A planet's orbit, rotation, and shape create its diurnal heating pattern, seasons, and climate regimes. To understand how the Earth is heated from the Sun's radiation, we need to explore time and space in a variety of scales and perspectives since viewing a moving, rotating sphere cannot be accomplished from one vantage point.

Declination circles map the path of the Sun across the sky for a given latitude and time of year. These are essential to understand, create, and use to navigate, build more energy efficient homes and buildings, plant gardens that thrive, take photographs, film movies, design cities, etc. Since this is such a visual process, interactive software will be used, but there are ways to work on paper that help you better understand the concepts. Try these after you explore the software available below.

Articles

Solar Radiation and Earth's Energy Budget and Earth's Radiation Budget

Suggested Time: 60 min.

Screenshot from the Sun-Earth Connection software showing the path of the Sun for Nov 18 at 34ºN.

Described in the Earth's Coordinate System activities.

If you do this activity, compare the results from the Sundial Application in the Sun-Earth Connection software. Examine how the trace of the sundial's shadow changes throughout the year - rather amazing!

I have run this sundial activity for classes and Earth Day celebrations for the past 15 years, and I generally had the same shape for the trace of the shadows throughout the day. As I wrote the software, Sun-Earth Connection, I realized I was always using sundials on the summer-side of the equinoxes (April and September), which explained why I had similar shadow patterns each time but the software showed me that there is a huge change of shape during the year. Talk about realizing how mind grooving inhibited me from thinking more deeply (see the Learning Experiments to explore mind grooving).

Suggested Time: About 2 hours of total time building, making measurements periodically (each takes 2-5 minutes), and taking down.

Using a tall gnomon (in this case a vertical pole) allows you to realize how quickly shadows move!

Sun-Earth Connection explores how the Earth's orbit, rotation, and shape create the seasons, night-day heating patterns, and climate regimes for any latitude on Earth and for any date of the year. There are also explorations of how we apply these patterns of illumination as a clock, compass, and calendar.

Suggested Time: 2 to 3 60-minute blocks to explore, complete challenges, and think about the big ideas. Closer to 3 hours total if make drawings and take detailed notes.

Acknowledgements

A special thank you to the beta testers of version 1-0. Their insightful comments, meticulous attention to detail, and creative ideas improved the software greatly!

Denise Alfonso, Lincoln Berkley, Elliot Blume-Pickle, Xiomara Contreras, Allison Culbert, Wilder Daniel, Carolina Diez, Mason Glidden, Alan Gould, Hyowon (Raphi) Kang, Becca Kranz, Audrey Lin, Mike Pappas, Kiley Remiszewski, and Corey Rost.

Click to see the features of the software before deciding to download the program.

Mac users: Download the zipped dmg file. Uncompress and double click on the dmg file. Drag the folder that pops up to the application folder on your computer.

Windows users: Select the location you want to put the files before uncompressing everything in the zip file.

View how the illumination of the Earth changes as it orbits the Sun. Change perspective to see what happens in the northern and southern hemisphere during the year.

Explore how the illumination at sunrise, local noon and sunset; hours of daylight; sun angle above the horizon at local noon; and total daily solar energy hitting the ground change at different locations throughout the year.

In addition to explaining Earth's seasons, climate regimes, and diurnal heating patterns, humans have used the apparent motion of the Sun in the sky to navigate and keep track of time and day of the year.

Compare how different latitudes are affected by the Sun's illumination throughout the year.

Use your understanding of the Sun's apparent motion to design awnings that will work at different latitudes to keep the summer sunlight from entering windows while allowing winter sunlight to enter and warm the room for free.

Explore shadows throughout the year to understand sun dials and how to design gardens and more energy efficient buildings.

In addition to key terms used in this topic, four illustrated step by step guides on creating and interpreting declination circles are available below. These are very useful when used with the software.

Suggested Time: 60-90 min for Using Declination Circles.

60 min for Calculating Time with Declination Circles (if comfortable with Geometry/Trigonometry)

60 min for Declination Circles of Any Planet

Nicky Longo and Isabelle Stromberg created an experiment to see how well awnings would work to cool a classroom at Concord Academy, Concord, MA. They found that the room shaded by the awning was significantly cooler than the nearby rooms without awnings. Surfaces in the room without awnings were up to 30ºF hotter than for the surfaces in the shaded room.

Although challenges are part of the software, these will test if you understand the concepts without relying on the software. Check your answers using the software.

The trigonometry primer is useful for the math challenges that follow.

Suggested Time: 20-30 min for Declination Circle Challenges 1

30-45 min for Declination Circle Challenges 2

60 min for Sun-Earth Connection Questions

30-60 min for Trig Primer

- Using a spreadsheet program (Excel, Numbers, or Sheets), create a graph of a circle where the intersection of the x and y axes is at the center of the circle. You may pick the radius.
- Using this circle as the path of the Sun for 24 hours, add dots to the circle where the hour position of the Sun is. The intersection of the circle with the positive y-axis is local noon, where it crosses the positive x-axis is 6 AM, and so forth. Have the program label each point so you know you are correct.
- Draw a vertical line that represents looking at a declination circle from the side, then place and label markers for the hourly position of the Sun. The top of the line will be local noon, the bottom will be local midnight, and the midpoint will be 6 AM and 6 PM. The length of the line is equal to the diameter of the circles you created in #1 and #2, and the line goes through the origin of your graph. On the North/South view of the declination circle using the Sun-Earth Connection software, this would represent a declination circle for the equator during either of the equinoxes.
- Do the same for a line with a slope of 45° that goes through the origin of your graph. This would represent a declination circle for 45°N during either of the equinoxes.
- Finally, using your experiences from above, draw a declination circle for 45°N at December 21 and mark and label the hourly positions of the Sun.
- (This would be a final project in a trig class) Draw the ellipse of the declination circle created in #5 when using the East/West view. Mark and label the hourly positions. Tip: draw the ellipse for #4 first since this is easier and will help you practice working with ellipses.
- Using the spreadsheet program, create awning calculations similar to those in the Applications tab of the Sun-Earth Connection software.
- If you have progressed in trigonometry to identify the equation of a trig function from its graph, find the equations of the sine function and a cosine function for the Daily Solar Declination graph found on the 'Daily Trends' tab of the Sun-Earth Connection software (use the popup menu in the upper right). Use the date slider to gather helpful data. Note that because the Earth's orbit is slightly elliptical, this graph isn't a perfect sine or cosine function, but it is quite close for this challenge.

Suggested Time for the Math Challenges: Highly variable since depends on how comfortable you are with spreadsheet software, the concepts of declination circles, and algebra and trigonometry.

Tree roots in light snow.