Will, C. M. & Yunes, N. Is Einstein Still Right?: Black Holes, Gravitational Waves, and the Quest to Verify Einstein’s Greatest Creation (Oxford Univ. Press, 2020).
Thorne, K. S., Price, R. H. & Macdonald, D. A. The Membrane Paradigm (Yale Univ. Press, 1986).
Apostolatos, T. A., Cutler, C., Sussman, G. J. & Thorne, K. S. Spin-induced orbital precession and its modulation of the gravitational waveforms from merging binaries. Phys. Rev. D 49, 6274 (1994).
O’Connell, R. F. A note on frame dragging. Class. Quantum Grav. 22, 3815–3816 (2005).
Ciufolini, I. Dragging of inertial frames. Nature 449, 41–47 (2007).
Ciufolini, I., Matzner, R., Gurzadyan, V. & Penrose, R. A new laser-ranged satellite for General Relativity and Space Geodesy III. De Sitter effect and the LARES 2 space experiment. Eur. Phys. J. C 77, 819 (2017).
Smith, T. L., Erickcek, A., Caldwell, R. & Kamionkowski, M. Effects of Chern–Simons gravity on bodies orbiting the Earth. Phys. Rev. D 77, 024015 (2008).
Stephon, A. & Yunes, N. New post-Newtonian parameter to test chern-simons gravity. Phys. Rev. Lett. 99, 241101 (2007).
Ciufolini, I. et al. A new laser-ranged satellite for general relativity and space geodesy: I. An introduction to the LARES 2 space experiment. Eur. Phys. J. Plus 132, 336 (2017).
Müller, J. et al. Lunar Laser Ranging: a tool for general relativity, lunar geophysics and Earth science. J. Geodesy 93, 2195 (2019).
Pearlman, M. et al. Laser geodetic satellites: a high-accuracy scientific tool. J. Geodesy 93, 2181 (2019).
Ciufolini, I. & Pavlis, E. C. A confirmation of the general relativistic prediction of the Lense–Thirring effect. Nature 431, 958–960 (2004).
Ciufolini, I. et al. An improved test of the general relativistic effect of frame-dragging using the LARES and LAGEOS satellites. Eur. Phys. J. C 79, 872 (2019).
Everitt, C. W. et al. Gravity Probe B: final results of a space experiment to test general relativity. Phys. Rev. Lett. 106, 221101 (2011).
Lense, J. & Thirring, H. Uber den Einfluss der Eigenrotation der Zentralko¨rper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Phys. Z. 19, 156–163 (1918).
Einstein, A. Grundgedanken der allgemeinen Relativitätstheorie und anwendung dieser theorie in der astronomie, sitzungsher. Preuss Akad. Wiss. 778–786, 799–801 (1915).
Zeldovich, YaB & Novikov, I. D. Relativistic Astrophysics Vol. I Stars and Relativity (Univ. Chicago Press, 1971).
Landau, L. D. & Lifshitz, E. M. The Classical Theory of Fields 3rd rev., English edn. (Pergamon, 1971).
Weinberg, S. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, 1972).
Hawking, S. W. & Ellis, G. F. R. The Large Structure of Space-time (Cambridge Univ. Press, Cambridge, 1973).
Misner, C. W., Thorne, K. S. & Wheeler, J. A. Gravitation (Freeman, 1973).
Hawking, S. & Penrose R. The Nature of Space and Time (Princeton Univ. Press, 2010).
Will, C. M. Theory and Experiment in Gravitational Physics (Cambridge Univ. Press, 2018).
Will, C. M. The confrontation between general relativity and experiment. Living Rev. Relativ. 17, 4 (2014).
Ciufolini, I. & Wheeler, J. A. Gravitation and Inertia (Princeton Univ. Press, 1995).
Kopeikin S. et al. Frontiers in Relativistic Celestial Mechanics Vol. 2 (de Gruyter, 2014).
Penrose, R. Gravitational collapse and space–time singularities. Phys. Rev. Lett. 14, 57 (1965).
Abbott, B. P. et al. Tests of general relativity with GW150914. Phys. Rev. Lett. 116, 221101 (2016).
Thorne, K. S. LIGO and gravitational waves, III: Nobel lecture, December 8, 2017. Ann. Phys. 531, 1800350 (2019).
Riess, A. G. et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009–1038 (1998).
Perlmutter, S. et al. Measurements of Omega and Lambda from 42 high-redshift supernovae. Astrophys. J. 517, 565–586 (1999).
Caldwell, R. R. Dark energy. Phys. World 17, 37 (2004).
Ciufolini, I. Measurement of the Lense–Thirring drag on high-altitude laser-ranged artificial satellites. Phys. Rev. Lett. 56, 278 (1986).
