Me and My Shadow
- Mills Brothers

Most days, Solar Time is slightly different from Standard Time (up to 16 min. fast or 14 min. slow). This time difference is known as the Equation of Time.

Due to the geometry of equatorial sundials, the gnomon shadow is the same length for the entire day (although its length varies from day-to-day according to the annual cycle of change in the declination of the Sun).

Therefore, the longitude of Washington, D.C. is 77°W. Simple, huh? Well, it wasn't always so easy! Read The Illustrated Longitude, the story of clockmaker John Harrison, who solved the problem that Newton and Galileo failed to conquer--how to determine longitude at sea. See also, Lost at Sea--the Search for Longitude from PBS/NOVA Online.

Long story short, sundials must be corrected for longitude (as well as the Equation of Time) so that Solar Time reads the same as Standard Time.

30 JUL 2002 Today's sunspot number is 304 / Sunspot No. Trend (past 24 hours) / Increasing -- Steady \ Decreasing Credits: Real-time image courtesy SOHO; sunspot number courtesy NOAA. Updated: 29 JUL 2002 ARCHIVES

The Moon, especially the Full Moon, is bright enough to cast shadows at night. So, how bright does an astronomical object have to be to cast shadows? Good question! In fact, the question may be impossible to answer, since there are so many factors involved. However it is possible to quantify the brightness or magnitude of a light source. Oddly, negative magnitudes are brighter than positive ones. The Sky & Telescope magnitude Web page lists the following magnitudes for the Sun, Moon, brightest planet, and brightest star (in the night sky):

• Sun = -26.7m
• Full Moon = -12.5m
• Venus = -4.4m
• Sirius = -1.5m

"Night is a shadow world. The only shadows we see at night are cast by the moonlight, or by artificial light, but night itself is a shadow."
- Soul of the Sky, an essay by Diane Ackerman

The Analemma

Ever notice the odd-looking figure eight that appears on many globes? It's called an analemma. Visit the Analemma Web site to learn more about, well, analemmas, including an explanation of how the analemma is derived from the stake you drove into the ground.

See Dennis di Cicco's award-winning time lapse photograph of the Sun (showing the analemma). See also Building an Analemma Curve, courtesy the Analemma Society. Construct an indoor analemma; construct an outdoor analemma. Calculate and chart an analemma for any location at any time of day.

A graph of the analemma for Washington, D.C. shows the Equation of Time (Offset of the Sun) corrected for the eight-minute solar time difference between Washington, D.C. (77°W) and 75°W--the Standard Time Meridian for the Eastern Time Zone. Can you tell when the maximum & minimum altitude of the midday Sun occurs during the year?

Close examination of an almanac reveals that the latest sunrise and earliest sunset do not occur--as one would expect--on the December Solstice (on average, 21 DEC), the day with the fewest hours of daylight in the Northern Hemisphere. As it turns out, the earliest sunsets occur in early December and the latest sunrises occur in early January. [A similar situation occurs before/after the June Solstice (on average, 21 JUN).] A puzzling mystery easily solved by the analemma! For details, see Why the earliest sunset, latest sunrise, and shortest day of the year occur on different dates.

Sun Calculators

Explore the daily and annual cycles of change in the apparent path of the Sun across the sky. Great Circle Studio's Solar Calculator will calculate the Sun's altitude and azimuth for a user-specified location, date & time, and data interval. A variety of output modes are available. Use this information to predict how the length of your shadow would change daily and annually (at the same time each day). Verify your predictions using the SCSA Shadow Length Calculator.

How can you determine the height of objects too tall to measure directly? Using shadows, of course! Use the SCSA Object Height Calculator to calculate the height of tall shadow-casters, e.g., buildings, flagpoles, utility poles, trees, etc.

Using user-specified times of sunrise and sunset, the SCSA Daylight Calculator calculates the number of hours of daylight, also known as the Duration of Insolation (Incoming Solar Radiation).

The Solar Noon Calendar calculates tables showing either the exact time of Solar Noon for your location for each day of the year, or the Standard Time Correction (the amount you have to add to, or to subtract from, solar time on your sundial to get the time shown on your wristwatch).

