Week Three: 23-27 September 2013


Have you ever needed to know where the sun appears in the sky on a particular day or when the sun would set in your town? Tracking the sun's path through the sky on a given day may be important if you would desire to install a solar energy collector. Knowledge of the time of sunset or sunrise may be needed for planning purposes, for legal matters or for scientific investigations.

Tracking the Sun across the sky

We know that during the summer, the sun passes high in the sky, while in winter the sun takes a low path across the sky. But can we accurately track the sun's path across our sky? One can calculate the path of the apparent sun across the sky for any place using well known angular relationships that take into account the latitude of the observer (how far one is from the equator in angular measure) and the day of the year (which essentially describes the seasonal course of the tilt of the earth's spin axis with respect to the sun). The Climate Studies text shows the paths of the sun on the first days of the astronomical seasons in the midlatitudes where most of us live. We are now in the part of the year when the combination of the inclination of the Earth's axis to its orbital plane and the movement of our planet along its orbital path are tilting the Northern Hemisphere more and more toward the Sun. Our daylight periods are getting longer and the noon sun is ever higher in the sky.

The U.S. Naval Observatory has an interactive online service that allows you to track the sun for your hometown or any other location in the United States and the world in a sun altitude/azimuth table. This table provides the position of the sun in the local sky at 10-minute intervals during any day, from approximately one hour before local sunrise to roughly one hour after sunset. The position of the sun is determined by two angles: the altitude angle of the sun and its azimuth angle. The altitude angle is the angle of that the sun is above the local theoretical horizon, with an altitude angle of zero degrees referring to the sun on the horizon, while a 90 degree altitude angle would be if the sun were directly above you (at the local zenith). A negative altitude angle means that the sun is below the horizon, such as before sunrise. The azimuth angle is the angle measured in a clockwise direction from true north (or to the east), commencing at zero or 360 degrees and passing through 90 degrees (due east).

Local Sunrise/sunset times

The local times of sunrise and sunset for each day of the year are provided by many almanacs and appear in the media, such as in the newspapers or on television. These times are defined as the instant when the top of the solar disk is just at the local level horizon. Like the positions of the sun at various times during the day, the sunrise/sunset times can be calculated using well-known trigonometric relationships for any latitude and the day of the year. The U.S. Naval Observatory has prepared sunrise-sunset tables for over 200 locations throughout the country. Inspecting these tabulations reveals several interesting features. An on-line, interactive service is available that allows you to determine the times of sunrise or sunset for individual days or the entire year at most cities in the United States.

Daily Changes in sunrise/sunset

At this time of the year -- the week before the autumnal equinox-- we are often struck by the rapid change in sunset (and sunrise) time from day to day, translating into a decrease in daylight. These changes are also related to latitude. On one extreme, northernmost Barrow, AK loses approximately 9 minutes of daylight per day during mid September, while at the same time, one of southern-most cities, Honolulu, HI loses 1 minute of possible sunshine per day. However, near the solstices the times of sunrise and sunset change very slowly on a daily basis; in fact, the word solstice is derived from the Greek word meaning "stand still".

The orientation of the earth's spin axis with respect to the sun is responsible for this seasonal variation in the timing of sunrise and sunset. At the equinoxes the earth's axis has no apparent inclination to the sun meaning that rapid day-to- day changes in the apparent position of the sun are greatest, while at the solstices, the inclination is greatest and daily changes of the apparent sun are smallest.

Effects of atmospheric refraction

If you have a chance, you should look at the published local times of sunrise and sunset for a close city on the day of the autumnal equinox (Sunday, 22 September 2013). If you had a chance, did you look at the published local times of sunrise and sunset for a close city on the autumnal equinox during this week? Otherwise, check on the day of the vernal equinox next spring. If you determined the length of sunlight from the time elapsed between local sunrise and sunset, you would find that on the equinox you would experience slightly more than 12 hours of possible sunlight; in mid latitudes this additional time is on the order of 8 minutes.

The primary reason for these extra minutes is the result of the slight bending of the sun's rays as they penetrate through an increasingly more dense planetary atmosphere. This phenomenon is called "atmospheric refraction". You have probably observed this refraction phenomenon when the pencil that is partially submerged in a glass of water appears crooked. In the morning, this ray bending causes the sun to appear above the horizon although the sun is actually below the horizon by approximately one half of a degree of arc. A second factor contributing to the extended time lies in the fact that the sun is not a point, but has a radius of one quarter of a degree of arc. At sunrise, the top rim of the apparent sun has been above the local horizon 4 minutes before the center of the actual sun would have reached the horizon without an atmosphere. Likewise at sunset, the sun appears to remain above the horizon for an additional 4 minutes, when in fact the solar disc has already disappeared.

Times of sunrise and sunset near the solstices

In December, you will notice that the earliest sunsets at most locales occurred during the first or second week of December, while the latest sunrise occurs during the first two weeks of January. (The exact dates depend upon your latitude.) So as not to worry about these apparent oddities, the shortest daylight period of the year does indeed fall on the winter solstice, on or about 21 December.

This apparent asymmetry in the timing of sunrise/sunset occurs because the sun is not as good a timekeeper as most of our clocks. Since the earth revolves around the sun in an elliptical orbit and the spin axis is tilted from the orbital plane, the sun appears to move across the local sky at somewhat variable speeds throughout the year, rather than at a precise 15 degrees per hour. While the differences on any one day are small, over several weeks these slight departures accumulate between true sun time and mean sun time. These accumulated discrepancies are very apparent at certain times of the year, such as the sun running 15 minutes "fast" in early November but by early February, the sun appears to have slowed to the point where it runs 12 minutes "slow". A change from the sun running fast to running slow occurs during December, the result of two events that occur relatively close together: winter solstice in late December and perihelion passage in early January.

This effect works in reverse in summer, when the earliest sunrises occur in early June while the latest sunsets can occur during the first week of July. However, the longest sunlight of the year does indeed culminate on about 21 June. At this time, the solar geometry associated with both aphelion passage and summer solstice contribute to an apparent slowing of the "solar clock".

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Prepared by Edward J. Hopkins, Ph.D., email
© Copyright, 2013, The American Meteorological Society.