Ciufolini, I. A comprehensive introduction to the Lageos gravitomagnetic experiment: from the importance of the gravitomagnetic field in physics to preliminary error analysis and error budget. Int. J. Mod. Phys. A 4, 3083–3145 (1989).
Ciufolini, I. et al. The LARES 2 satellite, general relativity and fundamental physics. Eur. Phys. J. C 83, 87 (2023).
Kaula, W. M. Theory of Satellite Geodesy (Blaisdell, 1966).
Ciufolini, I. Theory and experiments in general relativity and other metric theories. PhD Dissertation, Univ. Texas, Austin (1984).
Ries, J. C. Simulation of an experiment to measure the Lense–Thirring precession using a second LAGEOS satellite. PhD Dissertation, Univ. Texas, Austin (1989).
Peterson, G. E. Estimation of the Lense–Thirring precession using laser-ranged satellites. PhD Dissertation, Univ. of Texas, Austin (1997).
Tapley, B. D. & Ciufolini, I. Measuring the Lense-Thirring Precession Using a Second LAGEOS Satellite CSR-UT Report 89-3 (Texas Scholar Works depository, 1989); https://doi.org/10.26153/tsw/63964
Ciufolini, I. et al. A new laser-ranged satellite for general relativity and space geodesy: II. Monte Carlo simulations and covariance analyses of the LARES 2 experiment. Eur. Phys. J. Plus 132, 337 (2017).
Ciufolini, I. et al. A new laser-ranged satellite for general relativity and space geodesy: IV. Thermal drag and the LARES 2 space experiment. Eur. Phys. J. Plus 133, 333 (2018).
Ciufolini, I. et al. ASI-NASA Study on LAGEOS III (NASA, 1989); https://ntrs.nasa.gov/citations/19910004157
Ray, R. D. & Merrifield, M. A. The semiannual and 4.4-year modulations of extreme high tides. J. Geophys. Res. Oceans 124, 5907–5922 (2019).
Bertotti, B. & Carpino, M. Supplementary satellites and tidal perturbations. In ASI-NASA Study on LAGEOS III (ed. Ciufolini I. et al.) (NASA, 1989); https://ntrs.nasa.gov/citations/19910004157
Pucacco, G. & Lucchesi, D. M. Tidal effects on the LAGEOS–LARES satellites and the LARASE program. Celest. Mech. Dyn. Astr. 130, 66 (2018).
Gurzadyan, V. G., Ciufolini, I., Khachatryan, H. G., Mirzoyan, S. & Paolozzi, A. On the Earth’s tidal perturbations. II. LARES 2 satellite. Eur. Phys. J. Plus 140, 512 (2025).
Ries, J. C. et al. Development and Evaluation of the Global Gravity Model GGM05C CSR-16-02 (ICGEM, 2016); https://icgem.gfz.de/tom_longtime.
Tapley, B. D., Bettadpur, S., Watkins, M. & Reigber, C. The gravity recovery and climate experiment: mission overview and early results. Geophys. Res. Lett. 31, L09607 (2004).
Landerer, F. W. et al. Extending the global mass change data record: GRACE follow-on instrument and science data performance. Geophys. Res. Lett. 47, 12 (2020).
Chen, W. & Shen, W. New estimates of the inertia tensor and rotation of the triaxial nonrigid Earth. J. Geophys. Res. 115, B12419 (2010).
Petit, G. G. & Luzum, B. (eds) IERS Technical Note No. 36, 2010 IERS Conventions, Frankfurt am Main Verlag des Bundesamts für Kartographie und Geodaesie (IERS, 2010).
Ray, R. D. Precise comparisons of bottom-pressure and altimetric ocean tides. J. Geophys. Res. Oceans 118, 4570 (2013).
Ray, R. D. Documentation for Goddard Ocean Tide Solution GOT5: Global Tides from Multi-mission Satellite Altimetry TM-20250002085 (NASA, 2025).
Otsubo, T. et al. Rapid response quality control service for the laser ranging tracking network. J. Geod. 93, 2335–2344 (2019).
Lucchesi, D. M. & Balmino, G. The LAGEOS satellites orbital residuals determination and the Lense–Thirring effect measurement. Planet. Space Sci. 54, 581 (2006).
Pavlis, D. E. et al. GEODYN Systems Description Vols. 1 and 3 (NASA, 1998).
Pavlis, E. C. & Luceri, V. The ILRS contribution to ITRF2020 (ITRF, 2022); https://itrf.ign.fr/docs/solutions/itrf2020/The_ILRS_contribution_to_ITRF2020_description_2022.09.23.pdf
Sośnica, K. & Gałdyn, F. Orbital relativistic correction resulting from the Earth’s oblateness term. J. Geod. 99, 52 (2025).
