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Consider the celestial sphere $C$ with observer $O$.

Let $P$ and $Q$ be the north celestial pole and south celestial pole respectively.

Let $X$ be a point on $C$.

Let $PXQ$ be the vertical circle through $X$.

Let $D$ be the point where the celestial equator intersects $PXQ$.

The length of the arc $DX$ of $PXQ$ is known as the declination of $X$.


North Declination

If $X$ is in the northern celestial hemisphere, $DX$ is north declination.

South Declination

If $X$ is in the southern celestial hemisphere, $DX$ is south declination.

It is convenient to define the declination of $X$ as between $+90 \degrees$ and $-90 \degrees$, where a south declination is a negative quantity, from $0$ at the celestial equator and $-90 \degrees$ at the south celestial pole.