Chapter 37: Q7P (page 1145)

The premise of the Planet of the Apes movies and books is that hibernating astronauts travel far into Earth’s future, to a time when human civilization has been replaced by an ape civilization. Considering only special relativity, determine how far into Earth’s future the astronauts would travel if they slept for 120 y while traveling relative to Earth with a speed of 0.9990c, first outward from Earth and then back again?

Expert verified

The duration for future travel by astronaut is $2.683 \times 10^{3} y$ .

Step by step solution

The speed of astronauts relative to Earth is $v = 0.9990 c$

The duration of the sleep of an astronaut is $t = 120 y$

The time dilation is used to find the duration of particles before decaying from the detector.

The duration for future travel by astronaut is given as:

$∆ t = \frac{t}{\sqrt{1 - {(\frac{v}{c})}^{2}}}$

Here, is the speed of light and its value is $3 \times 10^{8} m / s$ .

Substitute all the values in equation.

$∆ t = \frac{120 y}{\sqrt{1 - {(\frac{0.9990 c}{c})}^{2}}} ∆ t = 2.683 \times 10^{3} y$

Therefore, the duration for future travel by astronaut is $2.683 \times 10^{3} y$ .

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