In the meridian radius of curvature formula, the denominator is raised to which exponent?

• A. 1/2
• B. 3/2
• C. 1
• D. 2

Answer: (B)

In the meridional radius of curvature for an ellipsoid, the curvature along the north-south direction depends on latitude through a factor (1 − e^2 sin^2 φ) in the denominator. When you work through the geometry and calculus of how the meridian arc length changes with latitude, this factor ends up raised to the 3/2 power. The extra power compared to other radii of curvature comes from combining the square-root nature of the metric term with the differentiation that defines curvature, yielding (1 − e^2 sin^2 φ)^(3/2) in the denominator. Therefore, the denominator is raised to the 3/2 power.