The NASA J-Track Web page shows where on Earth the Sun is currently directly overhead (see small Sun icon, correctly oriented with respect to latitude and longitude).

You Can Make a Sundial!

Tell time using shadows! Use the SCSA Pole-to-Dial Converter-Calculator to convert any vertical pole (e.g., a flagpole, utility pole, etc.) into a fully functional reduced horizontal sundial featuring declination lines ("date curves") for the equinoxes and solstices. Use the SCSA Object Height Calculator to calculate the height of tall shadow-casting poles, e.g., flagpoles, utility poles, etc.

As its name suggests, the You Can Make a Sundial! Web site generates sundials for a user-specified location. Several types of sundials are available in a variety of output formats (GIF, PDF, and EPS). Start by making a customized horizontal sundial similar to the "Sandburg Sundial," a ready-to-use horizontal sundial available for downloading in two file formats (some assembly required):

• Lower Resolution - dial.gif (16k) plus gnomon.gif (7k)
• Higher Resolution - sandburg_sundial.pdf (54k)
  [Download free Adobe Acrobat Reader.]
• Enhanced Sandburg Sundial (29k) - featuring arcs showing apparent solar altitude from 10-70 degrees above the horizon, courtesy sundialist Robert "Shadow Master" Hough [Note: The "dot" that appears along the upper edge of the gnomon (technically known as the style) is called the nodus. Determine the solar altitude by observing where the nodus shadow falls among the arcs on the dial face (mnemonic: notice the nodus).]
Print sundial templates using cover stock. For directions regarding set-up and use, visit the How to Set Up & Use a Horizontal Sundial Web page. For reference, visit the North American Sundial Society Horizontal Sundial Glossary.

Experiment with several other interesting types of sundials (designed for 39°N latitude):

• Combination Analemmatic-Horizontal Sundial - Unlike other types of sundials that must be carefully oriented before they will work properly, the combination analemmatic-horizontal sundial is self-orienting. How it works: Assemble the horizontal sundial (lower dial). Place the combination sundial on a horizontal surface. Using the analemmatic sundial (upper dial), stick a vertical pin in today's date along the date scale (vertical line, center of dial). [Note that pin placement is more precise on the first day of each month (and the equinoxes).] Keep the paper horizontal and turn it until the two sundials display the same time--both sundials are now properly oriented and the compass rose indicates true direction. That's cool--a combination sundial-Sun compass! Why it works: The analemmatic sundial measures time with respect to the azimuth of the Sun; the horizontal sundial measures time with respect to the distance of the Sun from the meridian.
• Analemmatic Sundial - A relatively uncommon type of sundial (derived from the equatorial sundial), the analemmatic sundial features a gnomon that moves throughout the year. See the Analemmatic Sundials Web page for numerous examples of analemmatic sundials located around the world.
• Equatorial Sundial (assembly instructions) - The foundation of all gnomonics, the art and science of sundials. From an educator's point of view, the equatorial sundial is by far the best type of sundial for teaching a wide range of fundamental concepts in astronomy, geography, and mathematics. See the SCSA Educator's Guide to Equatorial Sundials for background information and suggested teaching strategies.
See also, FCPS Equatorial Sundial template (featuring a compass rose for orienting the sundial and a chart for the Equation of Time).

You Can Construct a Sundial!

The preceding section features a variety of ready-made, ready-to-assemble sundials--little if any prerequisite knowledge is necessary to begin sundialing. Sooner or later, you'll want to know what makes a sundial tick (pun intended)--at that point in time, you are ready to construct a sundial from scratch. The following information resources should help to get you started.

Two highly recommended books from Dover Publications, Inc.: Sundials: Their Construction and Use, by R. Newton Mayall, Margaret W. Mayall, ©2000; and Sundials: Their Theory and Construction, by Albert Edmund Waugh, ©1973. Similar content; complementary coverage. Both books use the graphic (or geometric) method of sundial construction--a simple, non-mathematical approach to constructing sundials. In a word, these two books are a "must-have" for the novice sundialist.

