Yes, the Earth does experience a form of time dilation due to its speed through space relative to the rest frame of our galaxy's center. This phenomenon is a consequence of the theory of special relativity.
According to special relativity, when an object is in motion relative to an observer, time appears to pass more slowly for the moving object compared to a stationary observer. This effect is known as time dilation. The magnitude of time dilation depends on the relative velocity between the two frames of reference.
In the case of the Earth's motion through space, it orbits the center of the Milky Way galaxy at a speed of approximately 220 kilometers per second, or about 1.4 million miles per hour. This motion results in the Earth experiencing a time dilation effect.
However, it's important to note that the magnitude of this time dilation is extremely small. The relative velocity between the Earth and the rest frame of the galaxy's center is far below the speed of light, so the time dilation effect is minuscule and not readily observable in everyday life.
To put it into perspective, the time dilation experienced by an observer on Earth due to its orbital velocity is on the order of microseconds per year compared to a hypothetical stationary observer at the galactic center. This is an exceedingly small effect that is well beyond the capabilities of our current technology to measure directly.
Nonetheless, the phenomenon of time dilation due to relative motion is a fundamental aspect of the theory of special relativity and has been confirmed by numerous experiments and observations in other contexts where relative velocities are much higher, such as in particle accelerators or space missions.