And the Sun Stood Still

… And he said in the sight of Israel: “Sun, stand thou still upon Gibeon” … and the sun stood still; (Josh. 10:12-13) 

I have often thought that history writers and politicians should be required to get an imprimatur from a professional surveyor whenever they want to publish anything that mentions surveying matters. Amazing things have happened and are still happening in geometry if you believe the writers of history books. I have often read with amusement how educated and knowledgeable people struggle with surveying facts and figures. Failure to distinguish between square miles and miles square no longer surprises me, acreage values are probably greatly in error, writers interpret bearing changes as “rotation” of lines and properties, “north” is the direction to polaris, and “east” is where the sun comes up. I can never forget the incompetent legal description that the politicians made of the international boundary after the Mexican War. But it is the understanding, or rather the lack of it, of the apparent motion of the Sun that never ceases to amaze me.

I recently purchased a book entitled Latitude Zero – Tales of the Equator  [Carroll & Graf Publishers, New York, 2001] in which authors Gianni Guadalupi and Antony Shugaar made claims that reminded me of the biblical quotation above. The introduction to their book contains the following statement:

“It [the Equator] gets more sunlight than any other point on Earth, and the equatorial sun stands still, straight overhead. A few years ago one inventive photographer decided to make a very extended multiple exposure of the sun, every day at noon, for a year; the result was a luminous figure-eight in the sky. The same sequence of photographs shot at the Equator would have shown a single intense dot of light at the zenith.”

Poppycock. But let us examine one statement at a time. I deliberately capitalize the pertinent terms. Does the Equator get more sunlight than any other point on Earth? If with ‘sunlight’ the authors mean the amount of solar radiation per unit area, the statement is true enough, at least in the upper atmosphere. Nevertheless, the Equator is not a particularly hot place, the great, brutally hot deserts of the world lie along the Tropics, and no place along the Equator has ever come close to experiencing the temperatures measured in Death Valley. If the authors had in mind only good old sunshine, the Equator with its humid atmosphere and torrential rains throughout much of the year would seem to be far down on any list of sunny places. But if ‘sunlight’ is to mean simply daylight, in the course of a year the Equator receives no more daylight than the North Pole or any other point on Earth, it is only distributed differently.

Item two. Why should the equatorial Sun stand still, straight overhead or elsewhere? The Equator takes a ride on planet Earth just like Podunk, Massachusetts, and it does not really matter if one believes that the Earth revolves around the Sun, as co-author Guadalupi’s countryman Galileo claimed that it did, or whether it is the other way around. If the authors have ever been at the Equator, they didn’t look up. For the Sun to stand still the Earth must cease rotating around its [the Earths] axis. The late astronomer Carl Sagan once wrote, that it is not inconceivable that a catastrophic near-miss passage of a huge planet-size body could exerts enough gravitational force upon Earth to slow or even stop its rotation, but there seems to be no plausible way of getting it to start rotating again. 

Finally, and that is the main reason I am writing this article, let us examine the figure eight of that unnamed photographer. Any surveyor who has ever observed the Sun will immediately know what the poor fellow did. He had a watch; he may even have listened to the rhythmic tone of a time signal, and each day at the stroke of twelve o’clock he released the shutter of his camera. Unfortunately for him, even at the Standard Meridian for his time zone the Sun refuses to cooperate. Our clocks run on Civil Time and not Solar Time. Civil Time divides the year into 365 or 366 days, and the day into twenty-four hours of 3,600 seconds each, exactly. But the interval of time between two successive passages of the Sun of the vernal equinox (the length of the Tropical Year on which our calendar is based) is equal to 365.2422 mean solar days.

Part of the problem lies in the common definition of Noon. The word originally meant “nine”, from the Latin nonus, the ninth hour after sunrise. We say it is Noon when it is twelve o’clock, which is allright, except we go on to refer to the time prior as AM (ante meridiem) and after as PM (post meridiem), when the sun almost never crosses the Meridian at that time. 

Because the Earth travels along the perimeter of an ellipse (not precisely but close enough) in which the Sun occupies one of the two focii, the time it takes for any point on Earth to face the Sun (when the Sun passes the Meridian of the observer) varies with each day. Our time-obsessed, time-regulated civilization and our mechanical clocks can’t handle days of varying length. We have averaged the lengths of our days, some of which are in reality (as measured by successive Meridian passages of the Sun) as much as sixteen minutes longer or sixteen minutes shorter than that average. Surveyors call that difference the Equation of Time. Only four times each year will the Sun cross the Standard Meridian at twelve o’clock noon. The figure eight obtained by that photographer is a graphic representation of the Equation of Time.

What about that strange ‘single intense dot of light’ at the Equator? Just like elsewhere on Earth and using that same faulty method, the photographer would have obtained a figure eight, but here centered on the Zenith (everywhere else centered on the celestial co-latitude of the observer), about twenty-three degrees long on each side of the center (the angle of inclination of the Earth’s axis towards the orbital plane). Had he traveled north of the Arctic Circle an ever-increasing portion of his figure eight would have fallen below the Horizon, until at the Pole only a twenty-three degrees long elongated circle of light would appear above the Horizon. Only twice a year, on the days of the Equinoxes [see note], will the Sun at noon occupy the equatorial Zenith, on all other days it will be either to the north (March to September), or to the south (September to March) of it.

Had the good man first talked to a professional surveyor who could have established an exact point on the Meridian to allow him to point the camera due south, or who could have computed for him the Standard Time at Local Noon for each day of the year, the result would have been quite different. The photographer could have exposed his film at the precise moment the sun crossed the Local Meridian. After a year’s time the film would have shown a perfectly straight line of light, not quite forty-seven degrees long, the width of the solar disk. The lower end of that line would have shown the position of the sun at noon of the day of the Winter Solstice, the upper end its position at noon of the Summer Solstice. It is the same at the Equator and at Podunk. For those who want to try it at the North Pole, I suggest to pick up their equipment on the day of the Autumnal Equinox and get the other half of the line by occupying the South Pole.

The mistaken belief that the Sun passes daily through the equatorial Zenith appears to be fairly widespread, as I have encountered it a number of times in history and other texts. One does not have to be an astronomer to realize the fallacy of that notion. The equatorial Zenith is at a point of intersection of the Celestial Equator with the Celestial Meridian of the observer. Therefore, the Sun would have to travel each day on the path it traverses only on the Equinoxes, in other words, there would be
no seasons because all year long it would be the first day of spring (or fall) everywhere on Earth. With a little imagination one must realize that this could only happen if the Earth’s axis of rotation were perpendicular to its orbital plane.

“The trouble with people is not that they don’t know, it’s that they know so much that ain’t so.” 

NOTE: The Equinoxes are not days but points on the Ecliptic, or moments in time, at which the Sun on its path along the Ecliptic crosses the Celestial Equator. It follows that there is only a single point on the entire 24,900-mile length of the Equator where the Sun’s center is in the Zenith at noon, a point that shifts with each Equinox. But since it takes about thirty-two hours for the solar disk to clear the Celestial Equator, one can reasonably say that the Sun is in the Zenith twice a year at any point on the Equator.