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movies and book is that hibernating astronauts travel far into Earth's future, to a time when human civilization has been replaced by an ape civilization.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

907.80 y

Step-by-step 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

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

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

`$t=(128 \ y)/(√(1-0.9801))$`

`$t = (128)/(√(0.0199))$`

`$t = (128)/(0.141)}$`

`$t= 907.80 \ y$`