For the first time this month, our international team observed a minute deviation of the star’s orbit from a simple ellipse, on the order of a few hundred microseconds of angle, the size of a shoebox seen on the Moon.

To understand what this detection means, it is useful to take a step back and consider the evolution of ideas about the notion of the orbit of celestial bodies.

Most stars and planets have non-circular orbits, periodically approaching and then moving away from the object around which they orbit. The orbit of the star S2 is precessive, orbiting the supermassive black hole in the heart of the Milky Way, which means that the point in the orbit closest to the black hole changes as it rotates, generating the appearance of a rosette. This effect has never before been measured for a star orbiting a supermassive black hole.

#### Earth at the centre: the cosmos of the ancient Greeks

The school of Pythagoras brings two considerable advances in science: number is considered as the first principle of things and the systematization of geometry begins - Pythagoras generalizes his famous theorem, which was already known in practice by the Egyptians for particular triangles.

*© Wikipedia*

Plato, around 400 BC, proposed a model of the cosmos based on nested spheres: the Earth is at the centre, surrounded by the spheres of water, air and fire. The stars move beyond it, at increasing distances: first the Moon, then the other known planets and the Sun, and finally the sphere of fixed distant stars. This model, developed by Cnidus’ Eudoxus - a "doctoral student" of Plato’s, as we would say today - postulates that the stars move at constant speed following circular orbits along the nested spheres.

#### The Heliocentric System and the Advent of Modern Physics

Despite the developments brought by Ptolemy (1st century) to the Eudox model, the basic elements of the understanding of the cosmos did not radically change until the 16th century. Around 1530, the Copernican revolution placed the Sun, rather than the Earth, at the centre of the cosmos, and considered the stars in circular orbit around the Sun. Around 1580, Tycho Brahe made observations of astonishing precision on a very large number of light sources. At the turn of the 17th century, Johannes Kepler synthesized Tycho Brahe’s observations and Copernicus’ system to systematize them into Kepler’s famous laws, which are still taught today.

The result of the GRAVITY team, this ellipse in precession, must be analyzed with reference to Kepler’s laws. Indeed, Kepler brings two fundamental elements: on the one hand, the role of "motor" played by the Sun in the movement of the stars, whereas previous descriptions were content to confirm the fact that the stars revolve either around the Earth or around the Sun, without seeing a causal link between the presence of the central body and the movement of the stars around it. On the other hand, Tycho Brahe’s observations allowed him to replace the circular motion theory dating from Eudox with an elliptical motion. With Newton around 1680, Kepler’s advances are confirmed and included in a much broader system of explanation, which will form the cornerstone of astronomy until Einstein. Indeed, Newton’s theory shows mathematically that a body (e.g. a planet) undergoing the gravitational attraction of another body (e.g. the Sun) follows a conic - of which the simplest examples are circles and ellipses - thus validating Kepler’s ideas.

*© Thomas Heath/Flickr, CC BY*

#### General Relativity

Einstein, Newton’s direct heir, reformulated the laws of gravitation in 1915, and came up with the laws of general relativity, which encompass and considerably exceed Newtonian theory.

One of the consequences of general relativity concerns the orbits of celestial bodies. It predicts that the orbits of the planets around the Sun do not follow Keplerian ellipses, but gradually shift to form a rosette, in the "dance" movement mentioned at the beginning of the article.

Einstein then remembers that the French astronomer Urbain Le Verrier had highlighted in 1859 at the Paris Observatory the fact that the planet Mercury - the closest to the Sun, and thus the most strongly subjected to its gravitation - exhibited an unexplained movement, in disagreement with the laws of Kepler and Newton. Einstein seizes the problem and shows that the theory of general relativity explains exactly the inconsistency reported by The Glassmaker.

*© Lithographie de E. Jones & G.W. Newman, 1846. - Library of Congress*

Einstein, according to his own account, "was unable to work for three days because of excitement" following this very first experimental verification of his new theory, which validates his hard work over the previous decade. The GRAVITY team’s recent measurement is the latest experimental verification of the same effect, in a very different context since it is the orbit of a star around a black hole and not the orbit of a planet around a star.

#### Recently observed by GRAVITY

General relativity predicts the behaviour of all the stars, including that of the object of choice of the GRAVITY instrument - the black hole 4 million times the mass of the Sun at the centre of our Galaxy, Sagittarius A*.

The star with the poetic name of S2 is in relatively close orbit around this black hole. Its trajectory has been determined by GRAVITY: it is a rosette, corresponding to the slow shift of an ellipse. As Einstein did in 1915 with Mercury, the GRAVITY team compared the shift of the orbit of S2 to the value predicted by general relativity. The agreement is excellent, which is a new test of Einstein’s theory. This new test is carried out in a much more "extreme" context than that of Mercury: the observed star is here in orbit around a black hole, an object itself predicted by the theory of general relativity and which constitutes one of the most exotic members of the standard astronomical bestiary. The validation of Einstein’s theory in the environment of such an object is thus particularly interesting.

Beyond testing the validity of general relativity predictions, GRAVITY’s observation allows the study of the environment close to the black hole as well as its properties: its mass and distance are now constrained with great precision. An important question is to determine if the central mass around which S2 is in orbit is completely concentrated in the Sagittarius A* object itself, or if another, larger mass component is also present. This additional mass could be present as "dark matter" (composed of the famous dark matter, low-bright stars and an assembly of small black holes and isolated neutron stars) or as a companion black hole that is itself in orbit around Sagittarius A*. Recent observations by the GRAVITY team seem to point to a complete concentration of mass in the Sagittarius A* object itself, but further studies are needed to answer this complex question.

GRAVITY is not the only instrument that investigates the properties of the surroundings of black holes. The Event Horizon Telescope has recently published a first image of the surroundings of a black hole. On another level, gravitational wave detectors follow the evolution of colliding black holes. All these new observations will make it possible in the coming decades to test Einstein’s theory more and more, and, hopefully, to discover its limits.

Last update on 26 May 2020