The first step in designing a sundial is to determine your exact location (latitude and longitude):

• Use a relatively inexpensive Global Positioning System (GPS) receiver, such as the Garmin 12, eMap, or eTrex Vista.
• U.S. Naval Observatory Complete Sun and Moon Data for One Day Web page: Use Form A - U.S. Cities or Towns; select State or Territory; enter City or Town Name; click "Get data"; among other useful information (especially the time of "Sun transit"), the database returns the location name and its longitude & latitude.

Start simple. Your first homemade sundial should be either a horizontal sundial or an equatorial sundial. Before you start [tips from the North American Sundial Society (NASS)]....

1. Horizontal Sundial - Four methods for determining the hour lines on the dial face, including the graphic method of horizontal sundial construction, as well as three methods for calculating the hour lines (in order of difficulty):
   1. Graphic (or Geometric) Method of Construction: Make Your Own Horizontal Sundial, courtesy Paul R. Field, member, NASS.
      [Note: The horizontal sundial is derived from the equatorial sundial. See Figures 4-6.]
   2. Horizontal Sundial Hour Line Calculator: Calculates hour, half-hour, and quarter-hour lines for a user-specified latitude. Special thanks to Peter Daykin, Derbyshire Sundials, for this time-saving calculator! Use an FCC utility to convert from either deg/min/sec to decimal degrees, or decimal degrees to deg/min/sec.
   3. Microsoft® Excel Spreadsheet: Horizontal_Dial.xls, courtesy Dr. Robert L. Kellogg, Treasurer, NASS. Enter your latitude & longitude. In order to calculate the longitudinal offset of your location from the Standard Time Meridian (STM) in your time zone, enter the longitude of the STM and your longitude (again). Enter "yes/no" in response to query, "Correct for longitude?" Enter size of dial (radius, in centimeters). Note results in columns labeled "Time (hh.mm)" and "Dial Angle (degrees)."
   4. Mathematical Calculation (of Hour Lines): Five simple sundial projects for you to make, courtesy Sundials on the Internet. See Project 2 - A horizontal sundial. Check your answers using either the hour line calculator or horizontal dial spreadsheet. See also Basic Trigonometry, courtesy NASS.
      [Note: Project 3 provides further proof that the horizontal sundial is derived from the equatorial sundial. See Steps 3 & 6.]
2. Equatorial Sundial - The thickness of the gnomon determines the way in which the hour lines are drawn on the two dial faces: hour lines are spaced exactly 15 degrees apart and radiate from either the exact center of the dial face or tangentially from a small inner circle representing the diameter of the gnomon (for details, see Telling Time Using Shadows, Educator's Guide to Equatorial Sundials). Use the SCSA Equatorial Sundial Gnomon Length Calculator to calculate the length of the upper & lower segment of the gnomon.

Horizontal Sundials and the Earth's Rotation

The rotation of the Earth around its axis causes a daily cycle in the Sun's apparent path across the sky that can be observed indirectly using a horizontal sundial.

In the northern mid-latitudes, the Sun rises in an easterly direction, arches across the southern sky, and sets in a westerly direction. Facing south, the Sun rises on your left and sets on your right. Sun shadows fall in the opposite direction as the Sun. Therefore, morning times are located on the right (or western) side of the dial plate of a horizontal sundial (shown upper left); afternoon times are located on the left (or eastern) side. Because the Earth rotates counterclockwise (as viewed from above the Northern Hemisphere), shadows cast by the Sun move in a clockwise direction. See a six-hour time lapse movie that shows the clockwise motion of the gnomon shadow around the dial face of a horizontal sundial from roughly 6 a.m. to 12 noon: sundial.avi (1.02 MB); sundial.mov (1.01 MB). [Time-lapse movie courtesy Film & Video Stock Shots.]

Equatorial Sundials and the Earth's Revolution

Although horizontal sundials are more familiar to most people (due to the fact that horizontal sundials are by far the most common type of sundial), experience has shown that an equatorial sundial is better suited for making the connection between the Earth's rotation and solar time-keeping (see Are You Clock-wise? sidebar, left), as well as the connection between the Earth's revolution around the Sun and the annual cycle of change in the Sun's apparent path across the sky.

