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March 2005 Feature: The Solar Pendulum

Land of Eternal Spring?

If the Earth's rotational axis were perpendicular to the plane of Earth's orbit around the Sun, the Sun would always rise due east and set due west every day of the year everywhere on Earth. Every day, we would have about 12 hours of daylight followed by 12 hours of night. There'd be no change of seasons -- though I'm not no sure it'd be the idyllic land of eternal spring.

At present, the Earth's axis tilts some 23.5 degrees out of vertical. Therefore, on the December (Southern) solstice, the Earth's South Pole tilts most toward the Sun for the year, and the Sun shines at zenith over the tropic of Capricorn. A half year later, the Earth's North Pole most tilts toward the Sun at the June (Northern) solstice, the Sun now shining over the tropic of Cancer. On the day of a solstice, one hemisphere enjoys the longest day and shortest night of the year, while the opposite hemisphere must endure its shortest day and longest night. Then, one half year later, the tables are turned.

Halfway between the solstices -- the equinoxes -- neither pole tilts toward nor away from the Sun. The Sun shines right over the equator (0 degrees latitude), rising due east and setting due west everywhere around the world. On the day of an equinox, everyone receives about 12 hours of daylight followed by 12 hours of night.

If you map the noonday Sun over the course of a year, you'll notice the Sun swinging back and forth like a pendulum. At noon, the Sun resides on your meridian -- an imaginary half circle running north to south across your sky. On the day of the December Southern solstice, the Sun is at its southernmost point on the meridian. One half year later, after the Sun has traveled some 47 degrees northward, the Sun on the Northern solstice stands at its northernmost point on the meridian. Then, the noonday Sun swings 47 degrees from north to south in the next half a year, reaching the southernmost point on the Southern solstice.

In a year, the pendulum makes one swing back and forth, from Southern solstice to Northern solstice to Southern solstice again.

Sunrise & Sunset Calendar

Another way of keeping track of the seasons is to watch the sunrise and sunset points on the horizon. The Sun rises and sets at its southernmost point for the year on the day of the Southern solstice. On the day of the Northern solstice, the Sun rises and sets at its northernmost point for the year. Halfway between the solstices, the Sun rises and sets due east and west on the equinoxes.

You might think that the Sun would rise and set 23.5 degrees north of due east and west on the Northern solstice. Though this happens at the equator (0 degrees latitude), it doesn't at other latitudes. For instance, at 35 degrees latitude, the year's northernmost sunrise happens at about 30 degrees north of due east, and the year's northernmost sunset at about 30 degrees north of due west. At the December solstice, the southernmost sunrise and sunset happen 30 degrees south of due east and west. At a latitude of 35 degrees, the Sun's change of position from summer solstice to winter solstice measures 60 degrees along the horizon -- not 47 degrees.

At higher latitudes, it's even more extreme. At 65 degrees latitude, the Northern solstice Sun rises and sets about 70 degrees north of due east and west. At the Southern solstice, sunrise and sunset appear 70 degrees south of due east and west. As measured by the horizon, the sunrise and sunset positions shift by some 140 degrees from the summer solstice to the winter solstice! At 65 degrees latitude, there are about 22 hours of daylight on the summer solstice; whereas at 35 degrees latitude, it's about 14.5 hours of daylight.

Vagaries of the Seasons

You might think the Sun's declination changes at a uniform rate throughout the year. But that doesn't happen either. The solar pendulum quickly swings past the equinoxes but pauses at the solstices. To illustrate, consider that one month before and after the June solstice, the declination change is a scant 3 degrees. (See Northbound Sun.) This contrasts with the two month period centered around the September equinox, whereby the Sun's declination changes some 23 degrees.

Tale of Two Latitudes

At a latitude of 35 degrees North latitude -- Chattanooga, TN -- there is about 20 minutes less daylight a month before and after the June solstice than on the day of the June solstice. At 65 degrees North latitude -- Fairbanks, Alaska -- there is about 1.5 hours less daylight. The real change in daylength, however, takes place around the equinoxes. At Chattanooga, there's about 2 hours and 10 minutes less daylight one month after the September equinox than one month before. At Fairbanks, it's about 6 hours and 50 minutes less daylight after these two months.

Rotation and Revolution

This final section attempts to explain why the change in solar declination happens. First, it helps to picture the Earth rotating once (360 degrees) upon its axis in a period of 23 hours and 56 minutes. From solar noon to solar noon, the Earth rotates about 361 degrees in 24 hours. Our planet needs to rotate another degree -- for a total of 361 degrees -- for the Sun to return to its noontime position on the meridian. If you wish, you could say the Earth rotates once in reference to the stars of the zodiac in 23 hours and 56 minutes, and to the Sun in a mean period of 24 hours.

After one day, the Earth travels about one degree eastward in its orbit around the Sun. If you could see the stars at daytime, you'd see that with each passing day, the Sun appears to go one degree eastward through the constellations of the zodiac (which is really a reflection of the Earth's motion around the Sun). At solstice time, the Sun's daily eastward journey through the zodiac almost parallels the plane of the Earth's equator, resulting in little daily change in the Sun's declination.

Plane Geometry but is it Plain Talk?

This may be difficult, but I'll give it a go anyway. . .

At the solstices, the plane passing through these three points -- the Earth's North and South Poles, and the center of the Sun -- is perpendicular to the plane of the Earth's orbit around the Sun. (For future reference, we'll call Earth's orbital plane the ecliptic.) This plane defined by the poles and Sun stays nearly perpendicular to the ecliptic for an extended period of time, keeping the Sun at virtually the same declination -- at a near stand still -- in June and December.

At the equinoxes, the Earth's axis is perpendicular to the Sun -- in the respect that neither pole tilts away nor toward the Sun. Hence, the Sun shines at zenith over the Earth's equator. However, the plane that passes through the North and South Poles, and the center of the Sun, is tilted 23.5 degrees out of perpendicular to the plane of the ecliptic -- the maximum tilt for the year. The Sun's eastward motion through the stars is now at its greatest inclination relative to the Earth's equator. In September, the Sun's daily motion is most southeast, and in March, it's most northeast -- bringing about the fastest monthly changes in the Sun's declination.

Alas, this stuff isn't easy to explain! If you have a globe that shows the ecliptic, it may help you to visualize why the Sun's seasonal change of declination happens the way it does. For more on the subject of equinoxes, click on the September 2004 Feature: Southbound Sun and the September 2003 Feature: Equinox Geometry.

Back to The Northbound Sun

copyright 2005 by Bruce McClure

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