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Chapter 6: Q4E (page 1247)

A spaceship flies past Mars with a speed of 0.985c relative to the surface of the planet. When the spaceship is directly overhead, a signal light on the Martian surface blinks on and then off. An observer on Mars measures that the signal light was on for 75.0 碌 s. (a) Does the observer on Mars or the pilot on the spaceship measure the proper time? (b) What is the duration of the light pulse measured by the pilot of the spaceship?

Short Answer

Expert verified

(a) The proper time is the time measured by the observer on the surface of Mars. B) The duration of the light pulse is434.6渭蝉

Step by step solution

01

Concept of the time dilation equation.

The time dilation equation is given as螖t=纬螖t0/1-u2/c2where, 鈭�tis the duration of light pulse measured by the pilot of the spaceship (second frame of reference), u is the speed of the spaceship (second frame) relative to the rest frame (surface of planet Mars).

02

Concept of the proper time of mars and observer

The signal light blinked on the Martian surface, which is the same frame of reference of the observer at rest (rest frame). Thus, the time of the observer is the proper time鈭�t0

03

Calculate the duration of the light pulse

Apply the time dilation equation we have,

鈭�t=纬鈭�t0位=11-p2=11-u2c2

鈭�t=11-0.985c2c2脳75=434.6渭s

Therefore, the duration of the light pulse is434.6渭s

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