Simple science activities when visiting the dial

Go to: Project homepage Lookup today's solar noon time at the USNO Revised 2/2/20076

• Set your watch to an accurate time: To do many of the activities listed here, you will need a watch set to an accurate time. Use the United States Naval Observatory's "Master Clock Time" web application to check the time shown on your watch.
• Find your geographic latitude and longitude from your street address: Using the Microsoft TerraServer Web application, look up the geographic latitude and longitude of your home. Some activities below will use this information.
• Observe the noon mark on a solstice or equinox: Use Handy Table No. 1 to find the dates and watch times that these seasonal events occur through 2015.
• Using the Gallivan Center sundial, measure the azimuth of the Sun: The dial of the Asteroid Landed Softly sundial is laid out in the ancient Greek manner by being divided into 12 equal parts of 30°s each. The dial plate of the sundial is a big protractor aligned to the compass points. Using the shadow of the central gnomon, the azimuth - or horizon position of the Sun in an observer's local horizon system - can be found. In the local horizon system, an imaginary unit sphere surrounds the dial and a visitor. Due north is zero degrees. Proceeding clockwise around the horizon from due north, 90° is due east, 180° is due south, and 270° is due west. The shadow of the gnomon indicates the reciprocal bearing to the Sun's azimuth. To find the Sun's azimuth, take a reading from the dial and add 180°. For example, around 2pm in the afternoon, the shadow may cover the 45°s mark on the dial plate. 180° + 45° = 225° azimuth.
  
  Check your results against the United States Naval Observatory's "Table of the Altitude of the Sun and the Moon for One Day" webpage.
• Using the center and smallest post on the outer ring of the Gallivan Center sundial, measure the altitude of the Sun: During the day the Sun is too bright to look at safely. Using a vertical post and the Sun's shadow, its altitude in degrees in the local horizon system can be found. In the observer's local horizon system, altitude is measured in degrees starting at 0° at the horizon and ending at 90° directly above the observer - a point called the zenith. So the position of the Sun or the Moon can be described in the local horizon system using two coordinates - the Sun's azimuth bearing and its altitude bearing.
  
  To find the Sun's altitude from its shadow, use the center post of the outer ring - Post 4, or the two posts flanking Post 4 - Posts 3 and 5. The Sun's shadow must fall across the pavement of the plaza at a right angle to the post that you use. With a tape measure, find the height of the post and the length of the Sun's shadow. If you do not have tape measure, have a friend or parent stand next to the post and note the post's height on their body. Have the person lie down next to the shadow and note the same for the length of the shadow. When you get home, use a tape measure to find the height and length of the post.
  
  Divide the height of the post by the length of the shadow. This is the tangent of the angle formed by the Sun's altitude and your local horizon. Using a NASA Table of Tangents, lookup the altitude of the Sun in degrees.
  
