# Definition:Declination

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## Definition

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.

## Sources

- 1976: W.M. Smart:
*Textbook on Spherical Astronomy*(6th ed.) ... (previous) ... (next): Chapter $\text {II}$. The Celestial Sphere: $19$.*Declination and hour angle.*