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

Answer:

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:

$t = \frac{t_{1}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$

where

t = observed time on earth

Now,

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

Now, time required for 1.5 rev:

t = $1.5\times 4.83$ = 7.24 s