The complementary angle of polar distance in the hour angle system is ______.

In the context of the hour angle system and celestial navigation, the complementary angle of polar distance is indeed the declination of a celestial body.

To understand this, it's important to note that polar distance refers to the angular distance of a celestial object from the celestial pole. It is measured from the pole down to the object along a great circle. Thus, if we consider the celestial sphere, the declination is the angle measured from the celestial equator to the celestial object. Since a full circle is 360 degrees, the declination can be viewed as the complement of the polar distance—when added together, they sum to 90 degrees.

This relationship underlines the fundamental geometric principles of celestial mechanics, where angles defined in this manner help in predicting the positions of celestial bodies and understanding their movements relative to Earth. Consequently, recognizing the complementarity between polar distance and declination is essential for accurate celestial navigation and calculations in geodesy.