The Sun as a Natural Clock

By Matthew Rognstad

The sun can make an effective natural clock for measuring time between sunrise and sunset. It meets the criteria of a natural clock. The initial condition (sunrise) and final condition (sunset) are known. The progress of the sun in the sky is irreversible in that it always rises in the east and sets in the west. Its progress occurs at a relatively uniform rate from day to day, and adjustments can be made for the variations.

sun angle-time plotPeople have used the sun to tell time since time immemorial. It is possible to approximate the time of day just by glancing at the position of the sun in the sky. Without using tools, it is probably impossible to perfectly guess the time by looking at the sun for two reasons: (1) the period of daylight is longer during the summer than during the winter, and (2) the sun rises and sets at different times throughout the year. But for our purposes, it would be reasonable to say that on average there are twelve hours of daylight each day starting around 7:00 AM and ending at approximately7:00 PM. That would mean the sun is at its highest in the sky, a point called solar noon, around 1:00 PM. Technically, it is safer to say that you can estimate what fraction of sunlight is left before the sun goes down (i.e. a relative measurement) instead of saying you can guess the actual time (i.e. an absolute measurement), but that might not be as easy to understand or quite as useful.

sundialUnfortunately estimating the position of the sun in the sky is inexact. For example, it is very difficult to tell the difference between 2:00 PM and 2:30 PM just by looking at the sky. In order to solve this problem people need to use tools. Because the angle of the sun in the sky affects the shadows cast by objects, it is possible to use those shadows cast to tell time instead of using the sun itself. A sundial, a tool with an elevated point, called a gnomon, to cast a shadow and a series of markings to judge the movement of the shadow, makes possible much more accurate measurements. Scientists have discovered 3,500-year-old sundials from Egypt. These tools allowed the ancients to better measure the passage of time each day.

In the modern world, time has become a trickier proposition. Daily work schedules need to be consistent throughout the year. Businesses, governments, and the military need individuals separated by thousands of miles to act simultaneously. We use time zones, milliseconds, and atomic clocks. It is, however, possible to construct sundials that largely meet the demands of modern society. There are three main sources of difficulty: (1) the Earth’s orbit around the sun, (2) the modern time zone system, and (3) changing seasons.

equation of time - sun vs clock timeThe first problem, called the Equation of Time, is the combination of two factors. First, Earth’s orbit around the sun is elliptical, not truly circular. Second, Earth’s axis is inclined at an odd angle compared to the plane of its orbit. These problems cause the sun’s motion across the sky to be slightly variable, causing apparent sun time as measured by sundials to be up to sixteen minutes off compared to clock time. The Equation of Time is the process of adjusting apparent sun time in order to ensure its accuracy against normal clocks. The graph shows how obliquity (axis tilt) and eccentricity (elliptical orbit) combine to cause the total distortion between our clocks and the actual position of the sun.

Another adjustment must be made for the modern system of time zones because sundials measure local solar time. This modification depends on the longitude where the sundial is located. The one hour difference between time zones is an average based on the geographic center of each zone. So any sundials that are not exactly in the middle of a time zone need to be adjusted based on their distance from the center. The Earth rotates a full 360° around its axis every twenty-four hours, i.e. 15°/hour. Dividing the sixty minutes in an hour by fifteen degrees shows that each degree of longitudinal separation between two places will cause four minutes of difference in time readings. For example, Vermillion, SD and Chicago, IL are both in the Central Time Zone, but because they are separated by 9° of longitude, the apparent sun time in Chicago will be thirty-six minutes later than in Vermillion.

Earth's tilt toward the sun in different seasonsFinally, an adjustment needs to be made for different seasons of the year. Because the Earth’s axis is tilted, the sun’s path through the sky changes slightly every day. Moreover, sundials that cast shadows onto the ground face another problem. Earth’s surface is curved, so the surface onto which the gnomon is casting shadows is not parallel to the equator. That will cause the shadow to move at an uneven rate throughout the day. latitude adjustment for sundialsIf the demarcations are evenly spaced, then the sundial will only be accurate at noon. Alternatively, one would need to figure out the proper but irregular spacing of hour markings; this can be somewhat difficult without doing a good bit of trigonometry. Even with appropriate spacing (as in the graph to the right), the irregularity of the scale would make it less easily readable by humans. One solution to that problem is to create a sundial where the base plate is angled to match the latitude where the sundial is located. The gnomon is set perpendicular to the base plate. Hour marks can then be evenly spaced. Such sundials are called equatorial sundials. More detailed information about equatorial sundials can be found on the NASA website listed as link number one below. Suffice it to say that the math is comparatively simple.

