Two radar pulses sent from the earth at 6:00 a.m. and 8:00 a.m. one day bounce o

Question

Two radar pulses sent from the earth at 6:00 a.m. and 8:00 a.m. one day bounce off an alien spaceship and are detected on earth at 3:00 p.m. and 4:00 p.m. (but you aren't sure which reflected pulse corresponds to which emitted pulse). a) Is the spaceship moving toward earth or away? b) If the speed is constant (less than c), when will it (or did it) pass by the earth?

Answer shoud be moving at speed 1/3 towards earth and pass at midnight. Please explain why. Question also says drawing a spacetime diagram will help but I do not know how to do that.

Explanation / Answer

a) yes it is moving towards the earth with a velocity of (1/4)c, where c is the velocity of light, the reseason is that the time interval between the second signal get reduce so we can say that the distance get decrease. hence it is coming towards the earth.

B)in first case the distance is 4.5c and in second case the distance between satelite and earth is 4c,hence distance covered in 2 hour is 0.5c , let suppose the speed of setelite is v, hence

0.5c=2v

=> v=(1/4)c=0.25c

hence the time taken by the setelite to reach the earth = (4.5c)/0.25c =18 hour (from first position)

hence satelite reach earth at 6am+18=24 am means mid night

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