What term defines the shape that the surface of the oceans would take under Earth's gravitation and rotation?

The term that defines the shape the surface of the oceans would take under Earth's gravitation and rotation is known as the geoid. This concept represents the hypothetical shape of Earth, reflecting mean sea level and the gravitational field's effects. In essence, the geoid is a natural outcome of the balance between gravitational forces and centrifugal forces due to Earth's rotation, illustrating how these forces shape ocean surfaces in the absence of other influences like wind and tides.

The geoid is particularly significant in geodesy and surveying, where it serves as a reference for measuring elevations and depths on the Earth's surface. By providing a more accurate representation of sea level compared to a simple geometric shape, understanding the geoid is crucial for various applications, including navigation, mapping, and understanding ocean circulation patterns.

The other terms listed do not pertain to the shape of ocean surfaces influenced by gravitational and rotational forces. A hectare is a unit of area used primarily in land measurement. The angle of repose refers to the steepest angle at which loose material can remain stable. Spherical excess relates to the geometry of spherical triangles and is not relevant to ocean surfaces.