The subsolar point is the point on the Earth's surface at which the Sun is at the zenith at local solar noon. On any given day, the subsolar point moves east-west along a single line of latitude as the Earth rotates counterclockwise. The latitude of the subsolar point varies between zero degrees (0°) at the equinoxes and ±23.5° at the solstices. The latitude of the subsolar point varies directly with the declination of the Sun. The analemma--the odd-looking figure eight that appears on many globes--neatly traces the annual north-south migration of the subsolar point (caused by the tilt of the Earth's axis of rotation and the revolution of the Earth around the Sun).

Theoretically, the gnomon (or style) of a properly oriented equatorial sundial will not cast a shadow on the dial plate during the equinoxes. Because the dial plate of an equatorial sundial is parallel to the Earth's Equator, the Sun is directly over the edge of the dial plate on the equinoxes, when the subsolar point moves east-west along the Equator. From the March Equinox to the September Equinox, when the subsolar point is located in the Northern Hemisphere (between 0° and 23.5°N latitude), the gnomon shadow falls on the upper dial face; from the September Equinox to the March Equinox, when the subsolar point is located in the Southern Hemisphere (between 0° and 23.5°S latitude), the gnomon shadow falls on the lower dial face (see example).

Put a little theory into practice--assemble a simple equatorial sundial [courtesy StarDate Online and the University of Texas McDonald Observatory/SCOPE (Southwestern Consortium of Observatories for Public Education)] and empirically observe where the gnomon shadow falls as the seasons change. Gain valuable insight by checking the NASA J-Track Web page to see where on Earth the Sun is currently directly overhead (see small Sun icon, which is correctly oriented with respect to latitude and longitude). Related activity: calculate & chart a projection of the analemma.

Light & Shadow - Suggested Activities for Grade K-12

• Just Me and My Shadow - Kids create crazy creatures with shadows and a little sunshine. From Sesame Street Parents.
• Smithsonian Astrophysical Observatory Everyday Classroom Tools, featuring K-2, 2-4, and 4-6 threads for each activity:
  1. Hello, Sun!
  2. You Light Up My Life
  3. Me and My Shadow
  4. This is a Stickup! (sundials)
• From the National Science Teachers Association, Astronomy with a Stick - Daytime Astronomy for Elementary and Middle School Students
• SCSA Educator's Guide to Equatorial Sundials - Background information and suggested teaching strategies
, including the SCSA Equatorial Sundial Activity:
1. The Sandburg Planetarium Equatorial Sundial template (print using cover stock) - Designed for use with a pencil-sized gnomon, approximately 1/4" (7 mm) in diameter.
2. Assembly instructions (courtesy John Hoy)
3. Equatorial Sundial Activity Questions - Provide differentiated instruction by assigning multiple choice questions only, as appropriate. [Teacher's Answer Key available upon request.]
• From NASA Liftoff to Space Exploration, a set of sundial Web pages (upper elementary, middle school):
  1. Sundials
  2. How Sundials Work
  3. Building a Simple [Equatorial] Sundial
  4. Pondering Sundials
• From StarDate Online and the University of Texas McDonald Observatory/SCOPE (Southwestern Consortium of Observatories for Public Education), the SCOPE solar poster educational activities and resources, including:
  1. Equatorial Sundial Activity, two versions: HTML; PDF
  2. Dial Face Template (print using cover stock)
• Bill Nye the Science Guy Earth's Seasons video, Disney Educational Productions, No. 68A93VL00 - Entertaining demonstrations showing the reasons for the seasons. The program includes a brief segment (entitled "Try This") featuring a home-made horizontal sundial--the "Cardboard Sundial of Science"--that provides a fast-paced introduction to several fundamental concepts in sundialing, including the clockwise rotation of the gnomon shadow, style angle versus latitude (the style should be parallel to the Earth's axis), the noon line, and hour lines. The segment ends with a broadbrush introduction to the Equation of Time (EoT).
  [Editorial Commentary: The program script does not refer to the phenomenon as the EoT, rather it simply points out the observed difference between Solar Time and Standard Time ("noon won't quite stay noon; 9 in the morning won't quite stay 9 in the morning"). The program fails to mention the fact that the time difference could be caused, in part, by a difference in longitude between the location of the observer and the Standard Time Meridian. The complex topic of correcting Solar Time for Standard Time is perhaps better covered by the classroom teacher rather than Bill Nye's "MTV" presentation style.]
• Tracing the Analemma
  1. SCSA Calculate and Chart the Analemma - A year-long projection of the Sun's image on a horizontal surface. (See also Related Resources.)
  2. From the Smithsonian Institution, Eyes on the Sky, Feet on the Ground - Hands-On Astronomy Activities for Kids. See Chapter Two - The Earth's Orbit, Activity 2-4: The Analemma (constructing a ceiling analemma).
  3. Two interrelated activities from Paper Plate Education: Sub-Solar Cup; and Analemma Project.

