Sun Shadows: exploring the solstice and equinox

The path of the sun as it arcs through the sky shifts its position as the seasons move from winter, through spring, summer, and fall. Day length, the sun’s height in the sky, and the intensity of sunlight all change. These changes are subtle if you live on the equator, but dramatic as you approach the poles. These changes affect all life on the planet, from plants to birds, to insects and humans. You can follow or modify these lessons to track the changes with your family or class in age-appropriate lessons that integrate, mathematics, geography, and visual literacy.

I know you know this but… Do not look directly at the sun at any moment during this activity.

Activity 1: Nature Observations

Record observations throughout the day of weather and plant and animal activity. What cloud patterns do you see? What is the temperature? Are birds singing oe chirping? When did they start or end? What other seasonal observations can you make?

Activity 2: Sky Diagram

Draw a scaled 360˚ landscape before the celestial events and chart the sun’s position as it arcs across the sky. You will need a compass, a journal, and the tools necessary to estimate the altitude of the sun (see below).

  1. Mark the bottom of a page or two-page spread (preferred) with evenly spaced cardinal directions. In the northern hemisphere, the start with north, on the left side of the page, then move through east, south (in the middle of the page), west, and again to north on the right side of the page. In the southern hemisphere, start with south, on the left side of the page, then move through east, north (in the middle of the page), east, and again to south on the right side of the page.
  2. Divide the sky into nine evenly spaced horizontal strips. Label each to represent 10˚ of altitude. It is OK if your vertical scale is different from your horizontal scale.
  3. Optional (but really fun): Draw a scaled 360˚ landscape along the bottom of the page. Check the directions to prominent landmarks with a compass to make sure your drawing is to scale and features in the landscape are the proper distances from each other. If the horizontal and vertical scales are different, trees may look disproportionally skinny or tall. This is not a problem. You may estimate the height of trees and buildings around you using the methods described below (the one potato, two potato approach works well for this). Important: The compass points to magnetic north. For this exercise, you want true north. Learn how to use a compass and adjust your reading for this declination difference. You can find your declination here. Learn more about magnetic declination here.
  4. On the day of the solstice or equinox, document the sun’s direction (use the shadow of a vertical pole and your compass) and altitude (see below) throughout the day. Try to start at sunrise and follow the path of the sun through to sunset. Take multiple readings near the middle of the day. The sun’s highest point (the middle of the arc) may not be at noon like you expect!
  5. If you miss a few readings, you can look up the missing data: enter a specific time and run and a cool animation or generate a table of altitudes and azimuths throughout the day (make sure to enter your location).

Activity 3: Sun Target

Prepare a sun target and record the changes in the shadow length and direction. You will need a sun target, toothpick, glue, a compass, and a pencil. Special thanks to Shirley and David Adams for their work in developing this activity.

  1. Choose and print one of the four sun targets that is best for your location:
  2. Measure and cut a shadow stick (toothpick) to the exact length shown on the target (if you enlarge the target, the measurement on the shadow stick increases too).
  3. Glue the shadow stick in the center of the target, pointing straight up.
  4. On the day of the eclipse, orient the target to true north in a flat spot that will receive light for most of the day. Make sure you are not near metal or magnetic objects as these may affect your compass reading.
  5. Throughout the day, record the time and trace the shadows thereby recording the length and direction. The circles on the sun target give you the sun’s elevation in the sky!

How to Determine the Sun’s Direction in Degrees

  1. Find or place a vertical pole in a sunny spot (you could also use the wall of a building).
  2. Place a compass along its shadow edge and spin the housing (dial) until the floating needle is in the red open needle on the floor of the housing. Record the degree reading above the needle.
  3. Add or subtract the declination for your location. If your compass allows you to pre-set the declination, do this before alining the compass and then skip this step.

How to Estimate or Calculate the Sun’s Altitude in Degrees

One Potato, Two Potato Method (estimation)

This method is most effective when the sun is closer to the horizon and becomes less accurate as you go higher in the sky.