  Check your results against the United States Naval Observatory's "Table of the Altitude of the Sun and the Moon for One Day" webpage.
• Observe a sunset equinox using the 300 South Street, just north of the Gallivan Center sundial: On the date of the equinoxes, the Sun rises at due East (azimuth 90°) and sets due West (azimuth 270°). As intended by the plaza developers, the Gallivan Center Sundial is shaded by building interference at sunrise and sunset on the equinoxes. However, the street system in Salt Lake City, Utah is laid-out in a rectilinear grid oriented to the compass points. 300 South Street, directly north of the Gallivan Center Plaza, is aligned on a due east-west line. On the equinoxes, the Sun rises and sets down the center line of this street. The sunsets on the day of the spring (April 21) and autumnal (September 23) equinoxes are particularly striking. A pedestrian crossing, with a concrete protected barrier, allows the visitor to stand near the centerline of 300 South Street without exposing oneself to traffic hazards. After the spring equinox and until the autumnal equinox, the Sun spends part of each day directly illuminating the north sides of buildings. This has implications for building design and for the cooling loads of buildings during the summer. After the autumnal equinox, across the winter solstice, and until the spring equinox, the north sides of buildings spend six months in shade. This has implications for building heating loads.
• Observe part of the analemma figure over three or four months: Take a photo of the north or south analemmatic dial plate. Come back at the noon mark time once a month for several months and mark the location of the noon mark on the plate on to your photo. The noon mark will trace part of the analemma figure-8. You can also do this using the shadow of a tall basketball hoop at your school.
• Learn how to read the analemmatic dial and about the equation of time: The dial is located at 111.89° West longitude. If the Earth were a perfect sphere and the orbit of the Earth around the Sun was a perfect circle, the noon-mark would occur at exactly the same time each day. That time is 27 minutes and 54 seconds after the hour (the residual of 111.89° / 15° per hour). The difference between this standard time of local apparent noon (12:27:54 pm) and the standard times of the noon mark (Post 4) shown in Handy Table No. 5 is caused by the almost imperceptible elliptical shape of the Earth's orbit around the Sun - a deviation of only 0.00167 from a perfect circle. On our tiny scale of human existance, this minor variation in the Earth's 100 million kilometer orbit around the Sun appears as a one or two foot difference between the standard time noon mark and the actual noon mark of the Sun. This difference has an odd name in sundial nomenclature. It is called the "equation of time". For example, on June 4, two-weeks before the summer solstice, the noon mark is at 12:25pm, or 3 minutes before 28 minutes after the hour. This means the light gnomon at 28 minutes after the hour will appear slighty to the right of the centerline of the dial. Two weeks after the solstice on July 2, the noon mark occurs at 33 minutes after the hour or 5 minutes after 28 minutes after the hour. This means the light gnomon at 28 after the hour will appear slighty to the left of the centerline of the dial. The equation of time is best observed during the two-week period surrounding the summer solstice around June 21st. During this two-week period, if you view the noon mark at 12:28 pm each day (or once a week for four weeks), it will appear to walk around the bottom of the dial in a half-circle. This is the very bottom of the figure-8 annalemma. The same effect can be easily seen around the two weeks surrounding the winter solstice (12/4 to 1/2).
• Use the dial to tell standard (watch) time: Estimate the time of day using the Gallivan Center Dial, the dial's posts, and Handy Table No. 5.
• You are the gnomon: Estimate the time of day using your own shadow and Handy Table No. 6.
• For a day, tell time the way an average person did between 1500 B.C.E. to 1800 C.E.: For one day, try to tell time without a clock, using the methods that an average person would have used in 200 B.C.E. through the early 1800s. During the day use a sundial and your knowledge of seasonal hours by month shown in Handy Table No. 2. At night, a pre-clock person would have memorized their table of seasonal night hours shown in Handy Table No. 3. The average person in ancient times also would have memorized, just as we memorize multiplication tables in modern schools, a parapegma or table of rising constellations after sunset by month. For our purposes, use John Walker's "Your Sky" online planetarium program to find the rising constellation at midnight. Handy Table No. 8 is a modern parapegma for Salt Lake City, Utah. In Salt Lake City on the summer solstice, the zodiac constellation of Sagittarius is rising in the east. In six seasonal nightime hours shown in Handy Table No. 3 - or about 4 1/2 hours of standard (watch) time, Sagittarius will transit or "south". Using this information, two people could agree to meet at a particular time at night without having a watch. Near the full Moon, the night sky is washed-out and the constellations are not easily seen. Near the full Moon, a person's sundial acts as a Moon dial and tells seasonal hour time. After around 100 C.E., the astrolabe became a popular way to answer such questions. In modern practice, this type of computation is usually done with a planisphere - an inexpensive disk that can be purchased at your local planetarium.
