Just like velocity is relative, the rate of a time is also relative. No matter how fast we are moving on the surface of the earth relative to the sun or the galactic center or anything else, we can consider ourselves to be stationary and the sun or the galactic center to be what's moving which means time for us is perfectly normal and it is the sun and the galactic center that has slower rates of time. Of course, the sun or the galactic center can consider themselves to be stationary and we are the one that is moving. So we will see the sun's time as being slower by one rate and the galactic center to be slower by a different rate. The faster they are moving relative to us, the slower the rate of time we will consider them to be experiencing, and vice versa, by exactly the same amount.
It's just like relative velocity, if I see you going by me at some speed, you will see me going by you at exactly the same speed. And that speed will determine the rate of time slowing down that I will observe in you and you will observe in me.