### 3.3. Equatorial coordinates

The vast majority of objects in the sky, such as distant galaxies, are fixed relative to each other, for all practical purposes. We call this reference frame the sidereal reference frame.

By convention, coordinates in this reference frame are specified relative to the earth's plane of rotation. The celestial equator is the line around the celestial sphere that is directly overhead if you are standing on the earth's equator. So sidereal coordinates are also called equatorial coordinates. It takes two numbers to specify a location in the sidereal frame.

• The declination is the angle relative to the celestial equator. Positive angles are north of the equator.

• The right ascension is the angle relative to a reference point called the first point of Aries. The right ascension increases toward the east.

Right ascension is in units of hours, where an hour is defined as 15 degrees. Therefore, the right ascension of an object in celestial coordinates is in the half-open interval [0,24).

Below are some other important terms defined relative to sidereal positions.

#### 3.3.1. First point of Aries

This point is the origin of the equatorial coordinate system. It corresponds to right ascension zero, declination zero. It lies at the intersection of the plane of the earth's rotation with the plane of the earth's orbit around the Sun.

#### 3.3.2. Vernal equinox

Another name for the first point of Aries.

#### 3.3.3. The celestial poles

If we project the axis of the earth's rotation into the sky, the north and south celestial poles are the points where that axis intersects the sky.

Celestial objects appear to move in circles centered on these points. The north celestial pole has a declination of +π/2, and the south celestial pole is at declination -π/2.

#### 3.3.4. The meridian

From a given observer's position, the meridian is the line in the sky that passes through azimuth zero (north), the zenith (altitude 90°), and azimuth 180° (south).

#### 3.3.5. Transit

Transit is defined as the time at which an object at a given right ascension crosses the meridian.

#### 3.3.6. Hour angle

For a given celestial position, its hour angle is zero when that position transits the meridian. As that position moves from east to west in the sky, the hour angle increases at a rate of about 15° per hour until it wraps around from 2π to zero at its next transit.

#### 3.3.7. Sidereal time

Sidereal time is defined as the hour angle of the first point of Aries. Essentially, it describes a specific position of the sky relative to the earth.

Local sidereal time (LST) is the sidereal time for a given observer's position on the earth. Whenever the sidereal time is the same, the sky will look the same from that position.

Greenwich sidereal time (GST) is the sidereal time at longitude 0°.

Because the year is not an exact multiple of the earth's rotational period, the sidereal day is about four minutes shorter than 24 hours. Therefore, the sidereal times during the last four minutes before midnight duplicate that same range of sidereal times at the beginning of the day.