LENGTH OF DAY ON THE EQUINOX

At every turn of the seasons, discussion in my classes turns to the length of the daylight period and sunrise and sunset times that don't agree with what students have been taught to expect. For instance, I demonstrate and explain in my classes that the length of the daylight period is everywhere 12 hours on the Equinoxes, yet a check of published rise and set times always reveals a longer daylight period. How can the discrepancy be explained and quantified?

Earth's atmosphere causes refraction of the sunlight that passes through it. Near the horizon, refraction will raise an object on the horizon (like a star or the Sun) to an apparent position about 0.5 above the horizon (when the 'bottom' of the Sun is raised more than the 'top', the rising or setting sun can look quite flat). More variable local atmospheric effects, like the Novaya Zemyla Effect, can increase the effect of the refraction by an order of magnitude or more! This refraction effectively hastens the apparent rising of the Sun and delays the apparent setting of the Sun. Figure 1 presents a simple qualitative explanation of the refraction induced lengthening of the daylight period. This composite image presents an interesting view of the setting moon viewed from earth orbit.

FIGURE 1. If Earth had no atmosphere, the Daylight Circle (the boundary between night and day) would divide Earth exactly in half. But sunlight (and starlight, and Moonlight) entering Earth's atmosphere is refracted as it passes through the atmosphere on its way to the surface of Earth. When the Sun is nearly overhead (at A) the refraction is negligible. Near the horizon at B (where sunlight strikes the atmosphere at a low angle and must travel through significantly more air to reach Earth's surface), atmospheric refraction can raise the actual position of an object on the horizon to an apparent position 0.5 or more above the horizon. This effect 'moves' the Daylight Circle into the night (to the left in the diagram) effectively causing slightly more than one half of Earth to be illuminated, and thereby lengthens the daylight period that simple geometry would otherwise nicely predict.

Conveniently, the diameter of the Sun is also about 0.5, so atmospheric refraction raises the actual Sun that is just below the horizon to an apparent position that is just above the horizon. The refraction induced early rising and late setting of the Sun, then, lengthens the daylight period by (nearly) the amount of time it takes the Sun to rise and to set, and that time depends partially upon the observer's latitude.

(NOTE: The US Naval Observatory computes sunrise and sunset times using a refraction of 0.533 and a Solar diameter of 0.566 (see the USNO technical details page for more on this). By rounding to 0.5 for both values, daylight periods calculated on this page will be a little shorter than those provided by the Naval Observatory, with the differences being greater at higher latitudes.)

AT THE EQUATOR.....

At the Equator, the setting Sun's path is perpendicular to the horizon. The diagram to the left shows the apparent Sun (in yellow) just beginning to set, while the actual Sun (in white) has just set.
Since the Sun's rate of motion across the sky is 1 every 4 minutes (15/hour), the apparent Sun will set 2 minutes later than the actual Sun.
Similarly, the apparent sunrise occurs 2 minutes earlier than actual sunrise. The combined effect increases the length of the daylight period at the Equator by 4 minutes. A check of the USNO sun rise and set times near the Equator, however, indicates that the length of the equinox daylight is actually 6 minutes longer than 12 hours, as indicated by data supplied by the US Naval Observatory below:
Information provided for longitude 0.0, latitude 0.0
     Wednesday, 20 March 2002   Universal Time
     Begin civil twilight      05:44
     Sunrise                   06:05
     Sun transit               12:08
     Sunset                    18:11
     End civil twilight        18:32


The additional 2 minutes are explained by the fact that sunrise and sunset times are published for the first and last appearance of the Sun on the horizon, NOT the center of the Sun. The upper limb of the sun is 0.25 above the center of the Sun, and so rises 1 minute ahead of the center of the sun. Similarly, the upper limb of the Sun sets 1 minute after the center of the Sun has set.

....AT HIGHER LATITUDES

At higher latitudes, the rising and setting Sun makes an angle with the horizon of (90-L), where L is the observer's latitude. On the diagram to the right, drawn for NY at latitude 41 N, the apparent Sun is just beginning to set as the actual Sun (directly below it) is just finishing setting. Notice that the apparent Sun must move farther than 0.5 along it's oblique path (taking longer than 2 minutes) to bring it completely below the horizon. The time the sun takes to set can be calculated as (2 minutes/cos(L)). In NY, that time is about 2 minutes and 40 seconds. Atmospheric refraction at sunrise and sunset lengthens the NY day, then, by a total of about 5' 20".
Adding another 2' 40" for the fact that the upper limb of the Sun rises 1' 20" before and sets 1' 20" after the center of the Sun, we get an approximate 8 minute total lengthening of the daylight period, a nice match with the US Naval Observatory's published times:
Information provided for New York, New York W73.9,  N40.7
     Wednesday,  20 March 2002  Eastern Standard Time
     Begin civil twilight       5:32 a.m.
     Sunrise                    6:00 a.m.
     Sun transit               12:04 p.m.
     Sunset                     6:08 p.m.
     End civil twilight         6:36 p.m.


An interesting additional effect of atmospheric refraction is the fact that the apparent sunrise and sunset azimuths are shifted north (in the northern hemisphere) of due East by (0.5) (tan(L)).
The length of the daylight is further lengthened as the Sun's declination (distance from the equator) increases toward the solstices. This is because, while the Sun remains almost the same size in the sky, it is larger than 0.5 degrees of right ascension on the smaller declination circles north and south of the equator.

RELATED INFORMATION:
Go HERE for more on determining just how far north of east the solstice Suns rise and set....
....and HERE for a quick example and explanation of why the daylight period is usually not centered around noon.
Send comments to Steve Kluge at Resources for GeoScience Education