Question

There is a vertical and a horizontal component of

the centrifugal force. The horizontal component points into the negative y direction. However, this force is not explicitly present in the vector momentum equation: Dv/Dt = (−1/ρ) ∇p +v∇^2(v)−gk. The Earth's shape has adapted to this horizontal component of the centrifugal force and is therefore characterized by a slight oval shape instead of a perfect spherical shape. When including both components of the centrifugal force vector in our assessments the gravity vector no longer points to the center of the perfect sphere (like the gravitational force vector). Now, an angle between the two vectors g* vector and g vector exists.

A. Derive an equation for the enclosed angle a between the gravitational force and gravity force vectors at the surface of the earth as a function of latitude. Assume the radius of the Earth 'a' is constant (which ignores the oval shape in your calculation).