A ship is traveling at .8c, and sends a message to earth to saying he's fine. 15 minutes later he realizes he made a typo and sends another message. How long does it take for the second to message to arrive at earth after the first one arrives?
The Attempt at a Solution
So my class is currently in a debate whether the correct answer is 45 minutes or 20 minutes. The teacher says it's 20 minutes. I feel like 20 minutes is the answer it takes for the light to travel from the ships final position to the final position. I feel like the 20 minute answer is failing to take into account the 15 minutes the spaceship travels in it's reference frame BEFORE it sends the signal. Isn't 20 minutes only the correct answer if the signals are sent from point A and point B simultaneously???
Any grad student out there want to crack this problem for me real quick? Is my teacher correct? We have to add 25 minutes (15*γ) to the 20 minutes it takes from the signal to cover the distance the spaceship has moved in the earths frame.