In classical theories of gravitation, the changes in a gravitational field propagate. A change in the distribution of energy and momentum of matter results in subsequent alteration, at a distance, of the gravitational field which it produces. In the relativistic sense, the "speed of gravity" refers to the speed of a gravitational wave, which, as predicted by general relativity and confirmed by observation of the GW170817 neutron star merger, is equal to the speed of light (c).
Modern understanding The speed of gravitational waves in the general theory of relativity is equal to the speed of light in vacuum, . Within the theory of special relativity, the constant is not only about light; instead it is the highest possible speed for any interaction in nature. Formally, is a conversion factor for changing the unit of time to the unit of space. This makes it the only speed which does not depend either on the motion of an observer or a source of light and / or gravity. Thus, the speed of "light" is also the speed of gravitational waves, and further the speed of any massless particle. Such particles include the gluon (carrier of the strong force), the photons that make up light (hence carrier of electromagnetic force), and the hypothetical gravitons (which are the presumptive field particles associated with gravity; however, an understanding of the graviton, if it exists, requires an as-yet unavailable theory of quantum gravity).
Static fields The speed of physical changes in a gravitational or electromagnetic field should not be confused with "changes" in the behavior of static fields that are due to pure observer-effects. These changes in direction of a static field are, because of relativistic considerations, the same for an observer when a distant charge is moving, as when an observer (instead) decides to move with respect to a distant charge. Thus, constant motion of an observer with regard to a static charge and its extended static field (either a gravitational or electric field) does not change the field. For static fields, such as the electrostatic field connected with electric charge, or the gravitational field connected to a massive object, the field extends to infinity, and does not propagate. Motion of an observer does not cause the direction of such a field to change, and by symmetrical considerations, changing the observer frame so that the charge appears to be moving at a constant rate, also does not cause the direction of its field to change, but requires that it continues to "point" in the direction of the charge, at all distances from the charge.
The consequence of this is that static fields (either electric or gravitational) always point directly to the actual position of the bodies that they are connected to, without any delay that is due to any "signal" traveling (or propagating) from the charge, over a distance to an observer. This remains true if the charged bodies and their observers are made to "move" (or not), by simply changing reference frames. This fact sometimes causes confusion about the "speed" of such static fields, which sometimes appear to change infinitely quickly when the changes in the field are mere artifacts of the motion of the observer, or of observation.
In such cases, nothing actually changes infinitely quickly, save the point of view of an observer of the field. For example, when an observer begins to move with respect to a static field that already extends over light years, it appears as though "immediately" the entire field, along with its source, has begun moving at the speed of the observer. This, of course, includes the extended parts of the field. However, this "change" in the apparent behavior of the field source, along with its distant field, does not represent any sort of propagation that is faster than light.
Historical views
Newtonian gravitation Isaac Newton's formulation of a gravitational force law requires that each particle with mass respond instantaneously to every other particle with mass irrespective of the distance between them. In modern terms, Newtonian gravitation is described by the Poisson equation, according to which, when the mass distribution of a system changes, its gravitational field instantaneously adjusts. Therefore, the theory assumes the speed of gravity to be infinite. This assumption was adequate to account for all phenomena with the observational accuracy of that time. It was not until the 19th century that an anomaly in astronomical observations which could not be reconciled with the Newtonian gravitational model of instantaneous action was noted: the French astronomer Urbain Le Verrier determined in 1859 that the elliptical orbit of Mercury precesses at a significantly different rate from that predicted by Newtonian theory.
Laplace The first attempt to combine a finite gravitational speed with Newton's theory was made by Pierre-Simon Laplace in 1805. Based on Newton's force law he considered a model in which the gravitational field is defined as a radiation field or fluid. Changes in the motion of the attracting body are transmitted by some sort of waves.Laplace, P.S.: (1805) "A Treatise in Celestial Mechanics", Volume IV, Book X, Chapter VII, translated by N. Bowditch (Chelsea, New York, 1966) Therefore, the movements of the celestial bodies should be modified in the order v/c, where v is the relative speed between the bodies and c is the speed of gravity. The effect of a finite speed of gravity goes to zero as c goes to infinity, but not as 1/c2 as it does in modern theories. This led Laplace to conclude that the speed of gravitational interactions is at least times the speed of light. This velocity was used by many in the 19th century to criticize any model based on a finite speed of gravity, like electrical or mechanical explanations of gravitation.
