Neil A. Armstrong was the first person to walk on the moon. The distance between the earth and the moon is 3.85 × 108 m. Find the time it took for his voice to reach the earth via radio waves. (b) Someday a person will walk on Mars, which is 5.60 × 1010 m from the earth at the point of closest approach. Determine the minimum time that will be required for a message from Mars to reach the earth via radio waves.

a) Find the time it took for his voice to reach the earth via radio waves.

1.28s

b) Determine the minimum time that will be required for a message from Mars to reach the earth via radio waves.

186.6s

Explanation:

The electromagnetic spectrum is the distribution of radiation due to the different frequencies at which it radiates and its different intensities. That radiation is formed by electromagnetic waves, which are transverse waves formed by an electric field and a magnetic field perpendicular to it.

The distribution of the radiation in the electromagnetic spectrum is given in frequency, in the following order from the highest to the lower frequencies:

Light propagates as electromagnetic wave in vacuum with a speed of . Therefore, radio waves will have the same speed in vacuum.

a) Find the time it took for his voice to reach the earth via radio waves.

Then, to know the time that it took for Neil A. Armstrong's voice to reach the Earth via radio waves from the Moon, the next equation can be used:

  (1)

Where v is the speed of light, d is the distance and t is the time.

Notice that t can be isolated from equation 1.

 (2)

Hence, it took 1.28 seconds for his voice to reach the Earth via radio waves from the Moon.

(b) Determine the minimum time that will be required for a message from Mars to reach the earth via radio waves.

For this part, the same approach described above will be used.

For this case,

Hence, the minimum time that will be required for a message from Mars to reach the earth via radio waves is 186.6 seconds.

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