When Will We Arrive? Calculating Time Differences in Special Relativity

[Robin64]

Homework Statement

:
You are the first astronaut aboard a ship to travel to Alpha Centauri. Coincidentally, a scientist working on an outer space station post is one of your former classmate. Your ship, with your former classmate onboard, leaves the space station traveling at constant velocity v on its way to Alpha Centauri, a distance d away from the space station. You and your former classmate devise a clever plan to celebrate your arrival at Alpha Centauri exactly when scientists at the space station observe, through their telescope, your ship arriving at Alpha Centauri. To do this, you have to calculate the time according to the clock on the spaceship and the time at according to the clock at the space station.
[/B]

Homework Equations

t'=γt, L'=L/γ[/B]

The Attempt at a Solution

: as seen by the astronauts on Alpha Centari, the time elapsed in the space station frame from when they started their trip to when they saw the scientists on the space observe their arrival is: (d/v)/γ +2d/c where 2d/c is the time it takes the signal of the astronauts arrival to reach the space station plus the time it take the signal of the space station observing that arrival to reach the astronauts at Alpha Centari. From here, I'm stumped.[/B]

 

[mfb]

plus the time it take the signal of the space station observing that arrival to reach the astronauts at Alpha Centari.

I don't think you are supposed to add that. You celebrate when the space station crew sees the event, not when you see the crew seeing it.

The astronauts change their reference frame in between. It is easier to calculate everything as seen by the space station.

 

[Robin64]

That still means that d/c has to be added as that's the time it takes for the space station crew to receive the signal of the astronaut's arrival, right?

 

[mfb]

Sure.