# PHY115: Professional Skills in Physics and Astronomy

Positional Astronomy: Session 2

Hour Angle

The hour angle of a star is a measure of it's position relative to the observer's meridian. A star on the observer's meridian has an hour angle of zero, and it increases towards the west. Since stars move from east to west, a star's hour angle increases with time. Strictly defined, the hour angle is the angle between the observer's meridian and the meridian of RA which passes through the star. Hour angle (or HA) runs from -12 to 12h. Stars with negative hour angles are yet to transit the meridian.

Sidereal Time

Since a star's HA increases with time, it follows that hour angle can be used as a definition of time. In fact, astronomers use the hour angle of the first point of Aries, HA, as a measure of time known as sidereal time. Since the location of the observer's meridian is dependent on the longitude of the observer, the hour angle of the first point of Aries is known as the local sidereal time:

LST = HA

and is zero when the first point of Aries passes the observer's meridian.

The figure on the right shows the relationship between LST, HA and RA. The meridian which passes through the first point of Aries is drawn in yellow and labelled 0h RA.

RA is measured eastwards from this point, and the star's RA is shown in white. HA is measured westwards from the observer's meridian and the star's HA is shown in yellow. Remembering that the local sidereal time is equal to the hour angle of the first point of Aries, it is clear from the figure that

LST = HAx + RAx,

where HAx and RAx are the hour angle and right ascension of the star, respectively. This relationship holds for any celestial object. Since the hour angle of an object is zero when an object crosses the observer's meridian, it follows that a star transits when the local sidereal time is equal to its right ascension. This is a very useful relationship!

Sidereal Time Explorer
The image to the right will launch another of the University of Nebraska's applets, which allows you to explore the relationship between hour angle, right ascension and sidereal time.

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