Science Buddies: "Ask an Expert"

So I was considering time dilation particularly how as we approach the speed of light time slows down and I thought of a simple and confusing thought. If we imagine ourselves to be on a space ship just taken off from earth, we would assume that if we accelerate in any direction in space time will slow down for us. However, if the earth is already moving through space around the sun and the sun is moveing through space around the galaxy and so on, that would mean that we are already moving through space and thus our time is already slower than if we were stationary in space. So, in the space ship, if we were to accelerate in the opposite direction to that which we are already travelling through space, would time speed up for us until we reach a velocity of absolute zero? I’m
Sure there’s a simple principle which I’m missing I’m just curious

Hi,
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Willey