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Since the Sirius we see today from Earth is the Sirius of 9 years ago and the Sirius we would see on arrival would be the Sirius of 90 years from now, this means that in an elapsed time for us of 90 years we would see actually 99 years of change process. 99 years of visual history would be seen in 90 years time. So we would actually see it as a movie played in fast-forward motion, sped up by 10%. We would for example see the star moving 10% faster than what currently appears from Earth. Right?

And a related question, in an hypothetical era of space travel, if we wanted to travel to a star say 1,000 light years away (forget the speed / duration problem for a moment, say we travel at 0.2 c and we live long enough to wait for the 5,000 years journey), we would need to calculate a travel path, based on where we see the destination star today from Earth (where it was actually 1,000 years ago) and with arrival coordinates where it will be 5,000 years from now (= where it will be 6,000 years from where we see it today. I guess that we can calculate where a star will be 6,000 years ahead of the point where we see it today with quite good accuracy, but for large enough distances, would this need to predict the future motion of distant stars be a sizable problem for our hypothetical space travelers? (let alone the risk of the star or planet not being there anymore by the time we arrive :-)