An interstellar space probe is launched from Earth. After a brief period of acce

Question

An interstellar space probe is launched from Earth. After a brief period of acceleration it moves with a constant velocity, 77.0% of the speed of light. Its nuclear powered batteries supply the energy to keep its data transmitter active continuously. The batteries have a lifetime of 15.4 years as measured in a rest frame. (a) How long do the batteries on the space probe last as measured by mission control on Earth? (b) How far is the probe from Earth when its batteries fail, as measured by mission control? (c) How far is the probe from Earth, as measured by its built-in trip odometer; when its batteries fail? (d) For what total time after launch is data received from the probe by mission control? Note that radio waves travel at the speed of light and fill the space between the probe and Earth at the yr ly ly time the battery fails yr

Explanation / Answer

a) t' = t/sqrt(1-(v/c*v/c))

= 15.4/sqrt(1-0.77*0.77)

t' = 24.14 years

b) 0.77*c*24.14 year

= 18.58 light years

c) 0.77*c*15.4

= 11.86 light years

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