Soffel, M. et al. Relativistic effects in the motion of artificial satellites: the oblateness of the central body I. Celest. Mech. Dyn. Astr. 42, 81–89 (1987).
Will, C. M. Relativistic gravity in the Solar System. III. Experimental disproof of a class of linear theories of gravitation. Astrophys. J. 185, 31–42 (1973).
Will, C. M. & Nordtvedt, K. Jr. Conservation laws and preferred frames in relativistic gravity. Astrophys. J. 177, 757–774 (1972).
Nordtvedt, K. Jr & Will, C. M. Conservation laws and preferred frames in relativistic gravity. II. Experimental evidence to rule out preferred-frame theories of gravity. Astrophys. J. 177, 775–792 (1972).
Will, C. M. Theoretical frameworks for testing relativistic gravity. II. Parametrized post-Newtonian hydrodynamics, and the Nordtvedt effect. Astrophys. J. 163, 611–627 (1971).
Thorne, K. S. & Will, C. M. Theoretical frameworks for testing relativistic gravity. I. Foundations. Astrophys. J. 163, 595–610 (1971).
Nordtvedt, K. Jr. Equivalence principle for massive bodies. II. Theory. Phys. Rev. 169, 1017–1025 (1968).
Chandrasekhar, S. & Contopoulos, G. On a post-Galilean transformation appropriate to the post-Newtonian theory of Einstein, Infeld and Hoffmann. Proc. R. Soc. A 298, 123–141 (1967).
Schiff, L. I. in Relativity Theory and Astrophysics, 1: Relativity and Cosmology (ed. Ehlers, J.) 105 (American Mathematical Society, 1967).
Chandrasekhar, S. The post-Newtonian equations of hydrodynamics in general relativity. Astrophys. J. 142, 1488–1512 (1965).
Freire, P. C. C. & Wex, N. Gravity experiments with radio pulsars. Living Rev. Relativ. 27, 5 (2024).
Particle Data Group. Experimental Tests of Gravitational Theory (2025).
Soffel, M. et al. The IAU 2000 resolutions for astrometry, celestial mechanics and metrology in the relativistic framework: explanatory supplement. Astron. J. 126, 2687–2706 (2003).
Brumberg, V. Essential Relativistic Celestial Mechanics (CRC, 2017).
Damour, T., Soffel, M. & Xu, C. General-relativistic celestial mechanics. I. Method and definition of reference systems. Phys. Rev. D 43, 3273–3307 (1991).
Roh, K.-M., Kopeikin, S. M. & Cho, J.-H. Numerical simulation of the post-Newtonian equations of motion for the near-Earth satellite with an application to the LARES satellite. Adv. Space Res. 58, 2255–2268 (2016).
Ashby, N. & Bertotti, B. Relativistic perturbations of an Earth Satellite. Phys. Rev- Lett. 52, 485–488 (1984).
Ashby, N. & Bertotti, B. Relativistic effects in local inertial frames. Phys. Rev. D 34, 2246–2259 (1986).
Bertotti, B., Ciufolini, I. & Bender, P. L. New test of general relativity: measurement of de Sitter geodetic precession rate for lunar perigee. Phys. Rev. Lett. 58, 1062–1065 (1987).
Huang, C. et al. Relativistic effects for near-earth satellite orbit determination. Celest. Mech. Dyn. Astr. 48, 167–185 (1990).
Rubincam, D. P. Yarkovsky thermal drag on LAGEOS. J. Geophys. Res. Solid Earth 93, 13805–13810 (1988).
Rubincam, D. P. Drag on the LAGEOS satellite. J. Geophys. Res. Solid Earth 95, 4881–4886 (1990).
Andrés de la Fuente, J. I. & Noomen, R. Enhanced Modelling of the Non-Gravitational Forces Acting on LAGEOS. In Proc. 15th International Workshop on Laser Ranging Instrumentation (ILRS LW15) (Delft University of Technology, 2006).
Couhert, A. et al. Self-consistent determination of the Earth’s GM, geocenter motion and figure axis orientation. J. Geodesy 94, 113 (2020).
Gao, D. & Ni, W.-T. Frame-dragging effects in a gravitational quantum field theory. Phys. Rev. D 111, 084039 (2025).
Hartle, J. B. & Thorne, K. S. Slowly rotating relativistic stars. II. Models for neutron stars and supermassive stars. Astrophys. J. 153, 807–834 (1968).
Kerr, R. P. Gravitational field of a spinning mass as an example of algebraically special metrics. Phys. Rev. Lett. 11, 237–238 (1963).
Abac, A. G. et al. GW250114: Testing Hawking’s area law and the Kerr nature of black holes. Phys. Rev. Lett. 135, 111403 (2025).
Chandrasekhar, S. On stars, their evolution and their stability: Nobel lecture, December 8, 1983. Science 226, 497–505 (1984).
