A space probe is sent to the vicinity of the star Capella, which is 42.2 light-y

Question

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 0.9800 c relative to the earth. An astronaut recruit on board is 19 years old when the probe leaves the earth.

A.) What is her biological age when the probe reaches Capella, as measured by the astronaut?

Express your answer in years to three significant figures.

B.) What is her biological age when the probe reaches Capella, as measured by someone on earth?

Express your answer in years to three significant figures.

Explanation / Answer

= 1/sqrt[1-(v/c)^2] =1/sqrt[1-(0.98)^2] = 5.023

B)Earth time = t0 = d/v = 42.2ly/0.98c = 43.06 yr

Her biological age when the probe reaches Capella, as measured by someone on earth = 19yr + 43.06 yr = 62.06yr

B) spaceship time = t= t0/ = 43.06/5.023 = 8.57yr

Her biological age when the probe reaches Capella, as measured by astronaut = 19yr + 8.57 yr = 27.57yr

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