What is the formula for the radius of curvature in the meridian (M)?

The formula for the radius of curvature in the meridian (M) is derived from the geometry of an ellipsoid, which represents the shape of the Earth. In this context, the radius of curvature in the meridian is the distance from the center of the Earth to a point on the surface at a given latitude (Φ). This radius takes into account the flattening of the Earth, which is captured by the eccentricity (e) of the ellipse.

The correct formula, which can be expressed as a function of the semi-major axis (a) and the eccentricity (e) of the ellipsoid, is:

[ M = \frac{a(1 - e^2)}{(1 - e^2 \sin^2 \Phi)^{3/2}} ]

This formula indicates that the radius of curvature in the meridian is affected by both the latitude and the shape of the Earth. Specifically, the term ( (1 - e^2 \sin^2 \Phi)^{3/2} ) in the denominator reflects how the radius of curvature decreases as you move towards the poles due to the Earth's oblateness.

The choice indicating ( a(1-e^2)/(1-e^2\sin