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Problem 49 Hard Difficulty

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?

Answer

a) $\frac{\left(x^{2}\right)}{6378.137^{2}}+\frac{\left(y^{2}\right)}{6378.137^{2}}+\frac{\left(z^{2}\right)}{6356.532^{2}}=1$
b) circles
c) ellipses

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Video Transcript

So what we see at this problem is the Ellipse Lloyd Center at the origin. Um, it's going to look like this general form. So if the polls are on the Z axis, then see is going to equal 6356 523 and the equator is on the XY plane, so we can use that A is equal to be, which is equal to 6378.137 kilometers. So using that knowledge, we now have all the values that we can plug in here. So now that we have that this would be the final form in standard form of our ellipse oId centered at the origin, Um and this is how we would model it.