Earth's tilt affects the elevation of the sun in the skyIt is also worth noting that, in addition to measuring the passage of a day, the sun can also be used to measure the passage of a year. This is another effect of the tilt of Earth’s axis. The way this process works is much more easily explained by graphs than by text. anelemmaThe tilted axis results in the sun moving through the sky during the course of a year. anelemma and sun elevationIf you were to record the position of the sun at noon every day for a year, the result would be a figure eight-shaped graph called an anelemma. The anelemma can be rotated along the sun’s arc for every hour of the day. The end result is that during the winter, when the days or shorter, the sun cuts a significantly smaller arc across the sky than it does during the summer.

Using these methods, the sun can make an effective natural clock for telling both the time of day and the time of year.

More Information on Sundials:
  1. Schlecht, Clifford. August 24, 1999. Sundials. NASA Liftoff. Retrieved from http://liftoff.msfc.nasa.gov/Academy/Earth/Sundial/Sundial.html Last accessed 9-18-2005.
  1. History of the sundial. No date. National Maritime Museum. Retrieved from http://www.nmm.ac.uk/site/request/setTemplate:singlecontent/contentTypeA/conWebDoc/contentId/353 Last accessed 9-18-2005.
  1. Aubert, Jack. March 17, 1996. Sundials. Retrieved from http://cpcug.org/user/jaubert/jsundial.html Last accessed 9-18-2005.
More Information on the Equation of Time:
  1. The equation of time. No date. National Maritime Museum. Retrieved from http://www.nmm.ac.uk/server/show/conWebDoc.351 Last accessed 9-18-2005.
  1. Holtz, John. December 21, 2003. Eccentricity, Obliquity, and the Analemma's Width. Retrieved from http://members.aol.com/jwholtz/analemma/eq-of-time.htm Last accessed 9-18-2005.
  1. Mukai, Koji; Palmer, Koji; Kallman, Tim. January 16, 1998. The equation of time. NASA's Ask the Universe! Retrieved from http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/980116c.html Last accessed 9-18-2005.
  1. The equation of time. January 28, 2004. Sundials on the Internet. Retrieved from http://www.sundials.co.uk/equation.htm Last accessed 9-18-2005.
  1. The equation of time. October 14, 2005. Wikipedia. Retrieved from http://en.wikipedia.org/wiki/Equation_of_time Last accessed 12-2-2005.
  1. Science and Engineering Research Council at the Royal Greenwich Observatory. November 25, 1993. The equation of time. Information Leaflet No. 13. Retrieved from http://www.oarval.org/equation.htm Last accessed 9-18-2005.
  1. National Weather Service Forcast Office Austin/San Antonio, TX. December 12, 2004. Equation of Time. Retrieved from http://www.srh.noaa.gov/ewx/html/wxevent/2004/eoftw.htm Last accessed 9-18-2005.
  1. Barnes, Howard. July 29, 2005. Equation of time. Ask a Scientist by Argonne National Laboratory. Retrieved from http://www.newton.dep.anl.gov/askasci/ast99/ast99588.htm Last accessed 9-18-2005.
  1. Steiger, Walter R.; Bunton, George W. No date. Equation of time. Night and Day by Caltech Submillimeter Observatory. Retrieved from http://www.cso.caltech.edu/outreach/log/NIGHT_DAY/equation.htm Last accessed 9-18-2005.
  1. Tang, Donny. No date. The Equation of Time. Retrieved from http://www.ithaca.edu/students/dtang1/Pages/SophSem.html Last accessed 9-18-2005.
  1. Müller, M. 1993. Equation of Time - Problem in Astronomy. Retrieved from http://info.ifpan.edu.pl/firststep/aw-works/fsII/mul/mueller.html Last accessed 9-18-2005. (technical)
More Information on Anelemma:
  1. Holtz, John. December 21, 2003. Why the Earliest Sunset, Latest Sunrise, and Shortest Day of the Year Occur on Different Dates. Retrieved from http://members.aol.com/jwholtz/analemma/analemma.htm Last accessed 9-18-2005.
Cool Stuff:
  1. Giesen, Juergen. 2005. Sun & Earth applet. Retrieved from http://www.jgiesen.de/sunearth/index.htm Last accessed 9-18-2005. (Java applet to plot the sun’s position in the sky for any location at any time)