(Hint: it may help to draw a space-time diagram showing the events described in

Question

(Hint: it may help to draw a space-time diagram showing the events described in this scenario.)

The starship Enterprise leaves Starbase Q at 9:00 in the morning, according to clocks both on the ship and on the station. It then moves away from the station at a constant velocity of 0.59 c.

At 10:00 AM, the communications office on the Starbase sends a radio message to the Enterprise: "What time do your clocks read right now?" As soon as the Enterprise receives the message, they send a reply back.

At what time is their reply received at Starbase Q? Express your answer in 24-hour form, using format HH:MM. If the hour is less than 10, pad the answer with zeros; so if you think the answer is 9:35 AM, write 09:35.



What time is in the message?




For the second part, I get that the message was recieved at 12:26.
That answer is wrong :P

HELP PLEASE!!!

Explanation / Answer

Hi,

Take the stations frame of reference:
Ship leaves at 9 with 0,59c

At 10 a signal is sent with speed c .
When the signal meets the ship, the ship has travelled the same distance as the signal,
c * t = 0,59*c*1h+0,59*c*t
t = 1,439h

And it takes the same time for the signal to get back from the ship, so that makes the time at station:
10+2*1,439 = 12:52:40

The time in the message: Take ships reference frame :
Time at which signal is sent from spacestation is the 1 hour with delation of time.

t2 =t1/ , = 1/(sqrt(1-v^2/c^2))*t1 = 1,239h

The signal travels at speed of light, the distance 0,59c*1,239h and it takes it

t=0,59*1,239h =0,73h

So the total time from the liftoff to recieving the signal is 1,239h + 0,73h = 1,97h

That means the clock at the ship is 10:58

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