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Abstract In this paper we treat some aspects of the LARES 2 space experiment to test the general relativistic phenomenon of dragging of inertial frames, or frame-dragging, in particular we discuss some aspects of its relative accuracy which can approach one part in a thousand. We then, once again respond to the criticisms of the author of a recent paper about the accuracy in the measurement of frame-dragging with LARES 2. The claims of such a paper are not reproducible in any independent analyses. Indeed, it claims that the accuracy in the test of frame-dragging, which can be reached by the LARES 2 space experiment, is several orders of magnitude larger than previously estimated in a number of papers. Here we show that such a paper is based on a number of significant misunderstandings and conceptual mistakes. Furthermore, it is puzzling to observe that previous papers by the same author contained completely opposite statements about the accuracy which can be reached using two satellites with supplementary inclinations, such as in the LARES 2 space experiment, and in general with laser-ranged satellites.

Abstract LARES 2, successfully launched on July 13, 2022, is a new generation laser-ranged satellite. LARES is an acronym for LAser RElativity Satellite. The first LARES satellite was successfully launched on February 13, 2012 with the ESA-ASI-AVIO launch vehicle VEGA. LARES 2 was injected with extremely high precision onto a high-altitude orbit at about 5900 km altitude with the new ESA-ASI-AVIO launch vehicle VEGA C. Laser-ranged satellites have many applications, including to test Einstein’s theory of general relativity. The main general relativistic phenomenon that LARES 2 will test with high accuracy is the dragging of inertial frames, or frame-dragging. It will also test other aspects and principles of fundamental physics and general relativity, such as the weak equivalence principle at the foundation of viable gravitational theories. Frame-dragging is the name Einstein himself gave in 1913 to an intriguing phenomenon of general relativity which implies that a current of mass-energy, such as the rotation of a body, will generate spacetime curvature. Frame-dragging has a key role in high energy astrophysics, e.g., in the generation of gravitational waves by the collision of two black holes to form a rotating black hole. Frame-dragging by the rotating Earth was measured to a few percent accuracy by combining the data of the satellites LARES, LAGEOS and LAGEOS 2 (Ciufolini et al. in Eur Phys J C 79:872, 2019). LARES 2, thanks to its extremely high injection precision, is projected to improve the test of frame-dragging by at least an order of magnitude. LARES 2 has also relevant applications in space geodesy and geodynamics, e.g., in the study of the shape of the Earth and in the determination of the International Terrestrial Reference Frame (ITRF) by improving the determination of the Earth center of mass and by contributing to a better determination of its rotation axis.

Abstract 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 used the orbital estimator GEODYN (NASA). We measured frame-dragging to be equal to $$0.9910 \pm 0.02$$ 0.9910±0.02 , where 1 is the theoretical prediction of General Relativity normalized to its frame-dragging value and $$\pm 0.02$$ ±0.02 is the estimated systematic error due to modelling errors in the orbital perturbations, mainly due to the errors in the Earth’s gravity field determination. Therefore, our measurement confirms the prediction of General Relativity for frame-dragging with a few percent uncertainty.

Abstract In 2016, we published “A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth’s 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’s gravity model by I. Ciufolini et al.”” by L. Iorio [2] (called I2017 in the following), it was incorrectly claimed that, when comparing different Earth’s gravity field models, the systematic error in our test due to the Earth’s even zonal harmonics of degree 6, 8, 10 could be as large as 15%, 6% and 36%, respectively. Furthermore, I2017 contains other, also incorrect, claims about the number of necessary significant decimal digits of the coefficients used in our test (claimed to be nine), in order to eliminate the largest uncertainties in the even zonals of degree 2 and 4, and about the non-repeatability of our test. Here we analyze and rebut those claims in I2017.