## Encyclopedia > Polar distance

Article Content

# Polar distance

Polar distance (PD) is an astronomical term associated with the celestial equatorial coordinate system Σ(α, δ) and it is an angular distance of a celestial object on its meridian measured from the celestial pole, similar as declination (dec, δ) is measured from the celestial equator:

PD = 90° ± δ .

Polar distance are expressed in degrees and cannot exceed 90° in magnitude. An object on the celestial equator has a PD of 90°.

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

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.

In geometry a polar distance, typically denoted r is a coordinate in polar coordinate systems (r, θ) and (r, θ, h).

The distance d between two points P1 and P2 with their polar coordinates (r1, θ1) and (r2, θ2) in two dimensional circular polar coordinate system is given by the polar distance formula:

$d = \sqrt{r_{1}^{2} + r_{2}^{2} - 2 r_{1} r_{2} \cos (\theta_{1} - \theta_{2})}$.

Polar distance is used also in botany in classification of pollens.

All Wikipedia text is available under the terms of the GNU Free Documentation License

Search Encyclopedia
 Search over one million articles, find something about almost anything!

Featured Article
 Reformed churches ... to one another by a similar Calvinist system of doctrine. Each of the nations in which the Reformed movement was established has its own church government and most hav ...