Equinox and Equilux

[Radhakrishna Warrier]

Here is a recent Facebook post of mine.  Hope this will be of interest to those interested in astronomy in this group.

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Equinox and Equilux

 

Only a few more days of summer are left.  Fall colors are just around the corner, as autumn begins here in North America on September 22.  Isn’t that the day of the autumnal equinox?  Yes, equinox it is. Aren’t night and day equal at the equinox?   No, although most people think they are.  The day is always a few minutes longer than the night at the equinox.   The reasons are:

1.     The earth’s atmosphere refracts or bends the sun's rays.  This bending causes the sun to be visible a little before it rises above the horizon and a little after it sets below it. This adds a few minutes to the length of the day.

2.     The Sun is not a point, but a disc as seen from the earth. Unlike a point, a disc takes a definite amount of time to cross the horizon.  This too adds a few minutes to the length of the day.

If day and night are not equal at equinox, is there a day when they are equal or very nearly equal?  Yes, there are not one but two such days. Day and night become most nearly equal on two days a year at equilux meaning “equal light”.  Equilux comes a few days after the autumnal equinox and a few days before the vernal (spring) equinox.  In the town in the US where I live (latitude 47.5° N), the length of the day is 12 hours and 9.5 minutes at equinox on September 22.  Equilux occurs here three days after the equinox, on September 25. The length of the day will then be 11 hrs, 59 minutes and 22 seconds, which is practically 12 hours, meaning day and night will be very nearly equal on the day of equilux.

Fall Colors: The attached picture of fall colors was taken eleven years ago near my erstwhile home in Canada (we sold that home a few years ago).

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For those mathematically inclined, here is the calculation of the extra daytime on the day of equinox.

When day and night are equal, the sun travels an angle exactly 180° over the daytime sky from sunrise to sunset.

The refraction mentioned earlier introduces nearly 0.56° each at sunset and sunrise. So, the total angular addition to 180°due to sunrise and sunset is 0.56+0.56=1.12°.  

The diameter of the disc of the sun subtends an angle approximately 0.53°when viewed from the earth. This also adds to the 180°.

So, the additional angle that the sun travels (over the 180° of equal day and night) is 1.12+0.53=1.65°.

The sun requires 12 hours, or 12x60 minutes to travel 180°.

The time required to travel the additional 1.65° = 1.65x12x60/180 = 6.6 minutes.  This is at the equator (0° latitude).

At other places, the time would be 6.6/cosφ minutes where φ is the latitude of the place.  

This is plotted in the first graph. The second graph shows the number of days between equinox and equilux. This increases exponentially as we come closer to the equator and between about 4° N and S latitudes there is no equilux.

More information here:

https://www.wkyc.com/article/weather/equinox-vs-equilux-how-are-they-different/95-898bc1b2-505b-4604-a3e9-93365e33391d

http://stevekluge.com/astronomy/sunrise.html

https://www.aa.quae.nl/en/antwoorden/zonpositie.html#14