Chapter 12.7, Problem 14PPS

a.

To determine

Find out whether the longitude lines are great circles. Explain.

Answer to Problem 14PPS

Yes, the lines of the longitude form great circles.

Explanation of Solution

Given:

It is given in the question that the lines of latitude and longitude are used to describe positions on the Earth’s surface. By convention, ;ines of longitude divide Earth vertically, while lines of latitude divide it horizontally.

  

Concept Used:

In this, use the concept of observing the figures and find the conditions.

Calculation:

Here, It is seen in the figure, in order for figure to be a lines of longitude to be a great circle. It means that it must go through the poles of the sphere. Here the longitude lines do go through the poles

So, the lines are great circles in spherical geometry.

Conclusion:

The line of longitude are great circle.

b.

To determine

Find out whether the latitude lines are great circles. Explain.

Answer to Problem 14PPS

No, The lines of the latitude is not in a spherical Geometry.

Explanation of Solution

Given:

It is given in the question that the lines of latitude and longitude are used to describe positions on the Earth’s surface. By convention, ;ines of longitude divide Earth vertically, while lines of latitude divide it horizontally.

  

Concept Used:

In this, use the concept of observing the figures and find the conditions.

Calculation:

Here, It is seen in the figure, in order for figure to be a lines of latitude to be a great circle. It means that it must go through the poles of the sphere. Here the latitude lines do not go through the poles

So, the lines of the latitude are not great circles in spherical geometry.

Conclusion:

The lines of the latitude is not in the spherical geometry.