• My local time is not your local time. Use a cell phone and a friend to observe differences in local apparent time at the dial and another location across town: The noon mark occurs at slightly different times when two people are separated by a moderate distance. At Salt Lake City's 40° North latitude, two persons separated by 13 1/4 miles of east-west distance will experience the noon mark one minute apart. At about 6 1/2 miles, the difference will be 30 seconds. One person can go to the dial at the time of noon transit. Find that time using Handy Table No. 5. Call a friend or another school class 5 or more miles of east-west distance away on a cell phone. Have them use the side of north-south running wall as their noon mark. Have each observer announce the noon mark and see if there is a difference.
• Find your longitude like ships did at sea: Before the advent of the global positioning satellite system (GPS) in the late 1980s and early 1990s, ships at sea and travellers on land could locate their position in longitude by using the noon mark and an accurate clock - a chronometer - set to show the current time at a reference longitude - normally 0° longitude through Greenwich, England. The Gallivan Center sundial and the preceeding activity can be used to illustrate this method. Near the time of the noon mark at the Gallivan Center sundial, position yourself about 10 to 30 miles (16 to 48 kilometers) to the east or the west of the dial. Use Handy Table No. 5 to determine the time of a noon mark. Construct a gnomon and find the noon meridian line using the technique described below, under the activity "Find your local transit meridian using the method of equal altitudes". The Perless Sundagger Sundial at the Utah Valley State College campus in Heber, Utah, is a convenient pre-existing sundial with an accurate noon mark about 30 miles east of Salt Lake City. Using the Perless sundial as an example, since you are 30 miles east of Salt Lake City, the noon mark in Heber City will occur some time before the noon mark will occur at the Gallivan Center sundial in Salt Lake City. With an accurately calibrated watch, note the time of the noon mark at the Heber sundial. The time difference between the noon mark in Heber from that in Salt Lake City can be converted to a distance. At 40° North latitude, one second of time is about equal to 1164 feet of distance and 60 seconds or one minute of time is equal to about 13.23 miles. Using these conversion values, estimate your physical distance in longitude from the Gallivan Center dial. Compare your estimate to the distance measured using a map.
• Find your latitude like ships did at sea: Mariners and land travellers would also need to measure their latitude. This can be done with the Sun, the noon mark and reference tables during the day, but your unknown latitude is most easily found at night. Measure the angular number of degrees between the North Star - Polaris - your local zenith. Your latitude = 90° - Polaris's zenith angle.
• Adjust standard time to local apparent time: This computation - or reduction - has two steps. The standard time zones - Eastern, Central, Mountain and Pacific - are geographic bands several hundred miles wide within which for administrative purposes we agree all local time is the same. As we have seen, with a few miles of separation local apparent time is different. Reduction of standard time to local apparent time involves two steps. First, the difference between the administrative meridian of standard time is found and this is converted into degrees and into time by dividing that angular distance by 15. This first time adjustment is added to standard time if the administrative meridian is located to the West of your location and subtracted from standard time if the administrative meridian is to the East of your location. Second, the current value of the Equation of Time is subtracted or added as necessary. Find one of the sundial books listed in the Bibliography and read more on this topic.
• Make a noon mark on your window sill: For generations, farm homemakers used a knife to make a dent on south facing window sills to mark the noon hour. In homes built before 1900, these window sill marks can sometimes still be found. Make your own noon mark by putting a sticker or piece of tape on the window sill when the sun transits. This can be done on any day of the year, but the best time to place the mark is on an equinox. To estimate when the Sun will transit your east, south or west facing window, use Handy Table No. 5 for Salt Lake City, or for any city in the U.S., the United States Naval Observatory's "Complete Sun and Moon Data for One Day" webpage.
