Right ascension

Definition

Let $u$ be a direction on the celestial sphere other than the two celestial poles. The hour circle of $u$ is the half great circle from the north celestial pole through $u$ to the south celestial pole. The right ascension $\alpha$ of $u$ is the angle along the celestial equator from the March equinox to the hour circle of $u$ , measured eastward. It is the longitude of $u$ in the equatorial coordinate system, and it takes values in $[0^{\mathrm h}, 24^{\mathrm h})$ .

Remarks

The conversion is $1^{\mathrm h} = 15^\circ$ , $1^{\mathrm m} = 15'$ and $1^{\mathrm s} = 15''$ , where the minutes and seconds are of time. Example: the unit vector $(0, 1, 0)$ of the equatorial frame lies on the equator a quarter turn east of the equinox, so its right ascension is $6^{\mathrm h}$ . Non-example: the angle measured westward from the observer's meridian is the hour angle, not the right ascension; it depends on the time and the place. The right ascension of the Sun is $0^{\mathrm h}$ at the March equinox and grows by about $4$ minutes of time per day.

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Equatorial coordinate system concept
Right ascension definition

Tag	`45C7C349TK`
URI	`m2://45C7C349TK`
Kind	definition
Writing	W0 stub
MSC	85A04
Defines	Right ascension
Uses	Equatorial coordinate system
Changed	3 November 2026

Right ascension

Definition

Remarks

Reading path

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