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Geodetic latitude is used in mapping and navigation. It's the angle
between the equatorial plane and a line that passes through the point of
interest and is normal (perpendicular) to the ellipsoid. It's also the
declination at which the normal intersects the celestial sphere. E.g.,
at 40 degrees north latitude, +40 degrees declination is at your zenith.
This is why celestial sight reduction can use spherical trig and ignore
the ellipsoidal shape of Earth. In principle, the computation is done on
the celestial sphere.

Strictly speaking, there something else to consider: the deflection of
the vertical. Since Earth is not homogenous, its gravity field is
slightly irregular. A vertical referenced to gravity will therefore not
exactly coincide with the ellipsoidal normal through the same point.
Observations based on a gravity vertical give astronomic (not geodetic)
latitude and longitude. The discrepancy is normally just a few seconds
and is insignificant compared to other errors in a sextant observation.

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