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movies and book is that hibernating astronauts travel far into Earth's future, to a time when human civilization has been replaced by an ape civilization.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

Respuesta :

Answer:

907.80 y

Explanation:

Given :

The speed of the astronaut is v = 0.9900 c

The time spend by the astronaut is [tex]$t_0 $[/tex] = 128 years

Therefore, the time of dilation is given by

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

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

[tex]$t=\frac{128 \ y}{\sqrt{1-0.9801}}$[/tex]

[tex]$t = \frac{128}{\sqrt{0.0199}}$[/tex]

[tex]$t = \frac{128}{0.141}}$[/tex]

[tex]$t= 907.80 \ y$[/tex]

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