Question

A deep-space probe moves away from Earth with a speed of 0.51 c. An antenna on the probe requires 3.9 s (probe time) to rotate through 1.5 rev. How much time is required for 1.5 rev according to an observer on Earth? Answer in units of s.

Answer 1

Time required for 1.5 rev for an observer on earth = 7.24 s

Given:

velocity of probe, v = 0.51 c

`t_(1)` = 3.9 s

Solution:

Using Einstein's theory of relativity for time dilation:

`t = \frac{t_(1)}{\sqrt{1 - (v^(2))/(c^(2))}}`

where

t = observed time on earth

Now,

`t = \frac{3.9}{\sqrt{1 - ((0.59c)^(2))/(c^(2))}} = 4.83 s`

Now, time required for 1.5 rev:

t =
`1.5* 4.83` = 7.24 s