A, on Earth, signals with a flash light every 6 min. B is on a space station that is stationary with respect to Earth. C is on a rocket travelling from A to B with constant velocity of 0.6c relative to A; as shown in the figure. (a) We have to calculate the time intervals between the signals emitted by A as they are received by B and C. (b) If C flashes a light every time a flash is received from A, we have to find the time interval between the flashes emitted by C as received by B.
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Solution: Click For PDF Version Space station B is stationary with respect to the observer A on Earth. An observer C is on a rocket that is travelling with speed 0.6c relative to A.From A flash light signals are emitted every six minutes which travel to the space ship along the line of sight from A to B. As B is stationary with respect to A, the time interval between the pulses received at B will also be six minutes. We calculate the time interval, T, as measured by A between the signals as they reach the observer on the rocket.
In the frame
of reference of S let the co-ordinates be indicated by the pair
The
coordinates of the event when the next flash signal is emitted at A
after a lapse of
As
This time interval as measured in the moving reference frame of C will be given by the Lorentz time dilatation relation. In C’s clock the interval T will be measured to be
(c) If C flashes a light every time a light flash is received from A, the situation is equivalent to absence of C. Therefore, the time interval between the light flashes as these arrive at B, which is stationary with respect to A, will also be 6 min.
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,
where
is the distance from A
on the line of sight. Let the co-ordinate of the event when a signal
is emitted by A be
and that of this event when this signal reaches C
be
will be
.
Let the observer A
note that this signal in his frame of reference is received by C
at time
.
Therefore, the coordinates of the event when the second signal
reaches C will be
.
As we are considering light signals
,
we find
