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Speed must be measured relative to something else, as must time. The rest of the universe is measured in relation to us. There isn't actually an alternative.
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so there is no way of estimating the speed of our galaxy?
I watched one video from a site which I can't remember and am not sure if it is accurate, that said that hubble saw galaxies moving faster than the speed of light, if this is true than It would be safe to assume that our galaxy and those galaxies are moving in opposite directions as faster than light speed is thought to be impossable, in which case we could calculate that our galaxy is going faster than a certain speed
note: this is speculation based on a questionable source