The time taken a radio signal to travel form the given distance to Earth is [tex]2.65 \times 10^8 \ s[/tex].
The given parameters;
- distance between the astronaut and Earth, d = 9 x 10¹⁰ m
The time taken a radio signal to travel form the given distance to Earth is calculated by using Echo formula as shown below;
[tex]2d = v \times t\\\\t = \frac{2d}{v}[/tex]
where;
- v is the speed of sound sound in air = 340 m/s
- t is the time taken for the signal to be heard (to and fro)
The time taken for the signal to travel in a single forward motion is calculated as;
[tex]t = \frac{1}{2} \times \frac{2d}{v} = \frac{d}{v} \\\\t = \frac{9\times 10^{10}}{340} \\\\t = 2.65 \times 10^8 \ s[/tex]
Thus, the time taken a radio signal to travel form the given distance to Earth is [tex]2.65 \times 10^8 \ s[/tex].
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