What is described as an equipotential representation of the Earth's surface where gravity is always perpendicular?

The correct choice, the geoid, is defined as the equipotential surface of the Earth's gravity field, where the force of gravity is always directed perpendicular to the surface at all points. This means that if you were to imagine a surface that represents mean sea level and extends across the continents, it would conform to the variations in the gravitational field caused by the distribution of mass within the Earth, such as mountains and ocean trenches.

The geoid is essential for understanding sea level and serves as a reference point for measuring elevation and depth. It allows surveyors and geographers to derive meaningful information about the Earth's geometry and topography, taking into account the irregularities of the Earth's shape due to gravitational variations.

In contrast, the equatorial and polar radii differ, forming an ellipsoid, which is a mathematically simplified model of the Earth's shape, but it does not account for the actual gravitational variations. The gravitational field refers to the gravitational forces at play in the vicinity of the Earth, but it is not a specific representation of the surface itself. The geoidal surface is a closely related concept, but the term "geoid" specifically defines that equipotential aspect and the relationship with gravity at all points, making it the most accurate term.