Distinguish between an ellipsoid and the geoid.

• A. Ellipsoid is a smooth mathematical surface; geoid is an undulating surface of equal gravitational potential approximating mean sea level.
• B. Ellipsoid is the actual Earth's surface; geoid is the spherical smooth approximation.
• C. Ellipsoid is used for gravity modeling; geoid defines tectonic boundaries.
• D. Ellipsoid equals mean sea level; geoid equals sea surface.

Answer: (A)

The main idea here is that two surfaces serve different roles in describing Earth’s shape. An ellipsoid is a smooth mathematical surface of revolution chosen as a simple, regular reference shape for coordinates and map projections. It’s designed for practicality and has a neat, well-defined geometry. The geoid, by contrast, is a physical surface defined by gravity: it is the locus of points sharing the same gravitational potential, which effectively corresponds to mean sea level extended through the continents. Because the gravity field varies with Earth’s mass distribution, the geoid undulates rather than being perfectly smooth—points can lie hundreds of meters above or below the ellipsoid.

This distinction is why the statement is best: the ellipsoid is a smooth mathematical surface, while the geoid is an undulating surface of equal gravitational potential approximating mean sea level. In practice, we use the ellipsoid as a horizontal reference for positioning, and the geoid as a vertical reference (a height datum) that relates to mean sea level.