Has anyone looked at the relativistic effects of time that would take place with planets orbiting a star moving at such speeds? For example if the vector of the

Has anyone looked at the relativistic effects of time that would take place with planets orbiting a star moving at such speeds? For example if the vector of the stars movement lied along the same plane as the planet's orbit, the definition of a second would change with the seasons. Even if the time of day. If you look thought a telescope to observe a pulsar you'd see massive spectral and frequency shifts depending on the season! It would be interesting to know if these factors lead aliens to developing relativistic theories faster then humans. I'm just a science fiction nerd at heart, so this is instantly where my mind jumps too.