What is the relationship between geocentric and reduced latitude?

The correct answer illustrates a fundamental relationship in geodesy concerning the transformation between reduced latitude and geocentric latitude. In this context, the relationship expresses how the tangent of the reduced latitude (ψ) can be derived from the tangent of the geocentric latitude (β) while incorporating the semi-major axis (a) and the semi-minor axis (b) of the reference ellipsoid.

This relationship is significant because it helps in understanding how latitudinal definitions are affected by the Earth's shape. The equation takes into account the Earth's oblateness by using the ratios of the semi-minor and semi-major axes, which are crucial for accurate geodetic calculations.

The formula tan ψ = (b/a) tan β shows that the proportion of the semi-minor axis to the semi-major axis (b/a) scales the tangent of the geocentric latitude, allowing for the conversion to reduced latitude. This conversion is essential for applications in surveying, mapping, and understanding geospatial data related to the Earth’s surface.

The other relationships presented do not accurately capture the nature of this transformation or involve incorrect variables, which could lead to misunderstandings in geodetic computations. The chosen relationship correctly identifies how the geometric qualities of the Earth's shape influence the latitude