Me and My Shadow - A Rule-of-Thumb for Safe Sun Exposure

The Sun is a star that radiates energy at all wavelengths of the electromagnetic spectrum; some wavelengths of solar radiation are hazardous to plants and animals. Visit the EPA Stay Healthy in the Sun Web site for information about the health risks posed by ultraviolet (UV) radiation, as well as the steps people can take to protect themselves from overexposure to the Sun.

An easy way to tell how much ultraviolet (UV) radiation exposure you are getting is to look for your shadow:

• If your shadow is taller than you are (in the early morning and late afternoon), then your UV exposure is likely to be low.
• If your shadow is shorter than you are (around midday), then you are being exposed to high levels of UV radiation. Seek shade and protect your skin and eyes.

The Ultraviolet Index (UV Index) overview includes a link to EPA's new SunWise School Program regarding Sun safety. The National Oceanic and Atmospheric Administration (NOAA) produces a daily UV Index U.S. map (showing predicted exposure levels).

Sunspots and the Solar Cycle

What is "The Solar Cycle?" In a regular cycle, the Sun undergoes a period of great activity called the "solar maximum" (predicted to occur during 2000-2001), followed by a period of quiet called the "solar minimum." One way scientists track solar activity is by observing sunspots. Sunspots are relatively cool areas that appear as dark blemishes on the face of the Sun. During solar maximum there are many sunspots; during solar minimum there are few. See sidebar (left) for today's sunspot number.

For more information about sunspots, Solar Maximum, and the Sun-Earth Connection, visit the SCSA Themes Web page. For classroom teachers, a couple of suggested sunspot-related activities...

• Happy Birthday Sunspot Plot - Sunspots and the Solar Cycle (Grade Level 4-8) [Teacher's Answer Key available upon request.]
• Estimating the Size of Sunspots - Use the Internet to safely observe & measure sunspots [Teacher's Answer Key available upon request.]

Sun-Earth Day, Astronomy Week/Day, Sky Awareness Week, and Space Day

Plan to celebrate Sun-Earth Day--a national celebration of the Sun, the space around the Earth (geospace), and how all of it affects life on our planet--on 20 March 2002. Its theme is: "Celebrate the Equinox and the Seasons." Celebrate Astronomy Week/Day: Astronomy Week is April 15-21, 2002; Astronomy Day is Saturday, April 20th. Celebrate National Sky Awareness Week (NSAW), April 21-27, 2002. Its theme is: "THE SKY - Where Meteorology Meets the Heavens and the Earth."

Locally, the Sandburg Planetarium will host two special events:

• "Astronomy Day at Huntley Meadows Park," Saturday, 20 April 2002. (Rain Date: Sunday, 28 April 2002.)
• "Sun-Earth-Moon Day" on Mon., 06 May 2002, from 8:30 a.m. 'til 2:40 p.m. (Rain Date: Tue., 07 May.) The event is timed to coincide as closely as possible with Space Day (Thu., 02 May) and the Last Quarter Moon (Sat., 04 May). Amateur astronomers from the Maryland Sidewalk Astronomers (MSA), National Capital Astronomers (NCA), Northern Virginia Astronomy Club (NOVAC), and Shenandoah Astronomical Society (SAS) have volunteered to be our guides for a day of sundialing, safe sunspot observing, and Moon-watching.