• Learn how to measure things by both their angular size and their linear size or length: There are two ways to measure the size of an object - its linear size that we measure with a ruler - and its angular size. Read the handout "Seeing the Angular Way" about using body parts to quickly estimate angles and the angular size of objects. In summary, the finger-tip on an outstretched arm measures 1°, a fist at the end of an outstretched arm measures 10°, and a spread hand at the end of an outstretched arm measures 18°.
• Estimate the altitude of the Moon, a planet and a bright star at night using your hands: Then lookup the altitude of Moon using the United States Naval Observatory's "Table of the Altitude of the Sun and the Moon for One Day" webpage. Lookup the altitude of a planet using John Walker's "Your Sky" online planetarium program.
• Find your local transit meridian using the method of equal altitudes: Around 10AM, drive a stake into a grassy lawn. With spray paint, mark the spot of the Sun's shadow cast by the tip of the gnomon. Tie a piece of string to the stake. Using the string as a giant compass, use the spray paint to mark part of a circle from the 10AM to the 3PM position. Wait until around 2PM. When the shadow cast by the tip of the gnomon crosses this arc, the Sun is at the same altitude as it was around 10AM. Connect the 10AM and 2PM marks with a line. This line is oriented along and east-west axis. Using the tools of geometric construction, bisect this line and draw a second line perpendicular through the point of bisection. This line runs due north-south and is the "south" transit line of your local meridian. If disoriented and lost in the outdoors, this technique can also be used to determine direction.
• Make your own modern-form horizontal sundial: Take a piece of paper, construction paper or cardboard. Mark an 8" square on the paper. Divide one side in half. This will be the south or bottom of the dial. Divide the opposite side of the square in half. Connect the two half points to make a meridian line on the square dial plate. Using Handy Table No. 7 and protractor, draw the hour lines with the angles listed in the handy table. Number the hours of the day on the dial plate. Now make the triangular gnomon, using a second piece of paper or cardboard. The right-angle sits at the north or top end of the dial plate. The small angle will sit on at the south end of the dial plate. The base of the gnomon is length of the square. (Adding an extra tab to the base edge will aid in gluing the gnomon to the base.) The small angle at the south end of the plate is equal to your latitude. For Salt Lake City and the Gallivan Center that angle is about 40 3/4°. Anywhere between 40° and 41° will work. For cities other than Salt Lake City, Utah, use the Microsoft TerraServer Web application to look up your city's latitude. Using duct tape and square pieces of Styrofoam or wood, duct tape or glue the gnomon at a right angle to dial plate. Align your paper sundial with the gnomon aligned on a north-south line. The easiest way to align the sundial is to use the Handy Table No. 5 for Salt Lake City, or for any city in the U.S., the United States Naval Observatory's "Complete Sun and Moon Data for One Day" webpage to find the standard (watch) time of tomorrow's noon mark. At that time, take the paper sundial outside and align it with the right-angle of the gnomon to the north and the small angle of the gnomon to the north. Rotate the dial until the gnomon marks noon.
• Measure how fast stars near the horizon cross the 1° of angular size subtended by the central light gnomon: When you stand at the north end of the south analemmatic dial and look through the gnomon, the light gnomon's space is about 1 angular degree wide. At night, use this space, a planisphere or star map, and a second-hand of a watch to measure how long it takes a bright star or planet on the celestial sphere to move across the 1 angular degree of the gnomon's gap. Throughout the year, because our view of the celestial sphere changes, the speed at which bright stars or planets transit will change. Stars higher or lower on the celestial sphere will move faster across the gnomon's 1° gap. Stars near the celestial equator will move across the 1° gap in about 4 minutes. Why 4 minutes? There are 24 hours in a day and 60 minutes in an hour. There are 360° in a circle. Divide these amounts to get the number of minutes it takes the celestial sphere to move 1° as a result of the Earth's rotation.
• Observe the unequal speed at which the Sun crosses the dial during summer and winter: Compare the interval of time that it takes for the Gallivan Center light gnomon to sweep across 90° on the dial plate as listed in Handy Table No. 4 with the number of hours of daylight in Handy Table No. 2. When days are long and the Sun is high in the sky, the angular speed of the Sun at noon is high. In the winter when the Sun is low in the sky and days are short, the angular speed of the Sun is low. Observe these speeds in June and December. This contradiction - high angular speed and long days; low angular speeds and short days - is a result of the basic feature of how we perceive objects in three-dimensional space. The angular size of a degree is not uniform in your local horizon system.
  
