Changing Views of Declination Circles

Where you view a three-dimensional object defines what you can observe. For example, a two-dimensional declination circle cannot capture the three-dimensional motion of the sun across the local sky without some distortion or loss of data.  Use the web app View Declination Circles to explore three common views of declination circles to identify their strengths, limitations, and applications.  Then learn how to go from one view to another.

Acknowledgments: Matti Horne’s many contributions during our brainstorming and review sessions expanded this app in new directions.

Compare Sun Position

N/S-oriented declination circles (dark gray) are created by looking eastward from a distant point in the horizon plane (green).  From this perspective, the declination circle appears to be a straight line in which its tilt from the horizon is 90º minus the degrees of latitude. This is the easiest declination circle to draw, requiring only a straight edge and a protractor.

E/W-oriented declination circles are created by looking northward from a distant point in the horizon plane.  From this perspective, the declination circle appears as an ellipse with the longest axis parallel to the horizon and the short axis in the vertical.

In the adjacent animations, compare the sun’s hourly movement when viewed with each declination circle.  Does one view completely illustrate how the Sun appears to move throughout the day?

Map-view declination circles are created by looking down from directly overhead the location, so from the zenith.  From this perspective, the declination circle appears as an ellipse with the longest axis parallel to the east/west direction and the shortest axis oriented north/south.

In addition to comparing how the Sun appears to move in all three views, notice how the sun angle and direction grids are drawn.  Since both sun angle and direction are relative to the horizon, they are drawn differently depending on how the viewer is oriented to the horizon.

As you explore the three views, create a list of the strengths, limitations, and applications.

Animations of declination circles for 30ºN on the 21st of each month when viewed on North/South and East/West-oriented declination circles.  The sun position is based on 6 AM for each circle.

Animations of declination circles for January 21 as latitude changes when viewed on North/South and East/West-oriented declination circles.  The sun position is based on 6 AM for each circle.

Four Key Sun Positions

Regardless of how we view a declination circle, four sun positions define its orientation and shape:

1) Local Noon (blue dot)

2) Local Midnight (magenta dot)

3 & 4) 6 AM and 6 PM (red dots)

Local noon occurs when the Sun is highest in the sky. Therefore, the local noon Sun is the uppermost point when viewing the declination circle from the horizon (N/S and E/W views).  

Local Noon Sun Angle (LNSA) = 90° – Latitude + Solar Declination

When LNSA > 90°, then LNSA = 180° – LNSA

Remember, Southern Hemisphere latitudes are negative: 30°S = -30°

Local midnight is the opposite of local noon, so it is the lowest point on a declination circle viewed from the horizon.  Usually, the midnight sun is below the horizon (negative sun angle) except for polar latitudes near the summer solstice.

Local Midnight Sun Angle (LMSA) = 90° – Latitude – Solar Declination

When LMSA < -90°, then LMSA = -180° – LMSA

Halfway between 12 AM and 12 PM are 6 AM and 6 PM, and they both have the same sun angle, which is equal to the average of the noon and midnight sun angles.

Go from N/S to E/W View

Since both views are from the horizon plane, the sun angle grids are identical.  Thus, the sun angles for the four key points line up vertically (see the horizontal blue, red, and magenta lines in the adjacent diagram for 30ºN on January 21). Local noon and midnight intersect the north/south line in both diagrams.  To position the 6 AM and PM positions, use the sun direction grid.  Notice that the 6 AM position is approximately 20º south of east, and the 6 PM position is 20º south of west.

Once these four points are positioned on the E/W-oriented circle, you could sketch in the ellipse or find additional points to transfer from the N/S view, such as sunrise and sunset.

Go from N/S to Map View

To visually see the connection between the two circles, consider you are viewing the N/S view from far above the zenith.  Notice that the 6 AM and PM points are halfway between the horizontal distance between local noon and midnight.  Now it is easier to transfer the sun angle and directions of the four points from the N/S view to the map view circle.  The key is that the white/light gray circles in the map view are the sun angle, which 0º the largest circle and 90º at the center.

Once these four points are positioned on the map view circle, you could sketch in the ellipse or find additional points to transfer from the N/S view, such as sunrise and sunset or the times halfway between 6 AM/PM and the corresponding noon and midnight times.