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

Geodesy, which is sometimes called geodetics, is a scientific branch of geography which deals with describing the surface of the earth. 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 discipilne look at geodynamics, the crusts, the tides, or the motion of the geographical poles.

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