Solar Time, Angle, and Direction

Declination circles help us visualize how the Sun moves about a given location on Earth’s surface during 24 hours.  A declination circle tracks the apparent 24-hour path of the Sun around location on the surface of the rotating Earth, so we are viewing a circular path mapped onto a sphere with a radius of roughly 93 million miles.  Another way to think about a declination circle is that it represents a continuous path of Sun positions.

The Sun’s Position in the Local Sky

The sun angle and direction to the local horizon define the Sun’s position in the local sky, which is the sky viewed from a given location on Earth.  A declination circle represents the continuous position during a 24-hour period.  You can draw a declination circle when you know these two factors:

1. 1. The date, which depends on the place in Earth’s orbit around the Sun and creates the daily solar declination, and
   2. The latitude, which determines the orientation of the local horizon to Earth’s axis of rotation, and

The time of day, which is a measure of the orientation of the local horizon to the Sun, locates where the Sun will be on the declination circle, which is also defined by sun angle and direction.  

To predict and use the position of the Sun in the sky (for example, navigation, design buildings, design and install the most efficient solar technologies, etc.), we need a solid conceptual understanding of each of these components, which is where declination circles provide a visualization of the interrelationships of the five variables:

1. 1. Date,
   2. Latitude,
   3. Solar time,
   4. Sun angle, and
   5. Sun direction.

Sun Angle and Direction web app

Although earlier web apps explored one or two aspects of declination circles, this is the first app in which the five declination circle variables are explored more precisely to see how they interrelate with each other: date, latitude, solar time, and sun angle and direction.  Select the date and latitude to create a declination circle, then change the solar time to see the Sun’s position in the local sky, either with the angle and direction grid lines or with numerical output.

Several visualizations are available to help view what a location experiences throughout the day and year. 

Visualizations

• The Sun’s location on the declination circle for the selected solar time is shown as gray when below the horizon and orange when above.  During the morning hours, between midnight to noon, the declination circle is drawn through the Sun since it appears in the eastern hemisphere of the local sky.  The western portion of the declination circle is visible. Between noon and midnight, the Sun is within the western half of the horizon, so the eastern part of the declination circle is behind the Sun.
• Sun angle and direction grids are drawn every 15º.
• View the declination circles for the solstices and equinoxes, which quickly show the range of the astronomical seasons.
• 6 AM/PM positions throughout the year help visualize the midpoint of the declination circles so you can estimate the hours of daylight on any day of the year.
• See the adjacent animations to explore the visualizations of a sunbeam and sunbeams.

The first visualization of a sunbeam hitting the center of the local horizon when the sun is above the horizon shows what we experience at a given location as the sun moves throughout the day.

Mathematical Relationships

Mathematically, the function of the daily path of the Sun is equal to the function of the Sun’s current position in the sky:

Daily Path of the Sun(day, latitude, solar time) <=> Current Sun Position(angle, time)

There are five mathematically interconnected variables. If four are known, we can calculate the fifth by manipulating the formulas or drawing declination circles.  Remember, some events carry an implicit understanding of time or sun angle:

• • Sunrise or sunset: sun angle is 0°, so if we know the direction, we have a defined position in the sky.
  • Local noon and midnight: we know the solar time and the three options for the Sun’s direction (north, south, or overhead).

Finally, there is a connection between longitude, solar time, and clock time.  You can calculate your longitude if you know the clock time of the local clock time and that at the Prime Meridian (0°).  Safe navigation by mariners required accurate timekeeping on ships to calculate their longitude.  For a fascinating book about the invention of the chronometer, see Dava Sobel’s book, Longitude.