Frame-dragging, also known as the Lense–Thirring effect

According to Albert Einstein’s theory of General Relativity, neither space nor time are immutable or absolute entities; together they form the four-dimensional structure of the universe known as ‘spacetime’. Spacetime is warped in the presence of mass, and general relativity explains the curved orbits of the planets not because there is a gravitational force exerted by the Sun’s mass, but because spacetime itself is curved by the Sun’s mass; the projections of the satellites’ spacetime orbits onto space are the curved orbits that we observe. These curved orbits correspond to geodesics in 4-dimensional spacetime: geodesics are the generalisation of straight lines, that is, they are the trajectories that describe the shortest path in a given space. This warping also causes a slowing down of time due to the presence of mass, an effect measured directly and with great accuracy on atomic clocks in the 1970s by NASA’s Gravity Probe A experiment.
Since its publication in 1916, general relativity has been strongly supported by experimental evidence, although there are still profound issues to be understood. These include the possible unification of general relativity with the other great theory of the twentieth century, quantum mechanics; the prediction of spacetime singularities where the physics we know ceases to apply, physical quantities diverge and time loses its meaning; and, finally, the accelerating expansion of the universe, which is also explained by a mysterious form of energy known as ‘dark energy’.

In 1918, physicists Hans Lense and Joseph Thirring were the first to calculate the frame-dragging effect, which, in the weak gravitational field approximation (applicable to the case of a satellite orbiting the Earth), is therefore referred to as the Lense–Thirring effect. A rotating mass drags space and time along as if they were material entities. This effect is extremely weak around the planets of the Solar System, so much so that direct measurement requires particularly sensitive instruments, as in the case of the LARES and LARES 2 missions, but it is of particular importance in models describing astrophysical phenomena generated by rotating objects with a gravitational field much stronger than Earth’s, such as the phenomena occurring around supermassive black holes. Frame-dragging also plays an important role in models explaining the emission of jets from active galactic nuclei and in those describing the emission of gravitational waves from the merger of black holes or neutron stars. Furthermore, a deviation in the measured value of the frame-dragging effect from that predicted by theory could confirm the validity of theories of gravitation alternative to general relativity

The role of the LARES and LARES 2 satellites

The drag on inertial systems caused by the Earth’s rotation can be measured by determining the shift in the orbital node of the LARES and LARES 2 satellites. Measuring this effect is particularly difficult, not only because it is extremely small (for the LARES node it is about 4 metres per year, and for the LARES 2 node it is about 2 metres per year), but above all because of classical gravitational and non-gravitational perturbations that shift the nodes by much greater amounts (several tens of thousands of kilometres per year!) than that due to the general relativity. In other words, the relativistic effect is millions of times smaller than the classical one. For this reason, measuring the relativistic effect by separating it from the effects of classical perturbations is not currently possible with a single satellite, which is why the LARES 2 mission also uses data from the LAGEOS satellite, launched into orbit by NASA in 1976. The specific configuration of the orbits, with additional inclinations, allows the effects of non-relativistic gravitational perturbations to be eliminated. We also used the LARES satellite, launched by VEGA on 13 February 2012, together with data from the LAGEOS 2 satellite, operated by NASA and ASI and placed in orbit in 1992, and from the aforementioned LAGEOS.

Our team, with the contribution of various scientists from around the world, including Nobel laureate Sir Roger Penrose, has published several results from measurements of Earth’s frame-dragging, approaching an accuracy of one per cent. This result was made possible not only by combining orbital data from LARES, LAGEOS and LAGEOS 2, but also thanks to the satellite’s special design and the availability of highly accurate measurements of the classical Earth’s gravitational field provided by the GRACE space mission.
The latest findings were presented in late May 2022 at the second LARES 2 and fifth LARES International Science Workshop, attended by two Nobel laureates in physics: Kip Thorne, awarded in 2017 for the first direct experimental measurement of gravitational waves emitted by the collision of two black holes, and Roger Penrose in 2020 for demonstrating what even Einstein considered to be merely a mathematical curiosity, namely that the formation of black holes—or, to be more precise, of spacetime singularities within them—is inevitable in general relativity. Black holes play a fundamental role in various astrophysical phenomena, from the observed emission of gravitational waves, to plasma jets from active galactic nuclei and quasars, to the formation of galaxies.