From a modern point of view, Laplace's analysis is incorrect. Not knowing about Lorentz invariance of static fields, Laplace assumed that when an object like the Earth is moving around the Sun, the attraction of the Earth would not be toward the instantaneous position of the Sun, but toward where the Sun had been if its position was retarded using the relative velocity (this retardation actually does happen with the optical position of the Sun, and is called annual solar aberration). Putting the Sun immobile at the origin, when the Earth is moving in an orbit of radius R with velocity v presuming that the gravitational influence moves with velocity c, moves the Sun's true position ahead of its optical position, by an amount equal to vR/c, which is the travel time of gravity from the sun to the Earth times the relative velocity of the sun and the Earth. As seen in Fig. 1, the pull of gravity (if it behaved like a wave, such as light) would then always be displaced in the direction of the Earth's velocity, so that the Earth would always be pulled toward the optical position of the Sun, rather than its actual position. This would cause a pull ahead of the Earth, which would cause the orbit of the Earth to spiral outward. Such an outspiral would be suppressed by an amount v/c compared to the force which keeps the Earth in orbit; and since the Earth's orbit is observed to be stable, Laplace's c must be very large. As is now known, it may be considered to be infinite in the limit of straight-line motion, since as a static influence it is instantaneous at distance when seen by observers at constant transverse velocity. For orbits in which velocity (direction of speed) changes slowly, it is almost infinite.
The attraction toward an object moving with a steady velocity is towards its instantaneous position with no delay, for both gravity and electric charge. In a field equation consistent with special relativity (i.e., a Lorentz invariant equation), the attraction between static charges moving with constant relative velocity is always toward the instantaneous position of the charge (in this case, the "gravitational charge" of the Sun), not the time-retarded position of the Sun. When an object is moving in orbit at a steady speed but changing velocity v, the effect on the orbit is order v2/c2, and the effect preserves energy and angular momentum, so that orbits do not decay.
Electrodynamical analogies At the end of the 19th century, there were many attempts to combine Newton's force law with the established laws of electrodynamics, like those of Wilhelm Eduard Weber, Carl Friedrich Gauss, Bernhard Riemann and James Clerk Maxwell. Those theories are not invalidated by Laplace's critique, because although they are based on finite propagation speeds, they contain additional terms which maintain the stability of the planetary system. Those models were used to explain the perihelion advance of Mercury, but they could not provide exact values. One exception was Maurice Lévy in 1890, who succeeded in doing so by combining the laws of Weber and Riemann, whereby the speed of gravity is equal to the speed of light. However, those hypotheses were rejected.
However, a more important variation of those attempts was the theory of Paul Gerber, who derived in 1898 the identical formula, which was also derived later by Einstein for the perihelion advance. Based on that formula, Gerber calculated a propagation speed for gravity of , i.e. practically the speed of light. But Gerber's derivation of the formula was faulty, i.e., his conclusions did not follow from his premises, and therefore many (including Einstein) did not consider it to be a meaningful theoretical effort. Additionally, the value it predicted for the deflection of light in the gravitational field of the sun was too high by the factor 3/2.Zenneck, pp. 49–51
Aether theories In 1900, Hendrik Lorentz tried to explain gravity on the basis of his ether theory and the Maxwell's equations. After proposing (and rejecting) a Le Sage type model, he assumed like Ottaviano-Fabrizio Mossotti and Johann Karl Friedrich Zöllner that the attraction of opposite charged particles is stronger than the repulsion of equal charged particles. The resulting net force is exactly what is known as universal gravitation, in which the speed of gravity is that of light. This leads to a conflict with the law of gravitation by Isaac Newton, in which it was shown by Laplace that a finite speed of gravity leads to some sort of aberration and therefore makes the orbits unstable. However, Lorentz showed that the theory is not concerned by Laplace's critique, because due to the structure of the Maxwell equations only effects in the order v2/c2 arise. But Lorentz calculated that the value for the perihelion advance of Mercury was much too low. He wrote:
In 1908, Henri Poincaré examined the gravitational theory of Lorentz and classified it as compatible with the relativity principle, but (like Lorentz) he criticized the inaccurate indication of the perihelion advance of Mercury. Reprinted in Poincaré, Oeuvres, tome IX, S. 551–586 and in "Science and Method" (1908)
Henri Poincaré argued in 1904 that a propagation speed of gravity which is greater than c would contradict the concept of local time (based on synchronization by light signals) and the principle of relativity. He wrote:. English translation in Reprinted in "The value of science", Ch. 7–9
However, in 1905 Poincaré calculated that changes in the gravitational field can propagate with the speed of light if it is presupposed that such a theory is based on the Lorentz transformation. He wrote: See also the English Translation.