Chapter 22, Problem 13P

(a)

To determine

Time taken by a sent message when the Earth is nearest.

Answer to Problem 13P

The answer is $4.350\min$ .

Explanation of Solution

Given info:

Mean distance of mars from sun is $227.9\times {10}^{6}km=227.0\times {10}^{9}m$

Mean distance of earth from sun is $149.6\times {10}^{6}km=149.6\times {10}^{9}m$

Factor, $c=3.00\times {10}^{8}m/s$

Formula used:

Formula to calculate time: $\Delta t=\frac{L}{c}$

Where,

  $\Delta t$ is time

  $L$ is length

  $c$ is a factor

Calculation:

Substitute the given values in formula, $\Delta t=\frac{L}{c}$

  $\Delta t=\frac{\left(227.0\times {10}^{9}m-149.6\times {10}^{9}m\right)}{3.00\times {10}^{8}m/s}$

  $\Delta t=261.0s=4.350\min$

Conclusion: The required time is $4.350\min$ .

(b)

To determine

Time taken by a sent message when the Earth is farthest.

Answer to Problem 13P

The answer is $70.1\min$ .

Explanation of Solution

Given info:

Mean distance of saturn from sun is $1427\times {10}^{6}km=1427\times {10}^{9}m$

Mean distance of earth from sun is $149.6\times {10}^{6}km=149.6\times {10}^{9}m$

Factor, $c=3.00\times {10}^{8}m/s$

Formula used:

Formula to calculate time: $\Delta t=\frac{L}{c}$

Where,

  $\Delta t$ is time

  $L$ is length

  $c$ is a factor

Calculation:

Substitute the given values in formula, $\Delta t=\frac{L}{c}$

  $\Delta t=\frac{\left(1427\times {10}^{9}m-149.6\times {10}^{9}m\right)}{3.00\times {10}^{8}m/s}$

  $\Delta t=5238s=70.1\min$

Conclusion: The required time is $70.1\min$ .