Right Ascension and Declination Help (page 3)
Right Ascension and Declination
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.
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.
The Sun’s Annual “Lap”
As the days pass during the springtime, the Sun stays above the horizon for more and more of each day, and it follows a progressively higher course across the sky. The change is rapid during the early springtime and becomes more gradual with approach of the summer solstice , which takes place on June 22, give or take about a day.
At the summer solstice, the Sun has reached its northernmost declination point, approximately dec = +23.5 degrees. The Sun has made one-quarter of a complete circuit around its annual “lap” among the stars and sits at RA = 6 h. This situation is shown in Fig. 1-8 using the same two az/el coordinate schemes as those in Fig. 1-7. The gray line represents the Sun’s course across the sky. As in Fig. 1-7, the time of day is midafternoon. The observer’s geographic latitude is the same too: 39°N.
After the summer solstice, the Sun’s declination begins to decrease, slowly at first and then faster and faster. By late September, the autumnal equinox is reached, and the Sun is once again at the celestial equator, just as it was at the vernal equinox. Now, however, instead of moving from south to north, the Sun is moving from north to south in celestial latitude. At the autumnal equinox, the Sun’s RA is 12 h. This corresponds to 180 degrees.
Now it is the fall season in the northern hemisphere, and the days are growing short. The Sun stays above the horizon for less and less of each day, and it follows a progressively lower course across the sky. The change is rapid during the early fall and becomes slower and slower with approach of the winter solstice , which takes place on December 21, give or take about a day.
At the winter solstice, the Sun’s declination is at its southernmost point, approximately dec = –23.5 degrees. The Sun has made three-quarters of a complete circuit around its annual “lap” among the stars and sits at RA = 18 h. This is shown in Fig. 1-9 using the same two az/el coordinate schemes as those in Figs. 1-7 and 1-8. The gray line represents the Sun’s course across the sky. As in Figs. 1-7 and 1-8, the time of day is midafternoon. The observer hasn’t moved either, at least in terms of geographic latitude; this point is still at 39°N. (Maybe the observer is in Baltimore now or in the Azores. Winter at Lake Tahoe can be rough unless you like to ski.)
After the winter solstice, the Sun’s declination begins to increase gradually and then, as the weeks pass, faster and faster. By late March, the Sun reaches the vernal equinox again and crosses the celestial equator on its way to warming up the northern hemisphere for another spring and summer. The “lap” is complete. The Sun’s complete circuit around the heavens takes about 365 solar days plus 6 hours and is the commonly accepted length of the year in the modern calendar. In terms of the stars, there is one extra “day” because the Sun has passed from west to east against the far reaches of space by a full circle.
The path that the Sun follows against the background of stars during the year is a slanted celestial circle called the ecliptic . Imagine Earth’s orbit around the Sun; it is an ellipse (not quite a perfect circle, as we will later learn), and it lies in a flat geometric plane. This plane, called the plane of the ecliptic , is tilted by 23.5 degrees relative to the plane defined by Earth’s equator. If the plane of the ecliptic were made visible somehow, it would look like a thin gray line through the heavens that passes through the celestial equator at the equinoxes, reaching a northerly peak at the June solstice and a southerly peak at the December solstice. If you’ve ever been in a planetarium, you’ve seen the ecliptic projected in that artificial sky, complete with RA numbers proceeding from right to left from the vernal equinox.
Suppose that you convert the celestial latitude and longitude coordinate system to a Mercator projection, similar to those distorted maps of the world in which all the parallels and meridians show up as straight lines. The ecliptic would look like a sine wave on such a map, with a peak at +23.5 degrees (the summer solstice), a trough at –23.5 degrees (the winter solstice), and two nodes (one at each equinox). This is shown in Fig. 1-10. From this graph, you can see that the number of hours of daylight, and the course of the Sun across the sky, changes rapidly in March, April, September, and October and slowly in June, July, December, and January. Have you noticed this before and thought it was only your imagination?
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