Question

As you pilot your space utility vehicle at a constant speed toward the moon, a race pilot flies past you in her spaceracer at a constant speed of 0.8c (γ = 1.667) relative to you. At the instant the spaceracer passes you, both of you start your timers at zero.

a)At the instant you measure the spaceracer has traveled 1.2 × 108 m past you, what does the race pilot read on her timer?

b)When the race pilot reads the value calculated above (part a) on her timer, what does she measure to be your distance from her?

c)At the instant when the race pilot reads the value calculated above (part a) on her timer, what do you read on yours?

Answer 1

a)

The two events on your timer take place at the same place, so the interval is a proper time in your frame, of

TE = s/v = 1.2 x 10^8 / 0.8 x 3 x 10^8 = 0.5 sec

Consequently, it is a dilated time in the spaceracer’s frame, to be compared with her proper time TS .

TE = Ts = Ts / sqrt(1 - 0.8^2) = Ts / 0.6

Ts = TE*0.6 = 0.3 s

b)

She measures you to be receding at 0.8c, so when she reads 0.3 sec she knows that you are at 0.3 x 0.8 light-

seconds away = 0.24 x 3 x 10^8 = 7.2 x 10^7 m  

c)

Her interval of 0.3 s is between two events that happened in the same place in the spaceship. But you reading your

timer occurs in your frame, so you are reading a proper time corresponding to her dilated time. Consequently, you

read 0.6 times her reading, or 0.16 s.