Declination Circles

The Sun is not moving (actually it is, but it is not noticeable to us), but we perceive that the Sun is moving in the sky since Earth is rotating.   We turn 15º/hour (360º / 24 hours), but we also move a little less than 1º/day in our orbit around the Sun (360º / 365.25 day).  The effect of rotation dominates the apparent motion of the Sun, but the slight change in Earth’s orbital speed (see eccentricity of our orbit) affects the length of a solar day by up to 15 minutes during a year.

Declination circles map the path of the Sun across the sky as viewed from a point on the Earth’s surface at a given latitude and day of the year.  When viewing a declination circle, imagine you are standing in the middle of the diagram – essentially in the middle of your horizon. 

Declination circles are essential to understand so we may navigate, build more energy-efficient homes and buildings, design cities, plant gardens that thrive, take photographs, film movies, etc.

Sun-Day Challenges Web App

The easiest declination circle to draw is when viewing the Sun’s motion from exactly west looking east.  The path of the Sun appears to move in a straight line, which is easy to draw with a ruler.  Use the web app, Sun-Day Challenges to learn how to interpret these declination circles to identify the date, the solar declination, and the latitude.

The app has three types of activities:

1. 1. Explore how declination circles change as you select latitude and day.
   2. Practice identifying solar declination, day, and latitude for randomly generated declination circles.  Visual and written feedback are provided with each response.
   3. Quiz mode with less guidance to see how well you understand the processes.

Conventions for Declination Circles

We will use the following conventions for all declination circles:

• The horizon is green, the sky is a pale blue, and the ground is light brown.
• Solid circles mark the hourly positions of the Sun. When the Sun is above the horizon, it is orange, and when below it is gray.
• The declination circle with the hourly positions of the Sun is gray.
• 24-hour time is used to label the hour position of the Sun.  0 = midnight, 20 = 20 – 12 = 8 PM.
• Zenith, the point directly overhead an observer, is marked with “Z.”
• To measure angles of the declination circle, a dotted circle is drawn centered about a fictitious person standing in the middle of the horizon directly beneath the zenith.  Every ten degrees is marked with a red dot.
• Sunrise and sunset occur at the location where the declination circle intersects the horizon.
• Time on the declination circle does not refer to clock time but rather the time based on the Sun’s movement.  Clock time takes into account your longitudinal location in your time zone.
• On a North-South oriented declination circle:
  • Where the declination circle touches the outer circle at its highest point is local noon, which is always 12 PM.  Local noon is when the Sun is highest in the sky.
  • Where the declination circle touches the outer circle at its lowest point is local midnight, which is always 12 AM.  Local midnight is when the Sun is lowest in the sky (even when below the horizon).

View the declination circle from the side, so it looks like a tilted straight line.  North is to the left and south to the right. This means that west points out of the drawing, and it meets the horizon directly beneath the zenith (Z). East is looking directly into the drawing.

Sunrise is exactly east and occurs at 6 AM. Sunset is precisely west at 6 PM, and there are 12 hours of daylight and 12 hours of darkness.

The Sun is located 60º above the horizon and directly south at local noon.

The Sun is located 60º below the horizon and directly north at local midnight.

Now view the declination circle from the front, so it looks like a squashed circle.  West is to the left and east to the right. This means south points out of the drawing and it meets the horizon directly beneath the zenith (Z). north is looking directly into the drawing.

Since the Earth rotates from west to east, the Sun appears to move from east to west across the sky.  Near sunrise and sunset, the Sun changes angle above the horizon more quickly than at local noon.  Near local noon, the angle above the horizon doesn’t change much, but the east to west movement is more pronounced.

Viewing the Earth illumination at sunrise on March 21, notice that the sun shines parallel to the 30ºN latitude.  This means the Sun is due east at sunrise.

Viewing the Earth illumination at local noon on March 21, the sun is 30º due south from the zenith.

Every declination circle passes through the center of all horizons during an equinox.

The declination circle is perpendicular to the horizon at the Equator during an equinox.

Except for the poles, declination circles slope toward the north in the Northern Hemisphere and south in the Southern.

During an equinox, the Sun stays in the horizon all day at the North and South Poles. The declination circles at these latitudes are parallel to the horizon.

Declination circles are parallel for a given latitude throughout the year.  How far apart they are from each other depends on the rate of change in solar declination. Near the solstices, declination changes slowly.  Near the equinoxes, it changes most quickly.

Around the summer solstice, which is June 21 for the Northern Hemisphere, more of the declination circle is above the horizon.  The local noon sun angle is also higher.  Around the winter solstice (December 21), more of the declination circle is below the horizon (shorter duration of daylight), and the Sun is lower in the sky at local noon.