Astronaut Mark Uri is space-traveling from planet X to planet Y at a speed of o.

Question

Astronaut Mark Uri is space-traveling from planet X to planet Y at a speed of o.65c relative to the planets, which are at rest relative to each other. When he is precisely halfway between the planets, a distance of 1.0 light-hour from each one as measured in the planet frame, nuclear devices are detonated on both planets, The explosions are simultaneous in Mark's frame. What is the difference in the time of arrival of the flashes from the explosions as observed by Mark? 90 min 0 min 180 min 360 min 113 min

Explanation / Answer

Ans

Let us consider the stationary reference frame. In this frame, Mark is moving towards

the planet Y. Hence the 1st signal should come from it. let Mark's distance be x1 from the

central point between XY

Let t1 be the time taken for the signal from Y to rach Mark in stationary frame and it travels

a distance (1-x1) light hr.

Hence x1= 0.65C t1---(1)

and ct1= (1-x1) --(2)

from (1) & (2) we get:

t1= 1/1.65 hr=0.6060 hr ---(3)

similarly we can calculate t2. which is the time taken by light to come from planet X.

keeping in mind mark is moving away from X: we get;

x2=0.65 ct2 ---(4)

and 1+0.65 ct2=ct2 ---(5)

From (4) and (5) we get:

t2=1/0.35 hr=2.8571 hr --(6)

Hence from equ(3) and (6) we get:

the interval in stationary frame = t2-t1= (2.8571 -0.6060)= 2.2511 hr

But mark is moving with relativistic speed of 0.65 c.

hence in his frame, there will be time-dilation:

(t2-t1) X ( 1- v2/ c2) 1/2 = 1.71 hr

then

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