How do we know the speed of gravity?

Question

I have read things like if the sun disappeared, it would take 8 minutes or so before we knew this, cf. e.g. this Phys.SE post.

However, in real life the sun will never disappear and if it exploded, its center of mass would remain more or less the same anyway.

So what real life experiment or phenomenon reveals the speed of gravity?

If you had a very heavy mass and moved it using very sensitive equipment to detect this movement via change in gravitational attraction, would not the movement of the mass have to be a the speed of light or near it to prove that gravity propagated at the speed of light? Or is there in fact some experiment like that where a mass is moved at fairly slow speed to establish the speed of gravity?

EDIT: It seems to me that light-speed measurement is accomplished most easily by turning off and on a source or blocking a light source neither of which can be done with gravity.

EDIT 2: I think I am not understanding how the experiments work. How does a massive object in motion allow one to determine the speed of gravity since this motion is continuous? That is, the object is not suddenly some large distance away from where it was -- I could understand as previously indicated that if a mass was created from nothing somehow, one could watch how long this new source of gravity took to affect an existing mass but if the mass is merely moving relative to another mass, I can't visualize how this can be used to measure the speed of gravity which is always affecting the second mass, just slightly less so if the as the objects move apart.

Answer 1

direct measurement from gravitational waves

The closest analogue to directly measuring the flight time of gravity uses the gravitational waves (GW) and gamma ray burst (GRB) from GW170817 and GRB 170817A as described in this paper. Both signals were created by the merger of two neutron stars, and the GRB was detected about 2 seconds after the end of the GW signal. The speed of gravity can be determined by comparing it to the speed of light.

The time lag can be accounted for because the GRB was likely created after the merger of the two bodies when the GW signal ends. The distance traveled by the two signals was so great ($\sim30$ Mpc $\approx 100$ million light years) that even if they were emitted simultaneously the speeds must be very nearly the same.

Section 4.1 of that paper uses some conservative assumptions about the emission of the GRB relative to the end of the GW signal and constrains the speed of gravity $v_\mathrm{gw}$ to differ from the speed of light $c$ by no more than a few parts in $10^{15}$.

$$-3\times 10^{-15} \le \frac{v_\mathrm{gw}-c}{c} \le 7\times 10^{-16}$$

historical measurements

In the 19th century there were efforts to measure the speed of gravity looking at the gravity of a moving object. These were motivated by the analogue electromagnetic effect. The electric and magnetic fields at a point depend not on what the sources are doing now, but on what they were doing in the past accounting for the finite signal travel time.

These measurements come from observing astronomical objects. For example, Saturn is moving around the Sun and Saturn's moons are affected by Saturn's gravity. By watching Saturn's moons you can see if their motion depends on Saturn's motion.

Modern experiments like this are described as tests of the equivalence principle, a foundational assumption of General Relativity. For example, a recently discovered pulsar in a triple system with two white dwarfs was used in this paper.

Answer 2

The Wikipedia article referenced by @JohanLiebert says it very well: "The detection of the neutron star inspiral GW170817 in 2017, detected through both gravitational waves and gamma rays, currently provides by far the best limit on the difference between the speed of light and that of gravity. Photons were detected 1.7 seconds after peak gravitational wave emission; assuming a delay of zero to ten seconds, the difference between the speeds of gravitational and electromagnetic waves, vGW − vEM, is constrained to between −3×10−15 and +7×10−16 times the speed of light.[29]"

In essence, the event that emitted gravitational waves near- simultaneously emmitted a gamma ray pulse. The event occurred about 130 million lightyears away. The gravitational wave and the gamma ray signal arrived at our detectors at very nearly the same time, so we know that gravitational waves and gamma rays propagate at very nearly the same speed, and probably exactly the same speed.