In a moment I'm going to pose an interesting problem for us to peruse and ponder (I say "us" because I haven't yet worked this one out myself), but before we consider this cunning conundrum...
The other night I was helping my 13-year old son with his homework and I finally discovered what the word "equinox" means (actually, I probably knew it once upon a time, but I'm now at the stage in my life that every time I learn something new, it seems that something else "falls off the edge" and I forget it).
So, first of all we have the Summer Solstice, which is the longest day in the year (that is, the day with the greatest amount of daylight versus nighttime). This usually falls around June 21 in the northern hemisphere ("above" the equator), and December 21 in the southern hemisphere ("below" the equator; "down under" in Australia, for example).
By comparison, the Winter Solstice is the shortest day of the year (that is, the day with the least amount of daylight versus the amount of nighttime). This usually falls around December 21 in the northern hemisphere and June 21 in the southern hemisphere.
Now, the term "equinox" refers to a point in the year when the sun can be observed to be directly over the Earth's equator. This occurs twice in the year and corresponds to the amount of daylight and the amount of nighttime being equal (12 hours each).
The Vernal Equinox, which is considered to be the first day of spring, occurs around March 20 when the Sun crosses the equator moving northward; the Autumnal Equinox which is considered to be the first day of autumn/fall, occurs around September 22 when the Sun crosses the equator moving southward.
So, on to our problem... Let's assume that the diameter of the earth is 12,756 kilometers at the equator and 12,715 kilometers at the poles...
Problem #1: Suppose you are located at the equator and it's either the Vernal Equinox or the Autumnal Equinox. You are watching the Sun go down in the evening and you note the time when the top of the Sun's disk just disappears below the horizon. As soon as this occurs, you climb a ladder to stand on top of a platform 10 meters high. Again, you wait for the top of the Sun's disk to disappear below the horizon and you note this new time. So... what's the difference between the two times?
Problem #2: Extend your solution to Problem #1 to cover any day of the year (you are still located on the equator).
Problem #3: Extend your solution to Problem #2 to cover any latitude.
Questions? Comments? Feel free to email me – Clive "Max" Maxfield – at firstname.lastname@example.org). And, of course, if you haven't already done so, don't forget to Sign Up for our weekly Programmable Logic DesignLine Newsletter.