At the equator, which radius is equal to the semi-major axis length?

• A. N
• B. M
• C. a
• D. All statements are true

Answer: (A)

At the equator, the radius that matches the semi-major axis is the radius of curvature in the prime vertical. This radius is defined as N(φ) = a / sqrt(1 − e^2 sin^2 φ). At latitude φ = 0 (the equator), sin φ = 0, so N(0) = a. Since the semi-major axis a is the equatorial radius, N equals the semi-major axis length at the equator. The meridional radius M would be a(1 − e^2) at the equator (not equal to a in general), and the polar radius is b. So the radius that equals the semi-major axis at the equator is the radius of curvature in the prime vertical, N.