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Right Ascension and Declination Help

By — McGraw-Hill Professional
Updated on Sep 15, 2011

Right Ascension and Declination

There are two points in time every year when the Sun’s elevation, measured with respect to the center of its disk, is positive for exactly 12 hours and negative for exactly 12 hours. One of these time points, the vernal equinox , occurs on March 21, give or take about a day; the other, the autumnal equinox , occurs on September 22, give or take about a day. At the equinoxes, the Sun is exactly at the celestial equator; it rises exactly in the east and sets exactly in the west, assuming that the observer is not at either of the geographic poles.

The crude celestial maps of Fig. 1-7 show the situation at either of the equinoxes. That is, the date is on or around March 21 or September 22. You can deduce this because the Sun rises exactly in the east and sets exactly in the west, so it must be exactly at the celestial equator. At the latitude of Lake Tahoe, the Sun is 39 degrees away from the zenith (51 degrees above the southern horizon) at high noon on these days. Polaris is 39 degrees above the northern horizon all the time. The entire heavens seem to rotate counterclockwise around Polaris.

Coordinating the Heavens Right Ascension And Declination

Figure 1-7. Az/el sky maps for viewer lying flat, face-up. At A , top of head facing north; at B , top of head facing south.

The Vernal Equinox

What’s this about the Sun being above the horizon for exactly 12 hours and below the horizon for exactly 12 hours at the equinoxes? The stars in the heavens seem to revolve around Earth once every 23 hours and 56 minutes, approximately. Where do the 4 extra minutes come from?

The answer is that the Sun crosses the sky a little more slowly than the stars. Every day, the Sun moves slightly toward the east with respect to the background of stars. On March 21, the Sun is at the celestial equator and is located in a certain position with respect to the stars. This point among the stars is called, naturally enough, the vernal equinox (just as the date is called). It represents an important reference point in the system of celestial coordinates most often used by astronomers: right ascension (RA) and declination (dec). As time passes, the Sun rises about 4 minutes later each day relative to the background of stars. The sidereal (star-based) day is about 23 hours and 56 minutes long; the synodic (sun-based) day is precisely 24 hours long. We measure time with respect to the Sun, not the stars.

Declination is the same as celestial latitude, except that “north” is replaced by “positive” and “south” is replaced by “negative.” The south celestial pole is at dec = –90 degrees; the equator is at dec = 0 degrees; the north celestial pole is at dec = +90 degrees. In the drawings of Fig. 1-7, the Sun is at dec = 0 degrees. Suppose that these drawings represent the situation on March 21. This point among the stars is the zero point for right ascension (RA = 0 h). As springtime passes and the Sun follows a higher and higher course across the sky, the declination and right ascension both increase for a while. Right ascension is measured eastward along the celestial equator from the March equinox in units called hours . There are 24 hours of right ascension in a complete circle; therefore, 1 hour (written 1 h or 1 h ) of RA is equal to 15 angular degrees.

Coordinating the Heavens Right Ascension And Declination

Figure 1-7. Az/el sky maps for viewer lying flat, face-up. At A , top of head facing north; at B , top of head facing south.

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