Question

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movies and books is that hibernating astronauts travel far into Earth’s future, to a time when human civilization has been replaced by an ape civilization.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?

Short answer

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

Step-by-step solution

Identification of given data

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

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

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

Determination of duration for future travel by astronaut

The duration for future travel by astronaut is given as:

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

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

Substitute all the values in equation.

$$\begin{gathered} ∆t=\frac{120y}{\sqrt{1-{\left({\displaystyle \frac{0.9990c}{c}}\right)}^2}} \\ ∆t=2.683\times {10}^{3}y \end{gathered}$$

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