science of the geometric shape, orientation in space, and gravitational field of Earth

Geodesy, sometimes called geodetics, is a scientific branch of geography which accurately measures the surface of the Earth.

An old geodetic pillar (1855) at Ostend, Belgium
A Munich archive with lithography plates of maps of Bavaria

Friedrich Robert Helmert (1843–1917), who started the discipline, talked about measuring and mapping the surface of the earth. This includes its geometric description (the geoid) and the measurement and description of its gravitational field.

Some people involved in the discipline look at geodynamics, the crusts, the tides, or the movement of the geographical poles.