At some point in its solar orbit, Mars is a distance d away from Earth.
a. How long, in terms of distance d and the
b. How long would it take for a radio signal from Earth to reach the Rover telling it to stop?
c. Suppose that Mars is 144 million kilometers from Earth. Calculate the time that elapses between the moment the Mars rover sends a signal to Earth and the time the stop signal returns to the rover?
(a)
Time taken by the radio waves that are traveling from Mars to Earth.
Explanation of Solution
Introduction:
In the solar orbit, Mars is located at a distance
The distance travelled by the radio waves is
It is known that the radio wave will travel with the velocity of light,
The time taken by the radio waves to reach the Earth can be calculated as follows
This is the time taken by the radio wave to reach the Earth from Mars.
Conclusion:
The time taken by the radio wave to travel from Mars to the Earth is,
(b)
Time taken by the radio waves that are reflected from Earth to Mars.
Explanation of Solution
Introduction:
In the solar orbit, Mars is located at a distance
As the distance between Mars and the Earth is same and the velocity of the radio waves is equal to the velocity of light (
Therefore, the time by the radio wave to travel from Earth to Mars will be equal to
Conclusion:
The time taken by the radio waves to travel from the Earth to Mars is,
(c)
The time taken by the radio signal to travel from Mars to Earth and again back to the Mars.
Answer to Problem 68A
The elapsed time is,
Explanation of Solution
Given data:
The distance between Mars and the Earth,
The velocity of radio waves,
Formula:
The time taken by the radio wave to travel from Mars to Earth is calculated as follows
Calculations:
The radio waves required same time to travel from the Earth to Mars
Therefore, the elapsed time between the moment the Mars send signal to the Earth and to get the get the stop signal from earth will be equal to
Conclusion:
The elapsed time is
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