Chapter 27, Problem 68A

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 speed of light c, would it take for a radio wave sent by a video camera mounted on a Mars rover to tell people on Earth that the rover is about to go over a cliff?

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?

To determine

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 $d$ from the Earth.

The distance travelled by the radio waves is $d$

It is known that the radio wave will travel with the velocity of light, $c$

The time taken by the radio waves to reach the Earth can be calculated as follows

  $t=\frac{d}{c}$

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, $t=\frac{d}{c}$ .

To determine

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 $d$ from the Earth.

As the distance between Mars and the Earth is same and the velocity of the radio waves is equal to the velocity of light ( $c$ )

Therefore, the time by the radio wave to travel from Earth to Mars will be equal to

  $t=\frac{d}{c}$

Conclusion:

The time taken by the radio waves to travel from the Earth to Mars is, $t=\frac{d}{c}$ .

To determine

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, $T=960\text{ s}$

Explanation of Solution

Given data:

The distance between Mars and the Earth, $d=144\text{ million}=144\times {10}^6\text{km}$

The velocity of radio waves, $c=3\times {10}^8\text{ m/s}$

Formula:

The time taken by the radio wave to travel from Mars to Earth is calculated as follows

  $t=\frac{d}{c}$

Calculations:

  $\begin{array}{l}t=\frac{d}{c}\\ t=\frac{144\times {10}^6\text{ km}}{3\times {10}^8\text{ m/s}}\\ t=\frac{144\times {10}^9\text{ m}}{3\times {10}^8\text{ m/s}}\\ t=480\text{ s}\end{array}$

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

  $\begin{array}{l}T=2t\\ T=2\times 480\text{ s}\\ T=960\text{ s}\end{array}$

Conclusion:

The elapsed time is $T=960\text{ s}$ .