Monday, March 12, 2012

Day and night are NOT equal on the Equinox!

It is common knowledge that the length of the day and the night are equal on the Equinox day (after all, this is the reason that the day is called equinox in the first place). However a simple look at the calendar or almanac which gives sunrise and sunset times, reveals that this is not true. Let's check the times of sunrise and sunset on March 20 2012 in several cities. 

City          Latitude Sunrise Sunset  Day length  Day/Night difference
Quito         0        6:18    18:24   12:06       12 minutes
Tel Aviv      32       5:44    17:53   12:09       18 minutes
New York      40       6:58    19:08   12:10       20 minutes
Frankfurt     50       6:27    18:38   12:11       22 minutes 
St Petersburg 60       7:59    20:13   12:14       28 minutes   

A few quick conclusions which arise from the table above:
  1. The day and night are not equal, not even at the equator!
  2. The higher your latitude, the greater the difference.
Let's explain. Indeed the day and night lengths are equal in the equinox but only if you use the strict scientific definition,  which is that the times for sunset and sunrise is the hour when the CENTER of the sun crosses the horizon (either on the way up at sunrise or down at sunset).
However, this definition is not used commonly. Sunrise state is at the first moment that the top of the sun arises, and sunset state is when the last part of it sets. The sun's size is about half a degree, which takes about a minute to move from its center to its edge (the earth rotates about 1 degree in 4 minutes). This sums to two minutes (a minute for sunset and a minute for sunrise) that adds to 4 minutes in the total difference.

We see that the difference is much higher so we need to find another reason. The second reason which attribute most of the length difference is the fact that we can actually see the sun even when it is slightly below the horizon. The atmosphere of the earth works like a giant lens, and it slightly curves the sun's rays. When we look at the setting sun, the fact is that it was set already. However the times for sunrise and sunset take this extra time into account, and this makes the rest of the difference.
The sun is visible even below the horizon
The sun is visible even below the horizon

We now need to explain why the difference is larger for higher latitudes. This is due to the shallow angle of the sun. When the observer is near the horizon the sun's angle is steep and it will take it less time to go below the horizon. however when the observer is in a higher latitude the angle is much shallower and it will take the sun much more time to go below the horizon. See in the illustration below. At a higher latitude (the right side) the sun's path is much longer and it will take more time (thus making a beautiful long sunset).
The ecliptic angle cause longer or shorter sunrise/sunsets
The ecliptic angle cause longer or shorter sunrise/sunsets
PS: The equinox is a point in the Earth orbit around the sun. It is not really a day, so even when using the strict scientific definitions, day and night will not be equal on the equinox day since it take time from the equinox point to the sunset and during this time Earth moved a bit!. So day and night will be equal on all Earth only if you stop the Earth movement around the sun exactly at the equinox point, and let it be there for a whole day...

PS2: If you wonder about the common myth of leveling an egg on its narrow edge during equinox, forget it. This is possible (but hard) and no different than any other day of the year.

PS3: If you wonder when the day and night are equal it will be several days before or after equinox (Depends on which equinox, and in what hemisphere you are) depending on your latitude.