The radius of curvature in the meridian M is equal to which expression?

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Multiple Choice

The radius of curvature in the meridian M is equal to which expression?

The radius of curvature in the meridian is the curvature of the ellipsoid taken along a north–south profile, i.e., in a plane that contains the polar axis. For an ellipsoid of revolution with semi-major axis a and eccentricity e, this meridional radius at geographic latitude φ is M = a(1 − e^2) / [1 − e^2 sin^2 φ]^(3/2). The factor in the denominator raised to the 3/2 reflects how the curvature changes with latitude due to the ellipsoid’s flattening; as you move toward higher latitudes, the curvature along the meridian adjusts accordingly, which the 3/2 power captures correctly. This form also matches known checks: at the equator (φ = 0) M = b^2/a, and at the poles (φ = 90°) M = a^2/b, illustrating the impact of flattening on meridional curvature.

The radius of curvature in the meridian is the curvature of the ellipsoid taken along a north–south profile, i.e., in a plane that contains the polar axis. For an ellipsoid of revolution with semi-major axis a and eccentricity e, this meridional radius at geographic latitude φ is

M = a(1 − e^2) / [1 − e^2 sin^2 φ]^(3/2).

The factor in the denominator raised to the 3/2 reflects how the curvature changes with latitude due to the ellipsoid’s flattening; as you move toward higher latitudes, the curvature along the meridian adjusts accordingly, which the 3/2 power captures correctly. This form also matches known checks: at the equator (φ = 0) M = b^2/a, and at the poles (φ = 90°) M = a^2/b, illustrating the impact of flattening on meridional curvature.

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