Gravitational waves, like all forms of electromagnetic radiation, travel at the speed of light in a vacuum. In the case of gravitational waves originating from the Sun's center, they would also propagate at the speed of light, which is approximately 299,792,458 meters per second (or about 186,282 miles per second).
The speed of gravitational waves is a fundamental property that arises from the nature of spacetime itself. According to Einstein's theory of general relativity, gravitational waves are disturbances in the curvature of spacetime, and they propagate outward from their source at the speed of light.
It's worth noting that gravitational waves can travel through various media, including matter and other gravitational fields, without being significantly slowed down. This is because they interact very weakly with matter, allowing them to propagate largely unaffected by intervening objects or environments.
Therefore, whether the gravitational waves originate from the Sun's center or any other source, their speed will always be equal to the speed of light.