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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

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.

x2+y2=a2 (1)

Here,

a is the radius of the circle.

Consider the general equation of an ellipse.

x2a2+y2b2=1 (2)

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

x2a2+y2b2+z2c2=1 (3)

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 c=6356

(b)

To determine

To find: The shape of the curve.

(c)

To determine

To find: The shape of the curve.

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Chapter 12 Solutions

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P-38RECh-12 P-1PCh-12 P-2PCh-12 P-5P

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