system
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human
If we were to discover life on other planets, wouldn't time be moving at a completely different pace for them due to relativity?

I've thought about this a bit since my undergrad days; I have an advanced degree in math but never went beyond basic physics.

My thinking is this: The relative passage of time for an individual is dependent on its velocity, correct? So the relative speed of the passage of time here on earth is dependent on the planet's velocity around the sun, the solar system's velocity through the galaxy, the movement of the galaxy through the universe, and probably other stuff. All of these factor into the velocity at which we, as individuals, are moving through the universe and hence the speed at which we experience the passage of time.

So it seems to me that all of those factors (the planet's velocity around its star, the system's movement through the galaxy, etc.) would vary widely across the universe. And, since that is the case, an individual standing on the surface of a planet somewhere else in the galaxy would, relative to an observer on Earth at least, experience  time passing at a much different rate than we do here on Earth.

How different would it be, though? How much different would the factors I listed (motion of the galaxy, velocity of the planet's orbit, etc.) have to be in order for the relative time difference to be significant? Celestial velocities seem huge and I figure that even small variations could have significant effects, especially when compounded over millions of years.

So I guess that's it! Just something I've been thinking about off and on for several years, and I'm curious how accurate my thoughts on this topic are.

**Edit**: More precise language. And here is an example to (I hope) illustrate what I'm trying to describe.

Say we had two identical stopwatches. At the same moment, we place one stopwatch on Earth and the other on a distant planet. Then we wait. We millions or billions years. If, after that time, someone standing next to the Earth stopwatch were able to see the stopwatch that had been placed on another planet, how much of a difference could there potentially be between the two?
gpt
Celestial velocities may be huge, but at least for orbits in the galaxy they top out at hundreds of kilometers per second. Since the speed of light is about 300,000 km/s, the stars' velocities relative to us introduce only a very very very miniscule change in the passage of time. 

The amount of time dilation is proportional to the Lorentz factor, 1/sqrt(1-v^(2)/c^(2)). Even for an object traveling at 10% of the speed of light relative to us, this means that the time dilation we see for that object is only about a 0.5% change.

To clarify: in any object's own reference frame, time passes at a normal rate. It's just that when objects are moving at high speeds relative to each other, e.g. trains moving past each other, a passenger in one train will look at the clock on the other train and see it ticking slower than the clock on her own train, and vice versa. This goes both ways.