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Chapter 36: Q. 47 (page 1060)

A starship voyages to a distant planet 10lyaway. The explorers stay 1 year, return at the same speed, and arrive back on earth 26years, as measured on earth after they left. Assume that the time needed to accelerate and decelerate is negligible.

a. What is the speed of the starship?

b. How much time has elapsed on the astronauts’ chronometers?

Short Answer

Expert verified

a. the speed of the starship is v=0.8C.

b. t=16yearstime has elapsed on the astronauts’ chronometers.

Step by step solution

01

Part (a)Step 1: Given Information

We need to find the speed of the starship .

02

Part (a)step 2: Simplify

The total time taken by the spaceship in travel is26-1=25years.

The total distance covered by the spaceship is 2×10=20lightyears.

So the velocity of the ship is 20ly25ly=0.8C

Note:C=1lyly

03

Part (b) step 2: Given Information 

We need to find how much time has elapsed on the astronauts’ chronometers .

04

Part (b) step:2 Simplify

For one year the spaceship was stationary (in earth's frame of reference ) the time will be the same for that one year.

During travel, the time in the spaceship's chronometer is :

δt'=δtγ=25×1-0.8CC2=15y

So the total time that will be shown in spaceships chronometers is 15+1=16years.

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