Drawing Declination Circles

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.  You may use the desktop app, Sun-Earth Connection (download from the Software page), to draw a declination circle, but they are quite easy to draw by hand.  Even if you are away from your computer, you may calculate the positions of the Sun and shadows to navigate, estimate the time of day or day of the year, plant your first garden, design awnings for your house, decide if and where to install solar panels on your home, etc. Plus, understanding how the calculations work will help you catch mistakes while using the software.

Flattening 3D to 2D

The Sun makes a circular path around us on what we perceive to be a huge sphere surrounding us. It is challenging to draw a sphere accurately, so we are going to “flatten” it to a line make it easier to draw declination and interpret. The horizontal green line represents the horizon (what a person would see standing in a large, flat field). The vertical gray line is the zenith which is the point directly overhead a person.  In the displayed template, north is on the left and south on the right. Looking into the paper at the intersection of the horizon and zenith is east, and out of the paper is west.

Seeing Both Sides of the Declination Circle Simultaneously

The last sentence of the previous paragraph may not have jumped out at you, but it is critical to recognize that you see two directions simultaneously using any of these projections.  In the North-South projection, where north is to the left, south is to the right, zenith at the top, and the horizon the green line bisecting the circle, each point represents two directions: one into the drawing (labeled in blue) and the other extending from the drawing (labeled in purple).  And, to add to the fun, a direction may be described as degrees from one of the cardinal directions, but there are two acute angles to each intercardinal direction.

Changing Your Perspective

Declination circles show the Sun’s motion through thy local sky above the horizon, but we can view the setting from different locations.  Use the Rotate Horizon web app to explore how directions and sun angles change while viewing the scene from different angles.

Click the button to run the Rotate Horizon web app designed for desktops, laptops, and tablets.

Although you can view the animation made of the Rotate Horizon web app, running the app on your own has several advantages:

1. 1. The images will be larger.
   2. You may view any perspective as long as you like, so you may study and/or draw the images that help you most.
   3. You may save screenshots.

Suggestion: If you have set your computer screen/computer to sleep at a short time interval, you will lose what you are viewing when running the web app.  Consider changing your settings to give yourself time to work with the app as you like.

Drawing Declination Circles by Hand

The Drawing Declination Circle web app coaches you through the four basic steps to drawing a declination circle for any latitude and day of the year.  There are written and visual hints, tips, and feedback for each step, and you may set the date and latitude yourself or use the random option to challenge yourself.  

Click the button to run the Draw Declination Circles web app designed for desktops, laptops, and tablets.

Acknowledgments

Matti Horne’s insights, suggestions, and a keen eye for detail greatly improved the app during several iterations.

A plain North-South viewing template to draw declination circles.

Click on the image to download its template.

A North-South declination circle template with direction grid lines extending from the zenith to the nadir (point directly below the observer) and sun angle grid lines parallel to the horizon. Each set of grid lines is every 10º.

Drawing Three Key Declination Circles

As much as I love computers, to learn how something works, you need to try it in various ways.  The declination circle animations, illustrations, and software on this website are helpful, but to develop a much deeper understanding, try to draw and interpret declination circles created manually.  It is similar to using a calculator.  Will you become proficient in addition, subtraction, multiplication, and division if you always rely on this electronic marvel?

1) Equinox

Draw a declination circle for an equinox since these are the easiest to draw. All declination circles go through the center of the template during an equinox.

In this example, the latitude is 60ºN— all northern latitude declination circle slope toward the north.  Think of sliding down the line, and you are heading toward the hemisphere you are in.  Go the degrees latitude from the zenith toward the south and place a dot.

The declination circle intersects the ticked-marked outer circle representing two important times of the day: local noon (above the horizon) and local midnight (below the horizon).  The Sun is highest in the sky at local noon (Sun is crossing the observer’s longitude) and farthest below the horizon (or lowest in the sky if the Sun doesn’t set that day) at local midnight.  Notice that the Sun is only 30º above the horizon at local noon (90º (or zenith) – 60º = 30º) during the equinox when you are at 60ºN.

2) Summer Solstice

Draw the declination circle for the summer solstice.  Since 60ºN is in the Northern Hemisphere, the summer solstice occurs on June 21, which is the time the Sun is located “over” 23.5ºN, which is known as the Tropic of Cancer. You only need to establish two points to draw the declination circle, so go 23.5º (Earth’s obliquity) toward the north for both local noon and local midnight for the declination circle of the equinoxes (drawn during Step 1).

If drawn correctly, the new declination circle will be parallel to the first one drawn for the equinoxes. Notice that the majority of the declination circle is above the horizon, so the amount of daylight is much longer than 12 hours.  The intersection of the June 21 declination circle and the horizon is well north of east. Sunrise is north of east and sunset north of west. The Sun is well south of you at local noon.  Using the diagram, the Sun is 53.5º above the horizon at local noon (30º + 23.5º = 53.5º).

3) Winter Solstice

Draw the declination circle for the winter solstice.  Since the location is in the Northern Hemisphere, the winter solstice will occur on December 21, which is the time the Sun is located “over” the  23.5ºS or the Tropic of Capricorn. Go 23.5º toward the south for both local noon and local midnight for the declination circle of the equinoxes (drawn in Step 1).

Now the majority of the declination circle is below the horizon, so the amount of daylight is much shorter than 12 hours, and it is equal to the amount of darkness during the summer solstice.  The Sun rose well south of east and set well south of west (remember, look at the intersection of the declination circle and the horizon). The Sun was still south of you at local noon – but it is 6.5º above the horizon (30º-23.5º). 

Notice the symmetry between the winter and summer solstice declination circles. The location of sunrise and sunset for the two solstices are symmetric about east and west, respectively.  The sun rose at 53º north of east on June 21, then it rose 53º south of east on December 21. Similarly, the sunset was 53º  north of west on June 21 and 53º south of west on December 21. and The time of sunrise and sunset for the two solstices are symmetric about 6 AM and 6 PM, respectively:

6 AM – Sunrise_{Summer Solistice} = Sunrise_{Winter Solstice} – 6 AM

Sunset_{Summer Solistice} – 6 PM = 6 PM – Sunset_{Winter Solstice}

Also, the amount of daylight and nighttime for the solstices are symmetric about 12 hours, meaning the amount of daylight during June 21 equals the amount of darkness during December 21, and vice versa during June 21.

Declination Circles for Other Days of the Year

So we can draw declination circles for four days of the year, but what about the other 361 days?  You may use the circles already drawn to help bracket declination circles for different times of the year.  In drawing of the declinations circles for the 21^st of each month for 42ºN, notice that the spacing between months is not even. There is a greater change during the months around the equinox compared to around the solstices. 

To calculate the number of degrees away from the equinox declination circle, use the solar declination graph and web app. The declination for the summer solstice in the northern hemisphere is 23.5ºN or +23.5º; for the southern hemisphere, it is 23.5ºS or -23.5º. As you did when drawing the solstice, go the degrees declination from the local noon and local midnight points of the declination circle. 

Once you have drawn the declination circle for the chosen day of the year, use the information to plan your day, outing, how and when to photograph or shoot your movie, or where to plant your garden or what plants you should consider growing.