Special Relativity Question (for a paper)

[NotAName]

SR, Do you calculate closing speed to determine light arrival time?

Please evaluate the paragraphs below... what I'm most concerned about the very last statement. Do I integrate the "motion" of the distant object to determine the arrival time of light or is that already in the calculation?

Thanks in advance!

According to SR, a traveller going to a star .5 lightyears away at .5C takes 1 year according to the stationary frame but the traveller only records .866 as much time elapsing for a total of .866 years to arrive. The traveller believes himself to be stationary and that the distant object is approaching at .5C from a distance of .433 lightyears away.

According to SR, a beam of light traveling to that distant star would take .5 years in the stationary frame and would take .433 years in the moving frame less the movement of the distant star for a total of .2165 years according to the moving observer.

 

[NotAName]

Is this too simple of a question? I'm surprised nobody cares to answer.

 

[HallsofIvy]

It's not that it is too simple, it's just not clear what your question is. What do you mean by "integrate the motion"? What "motion" function are you talking about?

 

[NotAName]

I'm sorry, I used bad terminology. I was just asking if the transformation already included the speed of light in it and it would therefore take .433 years total for light to reach the distant point.

Or should I calculate that light should reach the distant point at an effective 1.5C because the distant point is closing on my location.

And I further confused it by fat fingering the calculation... should have been .288 not .2165 (oops!)

Thanks