 #1
Frostman
 115
 17
 Homework Statement:

A spaceship that is approaching the earth with an unknown speed, sends messages by communicating the time (of the spaceship) that is missing upon arrival, starting from the moment the message is sent.
In the first message, the missing time is ##T_1'##, in the second message it is ##T_2'##, and between the arrival of the two messages, a time interval ##\Delta T## elapses on earth.
1. What is the speed of the spaceship?
2. How long after (terrestrial), after the arrival of the second signal, will the starship arrive?
 Relevant Equations:
 Lorentz Transformations
I started by finding the main events:
##\Delta T## is the difference between ##T_2## and ##T_1##, measured on the earth.
We can do this table
I don't know if is it correct this scheme, and it could help me to find the speed and how soon will the spaceship arrive on earth.
 Sending the first message
 Receipt the first message
 Sending the second message
 Receipt the second message
##\Delta T## is the difference between ##T_2## and ##T_1##, measured on the earth.
We can do this table
Events  ##S'##  ##S## 
A: Sending 1  ##t_A'=0## ##x_A'=(cv)T_1'##  ##t_A=\gamma(t_A'+vx_A')=\gamma v(cv)T_1'## ##x_A=\gamma(x_A'+vT_A')=\gamma (cv)T_1'## 
B: Receipt 1  ##t_B = t_D\Delta T ##  
C: Sending 2  ##t_C'=T_2'T_1'## ##x_C'=(cv)T_2'##  ##t_C=\gamma(t_C'+vx_C')=\gamma(T_2'T_1'+v(cv)T_2')## ##x_C=\gamma(x_C'+vt_C')=\gamma((cv)T_2'+v(T_2'T_1'))## 
D: Receipt 2  ##t_D = \Delta T + t_B## 
I don't know if is it correct this scheme, and it could help me to find the speed and how soon will the spaceship arrive on earth.
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