Question

A space explorer travels from planet α to planet µ at a speed of 0.37 c. When she is precisely halfway between

the planets, a distance of 1 light-week from each in the planets’ frame, nuclear devices are detonated on

each planet. The explosions are simultaneous in the frame of the planets. What is the difference in time of

arrival of the flashes from the explosions as observed by the space explorer?

Answer 1

The traveler will measure a time of

$$\Delta t=t\bigg(\Delta t+\frac{v\Delta x}{c^2}\bigg),$$

where

$$\Delta t=0,\\ \Delta x=1\text{ light week}\cdot c\\ t=\frac{1}{\sqrt{1-0.37^2}}=1.0764\text{ week}.$$

Therefore:

$$\Delta t'=1.0764\bigg(\frac{0.37c\cdot1\cdot c}{c^2}\bigg)=0.398\text{ week, or } 240850\text{ s}.$$