  Consider a classroom globe and the lines of longitude as they converge at the North Pole. As latitude increases there are more degrees in a given linear area as compared to an equal area at the Earth's equator. The same thing occurs with respect to increasing altitude in your local horizon system and the zenith - the point directly over your head. Two objects moving at the same linear speed - say two airplanes or two clouds - one overhead and one near the horizon. The airplane overhead will appear to move faster - in terms of angular speed - than the one near the horizon. This occurs even though the two airplanes or two clouds are moving at the same linear speed. In the summer and winter, the Sun moves at the same linear speed. In the summer, the Sun is higher in the sky and appears to have a higher angular speed. This high angular speed is measured by the Asteroid Landed Softly sundial.
  
  Anyone who has caught a baseball hit into the outfield intuitively understands this principle of movement in three-dimensional space. When the outfielder tries to position themselves to catch a baseball, they look at the angular speed of the ball in their visual field - usually a featureless blue sky. As they run towards or away from the ball, if it appears to have a high angular speed, it will overshoot their position. If the ball appears to have a low angular speed, it will fall to the ground before they reach it. The outfielder runs so that the ball has no angular speed. In this condition, the baseball is on a trajectory towards the outfielder. This is how an outfielder makes positioning themselves, so the baseball seemingly falls into their mitt, to be so effortless.
• Prepare an solar azimuth-altitude chart using the web application at the Univ. of Oregon Solar Radiation Monitoring Laboratory: The University of Oregon "Sun path chart" web application quickly prepares a chart showing the Sun's azimuth and altitude over one year, particularized for your geographic latitude and longitude.
• Using the Univ. of Oregon Sun path chart, decide if you can plant a tree in your yard that will block the summer sun: Deciduous trees loose their leaves in the winter. So select a tree placement that will block the hot summer sun, but that will also let through the warming winter Sun.
• Design an over-hanging ledge for the south-facing side of your house that will block the hot summer Sun: Using your Univ. of Oregon Sun path chart and the NASA Table of Tangents, design an overhanging eave for a south facing window that will block the hot summer sun from entering the room, but that will allow the warming winter sun in.
• Consider the effect of building orientation on energy consumption: Using a light shoebox, either inside with a flashlight, or outside in the sunlight with a thermometer placed inside the box, consider how the orientation of a rectangular building with respect to the compass points effects heating and cooling loads and the building's energy consumption. Observe a sunset at an equinox as described above. Part of a building's north side is heated during the hot summer months between the spring equinox and the autumnal equinox. In the winter, the north side of a building remains in shade. Consider how a rectangular building might be oriented to achieve various energy consumption goals:
  • You live in southern part of New Mexico, where summer heating loads are extreme and winters are mild. How would you orient the building with respect to the compass points to reduce the rectangular building's summer cooling load?
  • You live near the north Utah-Wyoming border at a high-altitude. Summer cooling loads are light because of the high altitude, but winter heating loads are extreme. Which way would you orient the building to maximize winter heat gain?
  • You are building a home on the Salt Lake City valley floor. Summer cooling loads are high; winter heating loads are high. What is a good compromise orientation for your rectangular building?
  • Look at an Earthship house design. How did the designers minimize this home's energy consumption, considering what you now know about the Sun's path during the year?
• Go to a local astronomy club Sun party and look at the Sun through a Hydrogen-alpha filter.
• For more Sun-Earth activities: See the teacher-parent resources list.

The term "Handy Tables" has been used repeatedly throughout this website. This is also a historical allusion to Ptolemy's Algamest, a famous book written around 100 C.E. that crystalized then current knowledge about sundials and planetary motion. After completing The Algamest, Ptolemy issued a supplement, called the Handy Tables consisting of useful data lookup tables for solving solar and planetary motion questions. By writing convention, most books about sundials include an appendix of handy tables.

Prepared by and report errors or broken links to: K. Fisher 2/2007 fisherka@csolutions.net.