Question

Conversations with astronauts on lunar walks had an echo that was used to estimate the distance to the Moon. The sound spoken by the person on Earth was transformed into a radio signal sent to the Moon and transformed back into sound on a speaker inside the astronaut's space suit. This sound was picked up by the microphone in the space suit (intended for the astronaut's voice) and sent back to Earth as a radio echo of sorts. If the round-trip time was , what was the approximate distance to the Moon, neglecting any delays in the electronics?

Short answer

The approximate distance to the moon is$3.9\times {10}^8\mathrm{m}$

Step-by-step solution

Definition of Concept

Distance: The distance between two points or objects.

given data

The radio signals travel at $\mathrm{v}=3\times {10}^8\mathrm{m}/\mathrm{s}$speed.

Time taken in the round trip is, t = 2.60 s

Find the approximate distance to the moon

The relationship between distance and time for a round trip can be expressed as,

2s = vt

Substituting the given data in the above expression will give,

$$\begin{gathered} 2\mathrm{s}=\mathrm{vt} \\ \mathrm{s}=\frac{(3\times {10}^8\mathrm{m}/\mathrm{s})\times (2.60\mathrm{s})}{2} \\ \mathrm{s}=3.9\times {10}^8\mathrm{m} \end{gathered}$$

Therefore, the required distance is$3.9\times {10}^8\mathrm{m}$