Question

The premise of the Planet of the Apes movies and book is that hibernating astronauts travel far into Earth's future, to a time when human civilization has been replaced by an ape civilization.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 128 y while traveling relative to Earth with a speed of 0.9900c, first outward from Earth and then back again.

Answer 1

Answer:

907.80 y

Explanation:

Given :

The speed of the astronaut is v = 0.9900 c

The time spend by the astronaut is $t_0$ = 128 years

Therefore, the time of dilation is given by

$t=\frac{t_0}{\sqrt{1-\left(\frac{v}{c}\right)^2}}$

$t=\frac{128 \ y}{\sqrt{1-\left(\frac{0.9900 \ c}{c}\right)^2}}$

$t=\frac{128 \ y}{\sqrt{1-0.9801}}$

$t = \frac{128}{\sqrt{0.0199}}$

$t = \frac{128}{0.141}}$

$t= 907.80 \ y$