What is the relationship between geodetic and reduced latitude?

The relationship between geodetic latitude (Φ) and reduced latitude (β) is defined through a mathematical expression that accounts for the ellipsoidal shape of the Earth. In this context, the correct relationship states that the tangent of the reduced latitude is proportional to the product of the semi-minor axis and the tangent of the geodetic latitude, divided by the semi-major axis.

In the expression provided, tan β = (b/a) tan Φ, 'b' represents the semi-minor axis, and 'a' represents the semi-major axis of the Earth's ellipsoid. This relationship effectively modifies the tangent of the geodetic latitude to reflect the effects of the Earth's shape. The semi-major and semi-minor axes scale the tangent function of the geodetic latitude to yield a value for the reduced latitude, which is useful in various geodetic calculations and transformations.

It's important to understand that reduced latitude offers a different perspective on latitude measurement, adapting it for computations that involve the ellipsoidal model of Earth. Therefore, recognizing this relationship is fundamental when transitioning between these two types of latitude in geodetic computations.