Question

An astronaut takes what he measures to be a 10-min nap in a space station orbiting Earth at 8000 m/s. A signal is sent from the station to Earth at the instant he falls asleep, and a second signal is sent to Earth the instant he wakes. Part A Does an observer on Earth measure the astronaut's nap as being shorter than, longer than, or equal to 10 min? Does an observer on Earth measure the astronaut's nap as being shorter than, longer than, or equal to 10 ? a. equal b. shorter c. longer

Answer 1

Answer:

longer than

Explanation:

given,

time of nap = 10 min

speed of orbiting earth = 8000 m/s

c is the speed of light

using the equation of time dilation

$t' = \dfrac{t}{\sqrt{1-\dfrac{v^2}{c^2}}}$

now inserting all the values

$t' = \dfrac{10}{\sqrt{1-\dfrac{8000^2}{3\times 10^8)^2}}}$

$t' = \dfrac{10}{0.9999}$

t' = 10.001 s

on solving the above equation we will get a value greater than 10minutes.

hence, On earth time of nap measured will be longer than 10 min