Equinox ≠ Equal Nights
Published on Sep 23, 2007 at 2:57 pm.
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Filed under astronomy.
This morning, at 09:51 UT (4:51 CDT), the Autumnal Equinox occurred. The term “equinox” has as its root meaning in Latin “equal nights.” Many introductory books about astronomy, and virtually all K - 12 books, say that the equinox is the day that days and nights are equal length: 12 hours of each. On the surface this makes sense. The reason that Earth has seasons is that it is tilted by about 23.5° as it orbits the Sun. So, during part of the year, the northern hemisphere is tilted towards the Sun, and about six months later, the southern hemisphere is the one tilted towards the Sun. This makes summer and winter reversed in the northern and southern hemispheres. Here in Texas, in the northern hemisphere, Autumn is beginning. But, in Australia, spring is just starting.
Twice during the course of the year, though, the Earth is positioned so that the Sun appears directly over the equator. On those days, the Sun appears to be on the celestial equator in the sky (as seen in the image below). Traditionally, we are told that objects on the celestial equator rise due east and then set due west twelve hours later. But, that is actually a pretty simplistic view, and it is not exactly correct. You can see the problem just by looking at the sunrise and sunset times today. (You can determine the sunrise/sunset and moonrise/moonset data for any day using this USNO application.) For my location, the Sun rose today at 7:18 am CDT, and it will set later today at 7:25 pm CDT. That means that the Sun is up for 12 hours and 7 minutes. While that is not much longer than 12 hours, it is longer. By trying several other dates, I find that on September 26 the Sun will rise at 7:20 am CDT and set at 7:21 pm CDT (one minute past twelve hours later). On September 27, the Sun also rises at 7:20 am CDT, but it will set at 7:19 pm CDT (one minute shorter than twelve hours). So, why is the equinox September 23 this year, and not September 26 or 27?
The answer has to do with a number of variables. First of all, the equinox is not defined to be the day that the days and nights are each twelve hours long. Rather, the equinox is defined as the day (and moment in time) that the center of the Sun appears to be right on the celestial equator (and thus right over Earth’s equator).
But, the Sun is not a point source in the sky. It spans about 1/2 degree of arc. It takes the Earth about two minutes to rotate through 1/2 degree. So, as the Sun rises, the top edge of it comes into view about one minute before the center of the Sun, and about two minutes before the bottom of the Sun clear the horizon. Sunrise is defined as the moment that the Sun first appears, so about one minute before the center of the Sun. Likewise, sunset is when the Sun disappears, so about one minute after the center of the Sun sinks below the horizon. Thus, on the day of the equinox, you’d expect the day to be at least 12 hours and 2 minutes long, not an even 12 hours! But, that figure is really only for an observer watching sunrise and sunset at the equator. If you are not at the Earth’s equator, then the Sun will rise and set at an angle. That means that the Sun will rise and set slower. To a first approximation, the time needed for the Sun to rise and set would be extended by a factor of 1/cos(θ), where θ is the latitude of the observer. This approximation should hold except near the Arctic or Antarctic regions, where solar apparent motion along the ecliptic will begin to matter. At my latitude, this means that the length of the day is extended an additional half minute or so due to my latitude beyond the extra two minutes that you’d expect at the equator.
But, this only accounts for two to three minutes of the time difference, not the 7 minutes extra that I told you about at the beginning. Where does that come from? Part of the answer is that Earth’s atmosphere also has an effect. If Earth had no atmosphere, then the day of 12 hour days and nights would be only a day or two off of the equinox. But, Earth’s atmosphere refracts (bends) the light passing through it. This has the effect of lifting an object’s position higher in the sky when it is near the horizon than it would appear to be without the atmospheric refraction. That means that the Sun appears to rise when the disk of the Sun should geometrically still be below the horizon. The effect raises the position of objects at the horizon about 1/2 degree. So, the Sun would appear to rise two minutes early and set two minutes late due to the effect of the atmosphere. So, at the Earth’s equator, these effects combine to add six minutes to the length of the day. Again, the effect of latitude can be estimated by (6 min)/(cos (θ)). For my latitude of about 33° N, that comes out to be just over 7 minutes — the observed offset from 12 hours.
So, if anyone tells you that today is the day of equal day and night, then you now know that they are wrong.
-Astroprof
Orbit diagram courtesy of NASA
Sun views created using Stellarium.
A Ler…-- Rastos de Luz on September 24, 2007 at 1:25 pm: 1
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