Question

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 1

The WGS-84 model of the earth's surface is represented by an ellipsoid equation. Curves of equal latitude are circles on the ellipsoid, with smaller circles near the poles and larger circles near the equator. Meridians (curves of equal longitude) on the ellipsoid are ellipses with varying eccentricity.

Step-by-step explanation:

A) Finding the equation of the earth's surface as used by WGS-84:

The equation of the earth's surface as used by WGS-84 can be represented as an ellipsoid with the center at the origin (0,0,0). The equation is:

x²/a² + y²/a²+ z²/b²= 1

where 'a' is the distance from the center of the earth to a point on the equator (6378.137 km) and 'b' is the distance from the center of the earth to the poles (6356.523 km).

B) Shape of curves of equal latitude:

Curves of equal latitude, which are traces in the planes z = k, will be circles on the ellipsoid. These circles will be smaller near the poles and larger near the equator.

C) Shape of meridians (curves of equal longitude):

Meridians are traces in planes of the form y = mx. On the ellipsoid, these meridians will be ellipses with varying eccentricity based on the value of m.

Answer 2

Answer: You are smart, figure it out yourself

Step-by-step explanation: