从未测量过）; iii）直接测量太阳四极矩J2（目前不可用）的精度达到其预期尺寸的200分之一; iv）直接测量太阳重力磁场对光的“坐标系拖曳”效应，精确度达到1%。LATOR的主要测量通过寻找今天太阳系中的残余标量场，将对宇宙学相关的标量-张量引力理论的研究推向了前所未有的精度。我们讨论了这个实验的任务设计。
