Chapter 12.6, Problem 49E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Traditionally, the earth’s surface has been modeled as a sphere, but the World Geodetic System of 1984 (WGS-84) uses an ellipsoid as a more accurate model. It places the center of the earth at the origin and the north pole on the positive *z*-axis. The distance from the center to the poles is 6356.523 km and the distance to a point on the equator is 6378.137 km.

(a) Find an equation of the earth's surface as used by WGS-84.

(b) Curves of equal latitude are traces in the planes *z* = *k*. What is the shape of these curves?

(c) Meridians (curves of equal longitude) are traces in planes of the form *y* = *mx*. What is the shape of these meridians?

(a)

To determine

**To find**: An equation of the earth’s surface as used by WGS-84.

Explanation

**Given data:**

The distance from the center to the poles is 6356.523 km, distance to a point on the equator is 6378.137 km.

**Formula used:**

Consider the general equation of a circle.

Here,

*a* is the radius of the circle.

Consider the general equation of an ellipse.

Consider the general equation of an ellipsoid centered at the origin.

Here,

*a* is the intersection point on *x*-axis,

*b* is the intersection point on *y*-axis, and

*c* is the intersection point on *z*-axis.

Since North Pole placed on *z*-axis and earth is at the origin, the distance to a point on the equator is the intersection point on *z*-axis that is

(b)

To determine

**To find**: The shape of the curve.

(c)

To determine

**To find**: The shape of the curve.

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