polar distance

Polar distance is not affected by the precession of the equinoxes.

Polar distances are expressed in degrees and cannot exceed 90 in magnitude.

This would have allowed them to measure the north polar distance (declination) a measurement that gave the position in a xiu (right ascension).

Polar distance may refer to:

Polar distance (astronomy)

The polar distance is given by a complete elliptic integral of the second kind, which may be approximated by the Thomas Muir's formula:

The advantage of a transit circle over a mural circle (which can measure polar distances) is that it allows measuring right ascension and declination at the same time.

Polar distance (geometry), more correctly called radial distance, typically denoted r, a coordinate in polar coordinate systems (r, θ)

The distance d between two points P and P with polar coordinates (r, θ) and (r, θ) is given by the polar distance formula:

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 semi-major axis of the ellipse, a, is identified as the equatorial radius of the ellipsoid: the semi-minor axis of the ellipse, b, is identified with the polar distances (from the centre).

If the polar distance of the Sun is equal to the observer's latitude, the shadow path of a gnomon's tip on a sundial will be a parabola; at higher latitudes it will be an ellipse and lower, a hyperbola.

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.

Su Song also created a celestial atlas (in five separate maps), which had the hour circles between the xiu (lunar mansions) forming the astronomical meridians, with stars marked in an equidistant cylindrical projection on each side of the equator, and thus, was in accordance to their north polar distances.