Does gravity travel at the speed of light?

This question is very interesting and basic. It can be simply answered that gravitational waves travel at the speed of light in a weak field background.

"Weak field" refers to a field with very weak field strength. For example, the gravitational field of the solar system is a weak field, because gravity is very weak; The gravitational field around a black hole is a strong field, because gravity is very strong. Therefore, the propagation of gravity in the solar system is called the propagation under the background of weak field. Gravitational propagation around a black hole is not suitable for weak field analysis.

Newton's formula of universal gravitation obviously does not contain time, so Newton's gravity is instantaneous and is a kind of "action at a distance". Newton couldn't explain this, so he never made any assumptions about the cause of gravity. At this point, the law of gravity and Coulomb's law of electrostatic field are very similar, both of which explain how a "source" produces a "field". Given a "source"-mass or charge, a field-Newton gravitational field or electrostatic field is generated instantly in the surrounding space. Once the "source" disappears, the surrounding field disappears instantly. Without a source, Newton's gravitational field and electrostatic field cannot exist. Before Maxwell, people didn't know how electric or magnetic fields spread. But Coulomb's law is not the whole of electromagnetic field. So it was not until Maxwell combined Coulomb's law (corresponding to Gauss's law), Faraday's law of electromagnetic induction and the extended ampere's law to get a wave equation that people realized that both electric and magnetic fields spread in the form of waves, and speed is the speed of light. The most important thing is that electromagnetic waves can exist without the "source" and spread freely.