(a) Neil A. Armstrong was the first person to walk on the moon. The distance between the earth and the moon is . 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 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) It took 1.28 seconds to Neil Armstrong's voice to reach the Earth via radio waves.

b) The minimum time that will be required for a message from Mars to reach the Earth via radio waves is 192 seconds.

Explanation:

The electromagnetic spectrum is the distribution of radiation due to the different frequencies at which it radiates and its different intensitie. 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 can also be given in wavelengths, but it is more frequent to work with it at frequencies:

Any radiation that belongs to electromagnetic spectrum has a speed in vacuum of .  

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

To know the time that took for Neil Armstrong's voice to reach the Earth via radio waves, the following 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)

The distance from the Earth to the Moon is , therefore.

Hence, it took 1.28 seconds to Neil Armstrong's voice to reach the Earth via radio waves.

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

The distance from the Earth to the Mars at its closest approach is , therefore.

Hence, the minimum time that will be required for a message from Mars to reach the Earth via radio waves is 192 seconds.

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