Which statement about geodesics is true?

• A. Any meridian is a geodesic
• B. Any parallel is a geodesic
• C. Only great circles are geodesics on a sphere, not ellipsoid
• D. Geodesics do not exist on ellipsoids

Answer: (A)

Geodesics on a sphere are great circles—curves that lie along the intersection of the sphere with planes that pass through the center. A meridian, which is a line of longitude from the North Pole to the South Pole, sits in such a plane through the center. The intersection of that plane with the sphere is a great circle, so the meridian itself is a geodesic.

Parallels, or lines of latitude, lie in planes parallel to the equatorial plane and do not pass through the center, giving smaller circles. These curves have nonzero geodesic curvature and are not geodesics, except for the equator, which is a great circle.

On an ellipsoid, geodesics still exist, but they are not generally great circles. The statement that geodesics do not exist on ellipsoids is false.

Thus, any meridian is a geodesic.