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Why is the direction of gravity perpendicular to the geoid at every location?
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geoid
Deflection of the vertical from the geoid to the spheroid.
The direction of gravity is perpendicular to the geoid because the geoid is defined as an equipotential surface of Earth's gravitational field.12
By definition, an equipotential surface is one where the potential function—which accounts for both the gravitational attraction of Earth's mass and the centrifugal force resulting from its rotation—remains constant across its entire extent. In physics, the force of gravity acts as the gradient of this potential field. Because the potential is constant along the surface of the geoid, there is no component of gravitational force acting tangentially to it; consequently, the net force of gravity must act entirely in the direction normal, or perpendicular, to that surface at every point.21