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September 2003 Feature: Equinox Geometry


The autumnal equinox arrives on September 23. On this day the Sun rises due east and sets due west everywhere around the world, with everyone receiving equal hours of night and day.* By definition, the equinox comes to pass whenever the Sun is at zenith (or directly overhead) at the Earth's equator.

If you have access to a globe, it's pretty easy to figure out where the Sun is directly overhead when it's sunrise for you. On the day of an equinox, the zenith noonday Sun resides on the equator some 90 degrees of longitude to your east.

For example, I live at 75 degrees West longitude, the longitude of Philadelphia, PA. Looking 90 degrees to the east, the globe shows me where 15 degrees East longitude intersects the equator at Africa's Congo, near the border of Gabon. When I see sunrise on the equinox, I know the zenith sun is shining over the Congo.

Ninety degrees of longitude, as measured along the equator, is the equivalent of about 6,225 miles. So as the bird flies, the distance from the Congo to Columbia (15 degrees E. longitude to 75 degrees W. longitude) lies some 6,225 miles away.

Looking at the globe, notice that as you go northward from the equator along 75 degrees W. longitude, you cross Cuba at about 20 degrees North latitude, Philadelphia at 40 degrees N. latitude, and Baffin Island, Canada at 70 degrees N. latitude. As the bird flies, which destination (Cuba, Philadelphia or Baffin Island) looms as the the nearest and the farthest from the Congo?

If you're familiar with a right triangle in plane geometry, knowing that a2 + b2 = hypotenuse2, you might figure Cuba is the closest and Baffin Island the farthest. But spherical geometry presents a totally different picture. Actually, every place along 75 degrees W. longitude is an equal 6,225 miles of where 15 degrees E. longitude meets the equator. Measure with a string to find out if it isn't so.

In fact, everyone residing on your same longitude all the way from pole to pole sees sunrise and sunset at the same time on the equinox. This could only happen if every point on your meridian of longitude is evenly spaced from the equatorial points that are ninety degrees away.

At sunrise, the Sun's always at zenith at a point on the globe that's 6,225 miles distant, no matter the time of the year. The Sun, however, only rises ninety degrees of longitude to the east of you at equinox time.** Since the Earth rotates fifteen degrees per hour, that means on the equinox, sunrise comes six hours before noon (90 degrees divided by 15 degrees = 6 hours).

At sunrise in the dead of winter, the zenith Sun still stands 6,225 miles away, but at less than ninety degrees of longitude. On the other hand, sunrise at the heighth of summer features a zenith Sun that's an equal 6,225 miles away, but at more than ninety degrees of longitude.

Using a globe and a string representing 6,225 miles, pull the string taut from where you live to the tropic of Capricorn, and then to the tropic of Cancer. By so doing, you should be able to calculate the hours of daylight on the winter and summer solstices.

For the specific date and time of this equinox and other equinoxes, click here.

copyright 2003 by Bruce McClure

Another September 2003 Adventure: Harvest Moon
* Given a true horizon, as at sea, the center of the Sun on the equinox should set twelve hours after it rises -- at least in theory. Atmospheric refraction, however, brings the Sun into view a few minutes before this theoretical sunrise and keeps it up for a few minutes past theoretical sunset.
** except at the equator, where the Sun rises ninety degrees of longitude to the east all year round.