What is the deflection of the vertical in geodesy?

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Diagram showing the deflection of the vertical from the geoid to the ellipsoid or spheroid, with labeled lines for geoid, spheroid, rock surface, ocean, and geoid height in a geology context. — geoid Deflection of the vertical from the geoid to the spheroid.

In geodesy, the deflection of the vertical is defined as the angle between the local direction of gravity and the normal to the ellipsoid.

Because the local direction of gravity is always normal (perpendicular) to the geoid, this deflection effectively represents the slope of the geoid relative to the reference ellipsoid. Historically, these deflections were critical in astronomical determinations of latitude and longitude, as their components introduced errors into those measurements. Furthermore, calculating these deflections was essential for connecting independent geodetic triangulation networks into a unified global system.1