In 1915 European mathematical physicists were excited. Albert Einstein had launched into the arena of physics a new theory, general relativity, which explained what gravity was: a deformation of space due to the presence of objects with mass. For theorists, Einstein’s equations were beautiful and quite a challenge, since they had to be solved for different physical situations. That same year the Austrian Karl Schwarzschild, from the Russian front –we were in World War I-, **obtained the solutions for a very massive non-rotating object: he had just discovered the theoretical existence of a black hole** .

But everyone knew that celestial objects rotate on their axis. How to introduce this fact in the equations? It was Einstein, with the invaluable help of his friends Marcel Grossmann and Michele Besso, who was the first to introduce rotation into his theory. Two years later, in 1917, the Austrian **Hans Thirring** started a notebook entitled “ *Wirkung rotierender Massen* ”, the effect of rotating masses. It was a purely theoretical work in the framework of general relativity; To look for possible astronomical applications, he spoke with Josef Lense. Among his conclusions is what is now known as the Thirring-Lense effect, although the key he needed to progress in his work was given to him by Einstein himself in a letter dated August 2, 1917: perhaps it would be more appropriate to add the name of German genius to this effect.

The **Thirring-Lense effect** describes what happens to spacetime near a rotating object. In essence **, what occurs is a drag effect, similar to what happens with the atmosphere of our planet** : the air that surrounds us is carried along with the rotation of the Earth. If this were not the case, if the atmosphere remained static while it rotated, we would notice a wind blowing over our heads that would reach 265 km/h at the Equator. The same thing happens with the fabric of space-time. Planets and stars, when turning, drag with them the area closest to them. In this way, if we were to observe from a distance a clock that rotates with the Sun, we would see that it is ahead of ours. And, in the same way, the speed of light in the direction of rotation is greater than in the opposite.

Since that distant 1917, the Thirring-Lense effect **has not ceased to be a curious theoretical prediction impossible to prove experimentally** . In 1976 Van Patten and Everitt proposed that two satellites equipped with precision gyroscopes orbiting in opposite directions could be used to do this. The measurement requires to be very precise because it is almost undetectable -one twelfth of a millionth of a degree-, and it is also masked by other effects: from non-gravitational ones, such as tensions in the apparatus, vibrations…, to tiny variations in the gravitational field terrestrial because our planet is not a perfect sphere.

In 1998 and then in 2004 a team from the University of Lecce (Italy) led by Ignazio Ciufolini and Erricos C. Pavlis of the US Joint Center for Earth System Technology observed the shifts in the orbits of two geodetic satellites, LAGEOS 1 and LAGEOS 2 using laser ranging. “Our measurements agree 99% with what is predicted by general relativity, with our margin of error being plus or minus 5%,” said Pavlis.

However, not everyone is convinced that they have managed to measure this elusive effect of relativity. Some think that this experiment, which used data from 11 years of observation, was not fine enough. In order to do so **, we would need to have a model of the real Earth’s gravitational field as accurate as one part in a ten-millionth** .

For this, the Italian satellite LARES, *LAser Relativity Satellite* , was launched in 2012. It carries a tungsten sphere with 92 retroreflectors that allow its movement to be followed from Earth with great precision. It is 1,400 kilometers above the surface and its trajectory is monitored by the *International Laser Ranging Service* ‘s network of laser ranging stations spread across the globe. With a diameter of just over 36 centimeters and a weight of 400 kilos, its aim was **to measure the Thirring-Lense effect with an accuracy of 1%** , according to the mission director, the Italian Ciufolini.

But when it was launched, not everyone agreed: many considered it too optimistic a forecast and believed that the accuracy of this method would not give more than 10% because LARES was going to be placed in a much lower orbit than previous LAGEOS. and, therefore, it would be more sensitive to the subtle variations of the gravitational field caused by the rotation of an Earth that is not spherical. Time proved them right… in part. An analysis published in 2016 concluded that after three and a half years the accuracy of the measurements only reached 4%.

To solve the problem, on July 13, 2022, a second satellite called, at the time, LARES 2, was launched, with which it is intended to lower the precision to 0.2%. Now it remains to be seen if they succeed.

**References:**

Ciufolini, I.; Paolozzi A.; Pavlis EC; Ries JC; Koenig R.; Matzner RA; Sindoni G. & Neumayer H. (2009). ” *Towards a One Percent Measurement of Frame Dragging by Spin with Satellite Laser Ranging to LAGEOS, LAGEOS 2 and LARES and GRACE Gravity Models* “. Space Science Reviews. 148 (1–4): 71–104

Paolozzi, A.; Ciufolini I.; Vendittozzi C. (2011). ” *Engineering and scientific aspects of LARES satellite* “. Astronautical Act. 69 (3–4): 127–134