The colatitude angle in spherical coordinates is the angle used above.

The colatitude is useful in astronomy because it refers to the zenith distance of the celestial poles.

Stars whose declinations exceed the observer's colatitude are called circumpolar because they will never set as seen from that latitude.

If an object's declination is further south on the celestial sphere than the value of the colatitude, then it will never be seen from that location.

A general state has colatitude θ and azimuth φ determined by the coefficients and .

The polar angle may be called colatitude, zenith angle, normal angle, or inclination angle.

Therefore, along a north-south arc path (which equals 0 ), the primary quadrant form of latitude equals the transverse colatitude's at a given point.

However, as seen above, frame-dragging occurs about every rotating mass and at every radius r and colatitude θ, not only within the ergosphere.

Moreover, the angular coordinates are exactly the usual polar spherical angular coordinates: is sometimes called the colatitude and is usually called the longitude.

Adding the declination of a star to the observer's colatitude gives the maximum latitude of that star (its angle from the horizon at culmination or upper transit).

In spherical coordinates, colatitude is the complementary angle of the latitude, i.e. the difference between 90 and the latitude, where southern latitudes are denoted with a minus sign.

In a more sophisticated model, the auroral oval between about 15 and 20 colatitude (again simulated by a coaxial auroral zone), as a transition zone between the field reversal, has been taken into account.

The difference between the circle reading after observing a star and the reading corresponding to the zenith was the zenith distance of the star, and this plus the colatitude was the north polar distance.

The z-axis of the body-fixed frame has after these two rotations the longitudinal angle (commonly designated by ) and the colatitude angle (commonly designated by ), both with respect to the space-fixed frame.

Here is called a spherical harmonic function of degree ℓ and order m, is an associated Legendre polynomial, N is a normalization constant, and θ and φ represent colatitude and longitude, respectively.

This metric is equivalent to a co-rotating reference frame that is rotating with angular speed Ω that depends on both the radius r and the colatitude θ, where Ω is called the Killing horizon.

To determine absolute declinations or polar distances, it was necessary to determine the observatory's colatitude, or distance of the celestial pole from the zenith, by observing the upper and lower culmination of a number of circumpolar stars.

Since the gnomon's style is aligned with the Earth's rotation axis, it points true North and its angle with the horizontal equals the sundial's geographical latitude; consequently, its angle with the vertical face of the dial equals the colatitude, or 90 -latitude.

Due to the cosθ term in the square root, this outer surface resembles a flattened sphere that touches the inner surface at the poles of the rotation axis, where the colatitude θ equals 0 or π; the space between these two surfaces is called the ergosphere.