system
Given the following post, respond as if you're commenting on Reddit:
human
You have a stopwatch on Earth, and one in the center of the Milky Way, and you start them at the same time. In 10 years, what would be the time difference between the two stopwatches?

We have to adjust the clocks on satellites to account for their speed in relation to us. We must be moving very fast across the ecliptic of the Milky Way, in relation to the center. I wonder how much the difference in time will be.
gpt
Part of the reason clocks on satellites don't experience the same rate of time passage is due to gravitational time dilation.  The clock closer to the source of gravitation moves more slowly than a clock farther from that source.

That said, motion is also a factor.  The speed of the solar system relative to the center of the Milky Way is about 220 km/s, which is only .073% of the speed of light, so the Lorentz factor is still pretty close to 1.  The actual value is about 1.000000269, meaning we experience time at a rate that is 0.000027% slower than that at the center of the galaxy.

This equates to a little more than 2 hours and 21 minutes per 1000 years.

Edit: Just saw "10 years" in the title.  Over 10 years, our stopwatch would only experience about 85 seconds less time than the stopwatch in the Milky Way center.