Which of the following correctly defines the relationship between geocentric and geodetic latitude?

The relationship between geocentric latitude, usually denoted as ψ, and geodetic latitude, denoted as Φ, is fundamentally represented by the formula tan ψ = (b²/a²) tan Φ. This equation arises from the geometric definitions of these two types of latitude and their relationship to the Earth's dimensions.

In this formula, 'a' represents the semi-major axis of the Earth (the equatorial radius), while 'b' represents the semi-minor axis of the Earth (the polar radius). The use of the ratio of the squares of these axes is critical because it acknowledges how the spheroidal shape of the Earth affects the way we measure latitude.

Geodetic latitude is based on an ellipsoidal model of the Earth, while geocentric latitude is based on a spherical model. As such, this relationship accounts for the flattening of the Earth at the poles, characterized by the difference in length between the semi-major and semi-minor axes.

Understanding this relationship is essential for converting between these two types of latitude, which is vital for various applications in geodesy, cartography, and navigation. Implementing the correct mathematical transformation allows for accurate calculations and representations of geographic positions on the Earth's surface.