  1. Stand facing the sun, with your shoulders perpendicular to the direction of the sun.
  2. Keeping your shoulders square, make a fist, and extend your arm fully. Align the bottom of your fist with the horizon. The distance from the bottom to the top of your fist is about 10˚.
  3. Keeping your first fist in position, put your other fist on top of it and alternate fists as you work your way up the sky 10˚ at a time.
Shadow length (calculation)

This method is easiest when the sun is higher in the sky. When the sun is low, the shadow becomes very long and less distinct at the end.

  1. Find a place that will receive direct sunlight for most of the day. Drive a stick into flat ground and make sure it is straight-up (vertical). You can also find a vertical post such as a fence post or a volleyball pole. Measure the pole using one length form (eg. mm, cm, ft, or in instead of feet and inches, say 14 inches, not 1 foot, 2 inches)
  2. Mark the tip of the shadow with chalk or a line in the dirt. Measure the distance from the mark to the base of the pole using the same units of measurement that you used to measure the height of the pole.
  3. Imagine a triangle with one side being the post, one side the shadow on the ground, and one side the edge of the shadow in the air, extending from the tip of the shadow to the tip of the pole. We want to know the angle from the ground to the shadow edge at the far it of the shadow. This angle projects to the sun and so is the same as the angle of the sun in degrees. Now let’s use trigonometry to derive the angle of the sun. The pole length is the opposite side and the shadow length is the adjacent side of our triangle. The neumonic SOHCAHTOA reminds us to use the tangents to find the angle. Divide the pole height by the shadow length (pole/shadow or pole ÷ shadow). Then use a tangent table or a calculator to calculate the inverse tangent (arctangent or tan -1) of the quotient. The full formula is tan-1 (pole/shadow).
  4. Optional (but really fun): Instead of just marking the tip of the shadow, trace the whole shadow from its tip to the base. This looks really cool with chalk on a playground blacktop. This makes the pattern and changes easier to see.
Convert Shadow Length to Sun Angle on Any Post

Enter the height of any vertcal post and shadow length (using the same units) to calculate the sun’s altitude or angle in the sky from 0˚ (on the horizon) to 90˚ (overhead).

Post and Rope

Prepare a rope with tape markings at measured distances that represent every five degrees. Tie one end to a post and hold the rope along the post’s shadow. Use the tape markers to get the sun’s height in degrees.

  1. Establish a vertical post of known height in an area that will receive sun for most of the day. A volleyball pole on an open playground is a good choice.
  2. Tie a rope to the bottom of the post with a knot that is snug but still allows the rope to spin freely around the post.
  3. Enter the post height and each desired angle (e.g. 5, 10, 15, 20, 25…) into the calculator below to calculate the distances you need to mark on your rope to capture every 5˚ interval. The measurement units will be the same that you used to measure the post itself (e.g. meters, feet, inches).
  4. During the event, pull the rope taught along the shadow and read off the sun’s altitude from the markings on the rope.

Head Shadow and Compass

This technique allows you to get accurate angle readings without looking at the sun. You will need a compass with a mirror and a clinometer. It works best when the sun is higher in the sky. When the sun is too low, it is difficult to sight on the center of your head shadow.

  1. Spin the bezel so that east (E) lines up with the compass’ direction of travel arrow. E will be on the side with the mirror hinge and W will be toward the back of the compass.
  2. Optional: Attach a post-it to the back of the compass so that you can more easily read the clinometer against a light surface.
  3. Align the magnetic needle with east and west. Then rotate the compass sideways. The magnetic needle will stay in the same place, aligned with east and west and out of the way. The clinometer arrow will swing freely inside the compass and point down.
  4. Fold the mirror inward to about 45˚ so that you can read the clinometer in the mirror when you look through the sighting hole in the mirror.
  5. Aim the compass at the middle of your head’s shadow and read the clinometer in the mirror. This gives you the altitude of the sun. If you have a hard time seeing the midpoint of your head’s shadow through the aiming hole on the compass, move your head so that your shadow falls over a small, distinctive pebble or mark on the ground, then aim your compass at that target.