Which statement is true regarding N and the semi-major axis length at the equator?

The reasoning behind why the statement regarding N and the semi-major axis length at the equator is true lies in the definitions and relationships of the terms used in geodesy.

N, or the radius of curvature in the prime vertical, is a measurement derived from the ellipsoidal shape of the Earth. Specifically, it is calculated using the semi-major axis and the eccentricity of the ellipsoid. At the equator, the semi-major axis represents the widest part of the ellipsoidal model of Earth, and N reaches its maximum value at this point. Therefore, at the equator, N indeed equals the semi-major axis length.

This relationship highlights the unique geometric properties of the Earth's ellipsoid, where the semi-major axis is the maximum distance from the center to the surface of the ellipsoid, occurring along the equatorial plane.

In contrast, the other statements reference different relationships and points on the ellipsoid which do not hold true within the framework of geodesic definitions. Thus, the verification of the relationship between N and the semi-major axis at the equator is crucial for understanding geodetic measurements and calculations.