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Chapter 6: Q47P (page 1250)

A space probe is sent to the vicinity of the star Capella, which is 42.2 light-years from the earth. (A light-year is the distance light travels in a year.) The probe travels with a speed of 0.9930c . An astronaut recruit on board is 19 years old when the probe leaves the earth. What is her biological age when the probe reaches Capella?

Short Answer

Expert verified

When the probe reaches Capella, her biological age is years 24.02 .

Step by step solution

01

Given data

L=42.2cu=0.9930c

02

Define the proper time interval.

When the two events occur at the same point in a particular frame of reference, the time interval∆t0 between the two events in the frame is known as the proper time interval.

If the frame moves with constant velocity relative to second frame, the time interval between the events is observe in the second frame is longer than .

∆t=∆t01-u2/c2=γ∆t0γ=11-u2/c2

03

Determine the biological age.

Given that, the relative speed between and S' is 0.9930c , total distance L of the trip to Capella is 42.2c year.

The duration of trip is:

∆t=Lu=42.2cyr0.9930c=42.5yr

Now,

∆t0=∆t1-u2c2=42.5yr1-0.99302=5.02yr

Hence, the astronaut’s age at the end of the trip is19.0yr+5.02yr=24.02yr.

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