We like to recall that Italy played an important role in the 1970s in the detection of the first black hole candidate from the X-ray source known as Cygnus X-1. In fact, the School of Aerospace Engineering, headed by Luigi Broglio (the father of space activities in Italy), launched the Uhuru satellite into orbit using the Scout launch vehicle from the Italian base located on the equator (Malindi, Kenya) as part of the San Marco Project; the Nobel Prize-winning physicist Riccardo Giacconi also worked on this project. The data from the X-ray source detected by the satellite were analysed by none other than Kip Thorne and Igor Novikov, and gave rise to the famous bet between Kip Thorne and Stephen Hawking as to whether that source was indeed linked to the presence of a black hole. The enormous contribution made by the two Nobel laureates and the renowned Russian physicist Igor Novikov to our understanding of extreme gravitational phenomena, including the possibility of time travel predicted by general relativity, was recognised by awarding them the John Archibald Wheeler Prize during the opening ceremony of the Workshop, which was followed by a fascinating round-table discussion on time travel.

The round-table discussion, chaired by Richard Matzner of the University of Texas at Austin, featured the three award winners and the renowned physicist and science communicator Paul Davies, with contributions from many other leading scientists attending the workshop. This frame-dragging effect, so faint around the Earth, can be very significant if the rotating mass is that of a black hole or even a compact object such as a neutron star. In his Nobel lecture, Kip Thorne demonstrated that frame-dragging has been observed in a binary pulsar system (neutron stars). A recent confirmation of the relativistic frame-dragging effect is the observation of the tidal destruction of a star orbiting a black hole, published in 2025.
In both cases, these involve observations of astrophysical phenomena, whilst the significance of the LARES and LARES 2 missions lies in the fact that they enable a direct and repeatable experimental measurement of the Lense-Thirring effect (as these are long-duration missions, the laser ranging measurements can continue for decades).

L’esperimento LARES 2 permetterà di migliorare notevolmente l’accuratezza dell’esperimento condotto con il satellite LARES. Invero grazie all’elevata precisione con cui LARES 2 è stato messo in orbita dal lanciatore Vega C sarà possibile ottenere una misura del “frame-dragging” con un errore di circa una parte su mille soltanto. I requisiti di precisione di immissione orbitale di LARES non erano particolarmente elevati mentre erano più stringenti per il LARES 2, comunque, entrambi i lanci sono stati estremamente precisi. Vogliamo sottolineare che i due lanci inaugurali di Vega e Vega C hanno molto di Italiano in quanto i due lanciatori pur essendo dell’Agenzia Spaziale Europea (ESA), sono stati realizzati per la maggior parte in Italia ed in aggiunta hanno messo in orbita i due satelliti italiani dell’ASI: LARES e LARES 2.

For further reading:

1. Ciufolini, I., Paolozzi, A., Pavlis, E.C., Sindoni, G., Ries, J., Matzner, R., Koenig, R., Paris, C., Gurzadyan, V., Penrose R., An improved test of the general relativistic effect of frame-dragging using the LARES and LAGEOS satellites. Eur. Phys. J. C 79, 872 (2019). https://doi.org/10.1140/epjc/s10052-019-7386-z
2. Krishnan, V. Venkatraman, et al. “Lense–Thirring Frame Dragging Induced by a Fast-Rotating White Dwarf in a Binary Pulsar System.” Science, vol. 367, no. 6477, 2020, pp. 577–80. JSTOR, https://www.jstor.org/stable/26892215
3. Media INAF, Distruzione mareale mostra l’effetto Lense–Thirring, 11/12/2025 (in Italian), doi: https://doi.org/10.20371/INAF/2724-2641/1775165
4. Yanan Wang et al., Detection of disk-jet coprecession in a tidal disruption event.Sci. Adv.11,eady9068(2025), doi: https://doi.org/10.1126/sciadv.ady9068
5. D. Castelvecchi, Disco-ball satellite will put Einstein’s theory to strictest test yet, Nature, doi: https://doi.org/10.1038/d41586-022-02034-x, 25 Jul 2022, link: https://www.nature.com/articles/d41586-022-02034-x
6. Ciufolini, I., Paolozzi, A., Paris, C., LARES 2 messo in orbita dal VEGA C, Astronomia, n. 4, ottobre-dicembre 2022 (UAI)