3.4 Normal gravity

The normal gravity $\gamma_{0}$ is a function of latitude. Compute $\gamma_{0}$ by this formula (Heiskanen and Moritz, 1967, p.76, eq. 2-109):

$$\gamma_{0}(\varphi) = \gamma_{a}\frac{1+\kappa \sin^2\varphi} {\sqrt{1-e^{2}\sin^{2}\varphi}} \quad \kappa=\frac{b\gamma_{b}-a\gamma_{a}}{a\gamma_{a}}$$ (15)