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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Physical Science Because of the forces caused by its rotation, Earth is an oblate ellipsoid rather than a sphere. The equatorial radius is 3963 miles and the polar radius is 3950 miles. Find an equation of the ellipsoid. (Assume that the center of Earth is at the origin and that the trace formed by the plane z = 0 corresponds to the equator.)

Chapter 7.2, Problem 49E, Physical Science Because of the forces caused by its rotation, Earth is an oblate ellipsoid rather

To determine

To calculate: The equation of oblate ellipsoid shape of the Earth where the equatorial radius and polar radius of the Earth are 3963 miles and 3950 miles respectively and the centre of the Earth is at origin and trace formed by the plane z=0 corresponds to the equator.

Explanation

Given Information:

The equatorial radius and polar radius of the Earth are 3963 miles and 3950 miles respectively and the centre of the Earth is at origin and trace formed by the plane z=0 corresponds to the equator.

Formula used:

The standard equation of oblate ellipsoid is,

x2a2+y2b2+z2c2=1

wherea,b,careinterceptonx,y,zaxisrespectively

Calculation:

The standard form of equation of an ellipsoid for centre (0,0,0) is,

x2a2+y2b2+z2c2=1

Since, the trace of the Earth formed by the plane z=0 at the equator that means the z axis of the Earth must passes through the polar of the Earth.

The intercept on the z axis is c that means c is the polar radius of the Earth.

c=3950 miles

Now, the oblate ellipsoid is a type of ellipsoid in which the two intercepts are equal

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